# Maslina DarusUniversiti Kebangsaan Malaysia | ukm · School of Mathematical Sciences

Maslina Darus

BSc(Acadia, N. S, Canada), Phd (Swansea, Wales)

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707

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Introduction

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February 1993 - December 2015

## Publications

Publications (707)

Owning to the importance and great interest of linear operators, a generalization of linear derivative operator H m δ,p (α, β, a 1, b 1)f (z) is newly introduced in this study. The main objective of this paper is to investigate various subordination and superordination related to the aforementioned generalized linear derivative operator. Additional...

The purpose of the present paper is to find the necessary and sufficient condition and inclusion relation for Pascal distribution series to be in the subclass TCq(λ,α) of analytic functions defined by q-derivative operator. Further, we consider an integral operator related to Pascal distribution series, and several corollaries and consequences of t...

In this work, we introduce a new class of analytic functions defined by a combination of two operator. We obtain univalency condition of the new class, its integral representations, sufficient inclusion conditions and coefficient inequalities.

Let S H denote the class of functions = f h g + which are harmonic univalent and sense preserving in the unit disk U. Earlier we have introduced a class of harmonic functions defined by a generalised differential operator. In this paper we introduce a new subclass of this class and obtain results on coefficient bounds, distortion and extreme points...

Let A be the class of normalised and analytic functions defined in the unit disc { :| | 1}. U z z In this paper we study the expression 2 () 1 , , () () zf z z zU bf z bfz for some (0) and (\{0} bb as a criteria for starlikeness and convexity at analytic functions of complex order.

Let A be the class of normalised and analytic functions defined in the unit disc { :| | 1}. U z z In this paper we study the expression 2 () 1 , , () () zf z z zU bf z bfz for some (0) and (\{0} bb as a criteria for starlikeness and convexity at analytic functions of complex order.

In this article, we introduce a new subclass of analytic bi-univalent functions using the Ruscheweyh type q-analogue operator. In addition, we estimate upper bounds for general and early bounds of Taylor-Maclaurin coefficients in functions of the class which is considered by using Faber polynomial expansions.

The concern of this article is the calculation of an upper bound of second Hankel determinant for the subclasses of functions defined by Al-Oboudi differential operator in the unit disc. To study special cases of the results of this article, we give particular values to the parameters A, B and λ

In this article, we introduce a new subclass of meromorphic bi-univalent functions, using (p,q)-Jackson derivative. We obtain the general coefficient estimates |a_m | for such functions belonging to this subclass and examine their early coefficient bounds by applying Faber polynomial coefficient expansions.

The aim of this paper is to obtain an upper bound to the second Hankel Determinant 2 2 4 3 a a a for starlike and convex functions of order , 1 2 2

Owing to the importance and great interest of linear operators, a generalization of linear derivative operator D m λ,p (υ, ̺, a 1 , b 1)h(z) is newly introduced in this study. Thus, a new subclass of p-valent functions H m υ,̺ (a r , b s , λ; η, d, p) is defined by means of the aforementioned linear differential operator. In addition to this, diffe...

In this paper, we define new subclass of analytic functions, the so-called q-starlike functions of order α with respect to k-symmetric points. We explore some inclusion properties and find some sufficient conditions for this class.
Finally, we obtain the integral representation of functions belonging to this class.

This article attempts to define a new differential operator involving q-Mittag-Leffler function. Thus, a new starlike class of complex-valued harmonic univalent functions is defined by means of the aforementioned differential operator. In addition to this, different properties and characteristics were considered in the study for this class. Some of...

The aim of this paper is to investigate coefficient estimates , Fekete-Szeg˝ o inequality, and upper bound of third Hankel determinant for a subclass of analytic functions of reciprocal order defined by Srivastava-Attiya integral operator.

In this investigation, new integral (integrodifferential) operators in terms of the Hurwitz-Lerch Zeta Functions (HLZF) are posed. Moreover, convexity properties on new generalized uniformly convex and starlike regular functions subclasses associated with these considered operators are discussed.

The aim of this paper is to obtain an upper bound to the second Hankel the determinant for starlike and convex functions of order.

In this paper, we consider a new subclass of analytic and bi-univalent functions associated with q-Ruscheweyh differential operator in the open unit disk U. For functions belonging to the class Σ q (λ, φ), we obtain estimates on the first two Taylor-Maclaurin coefficients. Further, we derive another subclass of analytic and bi-univalent functions a...

In this paper, we introduce a subclass of p-valent non-bazilavec functions of order. Some subordination relations and the inequality properties of p-valent functions are discussed. The results presented here generalize and improve some known results.

This study defines a new linear differential operator via the Hadamard product between a q-hypergeometric function and Mittag–Leffler function. The application of the linear differential operator generates a new subclass of meromorphic function. Additionally, the study explores various properties and features, such as convex properties, distortion,...

In this work, by making use of the principle of subordination, we introduce a certain subclass of non-Bazilevic analytic functions defined by linear operator. Such results as subordination and superordination, sandwich theorem and inequality properties are given.

By using generalized differential operator, we introduce two new subclasses of analytic and m-fold symmetric bi-univalent functions in the open unit disk. U We also find coefficient estimates of 2 a and 3 a for these new subclasses. Keywords: Differential operator; m-fold symmetry; bi-univalent functions; coefficient bounds ABSTRAK Dengan menggunak...

In this work, a new generalized derivative operator M mα,β,λ is introduced. This operator obtained by using convolution (or Hadamard product) between the linear operator of the generalized Mittag-Leffler function in terms of the extensively-investigated Fox-Wright p Ψ q function and generalized polylogarithm functions defined by (formula presented)...

In the present paper, we introduce and investigate two new subclasses Q Σ (n; y;k) and B Σ (n;β;k) of bi-valent functions in the unit disk U. For functions belonging to the classes Q Σ (n;y;k) and B Σ (n;β;k), we obtain estimates on the first two Taylor-Maclaurin coefficients |a 2 | and |a 3 |.

In this paper, we introduce a new class k-US(q,γ,m,p)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\mathcal{US}(q,\gamma ,m,p)$\end{document}, γ∈C∖{0}\documentclass[12...

In this paper, we introduce a new subclass of analytic functions in open unit disc. We obtain coefficient estimates, extreme points, and distortion theorem. We also derived the radii of close-to-convexity and starlikeness for this class.

We propound the economic idea in terms of fractional derivatives, which involves the modified Caputo’s fractional derivative operator. The suggested economic interpretation is based on a generalization of average count and marginal value of economic indicators. We use the concepts of 𝑇 − 𝑖𝑛𝑑𝑖𝑐𝑎𝑡𝑜𝑟𝑠 which analyses the economic performance with the p...

In this paper, we study Tsallis’ fractional entropy (TFE) in a complex domain by applying the definition of the complex probability functions. We study the upper and lower bounds of TFE based on some special functions. Moreover, applications in complex neural networks (CNNs) are illustrated to recognize the accuracy of CNNs.

Bulletin of Mathematical Analysis and Applications

A typical problem in the theory of analytic functions is to study a functional made up of combinations of coefficients of the original function. Usually, there is a parameter over which the extremal value of the functional is needed. One of the important functionals of this type is the Fekete-Szegö functional defined on the class of analytic functi...

The main purpose of this investigation is to define new subclasses of analytic functions with respect to symmetrical points. These functions map the open unit disk onto certain conic regions in the right half plane. We consider various corollaries and consequences of our main results. We also point out relevant connections to some of the earlier kn...

Let Iμ(f1, f2, ...fl, g1, g2, ...gl)(z) be the integral operator defined by generalized hypergeometric functions where each of the functions fm and gm are, respectively, analytic functions in the open unit disk for all m = 1, ..., l. The object of this paper is to obtain several univalence conditions for this integral operator. Our main results con...

In this article, we introduce an operator L^{γ,q}_{k,α}(β,δ)(f)(z) associated with the generalizedK−Mittag-Leffler function in the unit diskU={z:|z|<1}. Further, the ratio of normalizedK−Mittag-Leffler functionQ^{γ,q}_{k,α,β,δ}(z) to its sequence of partial sums Q(^{γ,q}_{k,α,β,δ})m(z) are calculated.

We are mainly interested in some geometric properties for the combinations of generalized Bessel functions of the first kind and their derivatives known as Dini functions. In particular, we study the starlikeness of order α , convexity of order α , and close-to-convexity of order ( ( 1 + α ) / 2 ) for normalized Dini function. We also study close-t...

In this article, A linear operator associated with the λ-generalized Hurwitz-
Lerch zeta function and q-hypergeometric function by using the Hadamard product (or
convolution) is defined by the authors, a different interesting properties of certain subclass
of meromorphically univalent functions related to a linear operator in the punctured unit
dis...

In this article, we study certain properties of Hurwitz-âĂŞLerch zeta
function involving the generalized Srivastava-Attiya operator. The authors also
study the differential subordination, differential superordination and sandwich-type
properties for the new operator which is defined on the space of normalized analytic
function in the open unit disk...

The aim of this paper is to investigate the Fekete Szego
inequality for subclass of analytic functions de�ned by convolution
between generalized Al-Oboudi di�erential operator and Srivastava-
Attiya integral operator. Further, application to fractional derivatives
are also given.

In this article, a q-integral operator which is analogue to the well known Bernardi integral operator is investigated. Integral preserving property for a subclass of analytic functions defined by this q-operator is proved. Moreover, special new q-integral operators are obtained as consequences.

Hypergeometric functions are of special interests among the complex analysts especially in looking at the properties and criteria of univalent. Hypergeometric functions have been around since 1900’s and have special applications according to their own needs. Recently, we had an opportunity to study on q-hypergeometric functions and quite interestin...

In this paper, we introduce and investigate two subclasses H^*_β (n, b, φ) and K_β (n, b, φ) of analytic functions with negative coefficients of order β in the unit disk D. Silverman [6] determined certain coefficient inequalities and distortion theorems for univalent functions with negative coefficients that are starlike S(α), and convex K(α) of o...

A new integral operator by using Hadamard product (or convolution) is termed, and various new classes by
using this operator are introduced. A majorization problem involving starlike meromorphic functions of complex order
belonging to these classes is investigated.

Let fn(z) = z+ ∑ n k=2 a k z k be the sequence of partial sums of the analytic function f (z) = z + ∑ ∞ k=2 a k z k. In this paper, we determine sharp lower bounds for ℜ{f (z)/fn(z)}, ℜ{fn(z)/f (z)}, ℜ{f ′ (z)/f ′ n (z)} and ℜ{f ′ n (z)/f ′ (z)}. The efficiency of the main result not only provides the unification of the results discussed in the lit...

In this paper, we introduce a generalised derivative operator Dm(λ,ν,ς,ω,α)f(z): A→A as follow: Dm(λ,ν,ς,ω,α)f(z)=z+∑k=2∞(ν+(k−1)(ς+λ)ωαν)mαkzk. New subclass ℝm(λ,ν,ς,ω,α,θ) defined by the generalised derivative operator Dm(λ,ν,ς,ω,α) is obtained. Sharp bounds for the nonlinear functional |a2a4−a32| are found.

We have investigated a two-dimensional radiative flow of a boundary layer nature. The fluid under consideration is carbon nanotube (CNT)-based nanofluid and it flows over a curved surface. The heat transfer through the flow is analyzed under the influence of internal heat generation. Water (base fluid) along with single or multi-walled carbon nanot...

In this paper we introduce and study the class$\ \mathcal{VR}_{\delta ,\eta
}(n,\lambda ,\alpha )\ $of analytic functions with varying arguments of
coefficients. We obtain coefficients inequalities, distortion theorems
involving fractional calculus, radii of close to convexity, starlikeness and
convexity and square root transformation for functions...

In this article, we define a new class of analytic functions. This class generalizes the class of k-UCV\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$k-\mathcal {UCV}$...

In this article, a new class of meromorphic parabolic starlike functions with a fixed point in the punctured
unit disk :={ involving the q -hypergeometric functions is defined. Some properties such as the
coefficient condition, distortion inequalities are studied

In this article, we investigate the Fekete-Szeg¨o problem for the integral
operator associated with the most generalized K− Mittag-Leffler function. Our results
will focus on some of the subclasses of starlike and convex functions.

By utilizing a certain linear operator considered on mero-morphic multivalent functions (MMF) in the punctured unit disk U *. We investigate the third-order differential subordination and superordination results. The outcomes here are acquired by introducing appropriate class of admissible functions. Sufficient conditions are determined to gain the...

In this paper, we introduce a new class Σp*(A,B,k)a,c for -1 ≤ B < A ≤ 1 which consists of hypergeometric meromorphic functions of the form Lp* (a,c)f(z) = 1/ zp + Σn=0∞ (a)n+2/(c)n+2an+pzn+p in U* = [z: 0 < |z| < 1].We determine sufficient conditions, distortion properties, radii of starlikeness and convexity and inclusion properties for the class...

In this article, we look at certain properties of a sigmoid function and determine the starlikeness and the convexity of this function.

An attempt has been made to introduce a new criterion to make it possible to change meromorphic analytic function into a meromorphic starlike function of particular order. This criterion is based on a differential operator which is defined in a punctured unit disk U[double-struck]*. By using this criterion, one can find easily different types of me...

A new class in the open unit disc of analytic p-valent functions is introduced in this paper. This subclass S m,j λ,p (a1, b1, α, β, A, B, γ) is mainly defined by the generalized hypergeometric function. The majorization properties for the functions in this class are introduced. Moreover, we investigate the coefficient estimates for this class.

In this article, a new linear differential operator
k a
I ( Ls ( a ,bm ) f ( z )) l is defined by using Hadamard product of qhypergeometric
function and a function related to Hurwitz-Lerch zeta function.
By using this linear differential operator, a new subclass
k ,
Ls ,a ( , m ; A , B ,b ) l
of meromorphic functions is defined. Some
properti...

The purpose of the present paper is to introduce several new classes of meromorphic functions defined the generalized Cho-Kwon-Srivastava operator and investigate various
inclusion properties of these classes. Some interesting applications involving these and other
classes of integral operators are also considered.

In this paper, the Fekete-Szegö problem is considered for f ∈ B(λ,α,0) when μ is complex

In our present investigation, by using Salagean q-differential operator we introduce and define new subclass k − US(q, γ, m), γ ∈ C\{0}, and studied certain subclass of analytic functions in conic domains. We investigate the number of useful properties of this class such structural formula and coefficient estimates Fekete-Szego problem, we give som...

Various problems of pure and applied sciences can be studied in the unified framework of nonlinear equations. In this paper, a new family of iterative methods for solving nonlinear equations is developed by using a new decomposition technique. The convergence of the new methods is proven. For the implementation and performance of the new methods, s...

We derive the Fekete-Szegö theorem for new subclasses of analytic functions which are q -analogue of well-known classes introduced before.

We introduce in our present investigation a new subclass of analytic and biunivalent functions associated with Ruscheweyh q -differential operator in open unit disk E . We use the Faber polynomial expansions to find n th coefficients bounds of class of bisubordinate functions and also find initial coefficient estimates.

Considering a function f(z)=z/1-z2 which is analytic and starlike in the open unit disc U and a function f(z)=z/1-z which is analytic and convex in U, we introduce two new classes Sα⁎(β) and Kα(β) concerning fα(z)=z/1-zα (α>0) . The object of the present paper is to discuss some interesting properties for functions in the classes Sα⁎(β) and Kα(β).

By making use of new linear fractional differential operator, we introduce and study certain subclasses of analytic functions associated with Symmetric Conjugate Points and defined in the open unit disk 𝕌 = {z : |z| < 1}. Inclusion relationships are established and convolution properties of functions in these subclasses are discussed.

In the present paper, we introduce and investigate a new subclass of analytic and bi-univalent functions Σ q (ϕ) in the open unit disk with respect to q-derivative operator. For functions belonging to this class, we obtain estimates on the first two Taylor-Maclau-rin coefficients |a 2 | and |a 3 |. Various other results, which presented in this pap...

In the present paper, we introduce and investigate a new subclass of analytic and bi-univalent functions Σ q (ϕ) in the open unit disk with respect to q-derivative operator. For functions belonging to this class, we obtain estimates on the first two Taylor-Maclau-rin coefficients |a 2 | and |a 3 |. Various other results, which presented in this pap...

We investigate some subclasses of k -uniformly convex and k -uniformly starlike functions in open unit disc, which is generalization of class of convex and starlike functions. Some coefficient inequalities, a distortion theorem, the radii of close-to-convexity, and starlikeness and convexity for these classes of functions are studied. The behavior...

In this article, we study some results on meromorphic functions defined by q-hypergeometric functions. In addition, certain sufficient conditions for these meromorphic functions to satisfy a subordination property are also pointed out. In fact, these results extend known results of starlikeness, convexity, and close to convexity.

In this paper, we introduce new subclasses of harmonic starlike functions in an open unit disk U = {z: z < 1}. The aim of this work is to prove some properties such as coefficients bounds, distortion bounds and extreme points.

In this article, we derive a new class of meromorphically analytic functions, which is defined by means of a Hadamard product (or convolution) involving some suitably normalized meromorphically q-Hypergeometric functions. A characterization property giving the coefficient bounds is obtained. The other related properties, which are studied in this p...

This paper introduces classes of uniformly geometric functions involving constructed differential operators by means of convolution. Basic properties of those classes are studied, namely, coefficient bounds and inclusion relations.

The aim of this paper is to obtain an upper bound to the H3(p) Hankel determinant for certain subclass
of p-valent functions. To do so, we obtain best possible bounds for the functionals |a_(p+3) − a_(p+1)a_(p+2)|
and |a_(p+2) − a^2_(p+1)|, then using known upper bound for the functional |a_(p+1)a_(p+3) − a^2_(p+2)| we obtain the required sharp upp...

In this paper, a new differential operator Apⁿf(z) defined in the open unit disc U = {z ∈ ℂ: |z| < 1} is introduced. We then, using this operator and introduce a new subclass of analytic functions G(µ, λ, α, β, b, p). Moreover, we discuss coefficient estimates, growth and distortion theorems and inclusion properties for the function f belonging to...

In this article, the class Rⁿ(λ, α β γ δ) of analytic functions dened by using the combination of generalised operators of Salagean and Ruscheweyh is introduced. Inclusion relations, convolution properties and other properties for the class Rⁿ(λ, α β γ δ) are given.

This paper involves constructed differential operators in concave meromorphic function and studied its properties. In particular, coefficient bounds, distortion theorem, and extreme points are obtained. 2010 Mathematics Subject Classification: 33C45.

In this research work, we study the properties of a certain differential subordination involving an operator with respect to a symmetric point. We establish coefficient estimates as our main results.

The aim of present investigation is to calculate upper bound for third Hankel determinant for certain new classes of analytic functions related with Cassinian ovals (x² +y²) -2(x² -y²) = c² -1, which reduces to Lemniscate of Bernoulli for c = 1.

In the present paper, we study a certain class of meromorphic univalent functions f(z) dened by the linear operator L(α,β) f (z). The aim of the present paper is to prove some properties for the class Σα,β,kλ;(h) to satisfy the certain subordination.
AMS Subject Classification: 30C45.

In this paper, new subclasses of analytic functions in the open unit disk which are defined using generalized integral operator are introduced. Several interesting properties of these classes are obtained, such as inclusion relationships and integral preserving properties are derived.

We introduce a new subclass of meromorphically analytic functions, which is defined by means of a Hadamard product or convolution. A characterization property such as the coefficient bound is obtained for this class. The other related properties, which are investigated in this paper, include the distortion and the radius of starlikeness. We also co...

In this paper, we study a certain class of generalized Hurwitz-Lerch zeta functions. A new and useful property of the generalized Hurwitz-Lerch zeta functions such that their partial differential equations are derived.

An analysis of laminar magnetohydrodynamics (MHD) flow of an incompressible upper-convected Maxwell fluid past an infinite wall is carried out. A uniform magnetic field normal to the plate is applied. The suction velocity distribution consisting of a basic steady distribution with a superimposed weak transversely varying distribution is assumed. Th...

The primary objective for this artical, the authors present a new certain differential operator S wk f (z)with a new subclass S w* M (ξ,γ)the main motivation for this article is to explore the several essential results and attributes. Moreover, we infer numerous results in the hadamard products.

The primary motivation behind this paper is to present new generalized differential operator defined
through U we present a new contribution is subclass of analytic functions. Additionally, we
talk about some properties for univalent functions with many results for the subclass of analytic functions.
Furthermore, with given solve technical to appli...

The main purpose of this paper is to introduce new generalized differential operator Aμ, λm (α,β) f(z) defined in the open unit disc U = {z ∈ : ℂ|z| < 1}. We then, using this operator to introduce novel subclass ω∗m(δ,λ,αβ,b) by using the operator Aμ, λm (α,β)f(z). Then, we discuss coefficient estimates, growth and distortion theorems, closure theo...

The purpose of this paper is to derive some subordination and super- ordination results for functions of the form f(z) = zp + zP ∞ σk=p+1 akzk which are p¡valent in the open unit disk U = {z ϵ C : [z] < 1} by using certain differential operator Aⁿγp(α,β,μ)f(z) and integral operator Fmp (p,v)f(z). Some special cases are also con- sidered.