C. Ramachandran

• M.Sc.,M.Phil.,Ph.D.,B.Ed.,
• Professor (Associate) at University College of Engineering, Villupuram, Anna University

In this paper, the main contemplation is to reveal the radius of starlikeness of a certain order of the integral operator in which their functions beongs to the certain classes. Also acquiring the starlikeness conditions for these integral operator and the sufficient condition for a function to be in starlike with respect to the origin.

The object of the present paper is to prove new subordination results of analytic functions defined by Komatu Integral Transform. Several results and consequence of the main theorem are also considered. The aim of this paper is to generalize a result obtained by B.A.Frasin

The authors like to thank the referees for their helpful comments and suggestions. Abstract: In this paper we find a necessary and sufficient conditions and inclusion relations for Pascal distribution series to be in two subclasses of uniformly spirallike and convex functions. Further, we examined an integral operator related to Pascal distribution...

We estimate the coefficient bounds for certain subclasses of the starlike and convex functions using quasi-subordination and majorization relating with sigmoid functions.

The aim of this article is to estimate the coefficient bounds of certain subclasses of analytic functions. We claim that this is a novel and unique effort in combining the coefficient functional along with the new domains and the probability distributions which have not been found or are available in the literature of coefficients bounds. Here the...

The aim of the present study is to find the essential properties for some subclasses of analytic functions which are related to Poisson distribution that are member of the classes of spiral-like univalent functions. Further, we studied inclusion relations for such subclasses, and also we determined some properties of an integral operator related to...

The most essential and the needed concept used by the theory of complex function is the Quasi subordination. The subordination along with the majorization concepts are getting collaborated with the help of this Quasi subordination concept. In this article, a novel subclass consisting of univalent analytic functions are investigated, analyzed and re...

This work provides an extraordinary view of establishing the connections in between the different set of subclasses that exists in the univalent analytic functions, thereby utilizing some unique operator related to the convolutions that involves the Touchard polynomials. Exactly saying the analytic univalent function classes along with the positive...

In this paper we obtain some inclusion relations of k - starlike functions, k - uniformly convex functions and quasi-convex functions. Furthermore, we obtain coe¢ cient bounds for some subclasses of fractional q-derivative multivalent functions together with generalized Ruscheweyh derivative.

Many articles focus with differential subordination for analytic function in the unit disk, but only a few article deals with the upper half-plane. There has been no work in this area for the past one decade. The present paper aim is to investigate differential subordination for certain analytic function in the upper half-plane associated by suitab...

In the present paper, we introduce and investigate two new subclasses of the function class Σ of bi-univalent functions of complex order defined in the open unit disk, which are associated with the one of the orthogonal polynomial namely Generalized Meixner-Pollaczek polynomials, and satisfying subordinate conditions. Taylor-MacLaurin coefficients...

The error function occurs widely in multiple areas of mathematics, mathematical physics and natural sciences. There has been no work in this area for the past four decades. In this article, we estimate the coefficient bounds with q-difference operator for certain classes of the spirallike starlike and convex error function associated with convoluti...

Enough attentions to domains related to conical sections has not been done so far although it deserves more. Making use of the conical domain the authors have defined a new class of starlike and Convex Functions with respect to symmetric points involving the conical domain. Growth and distortion estimates are studied with convolution using domains...

In this paper, we introduce a new class of analytic functions of complex order involving a family of generalized differential operators and we discuss the sufficient conditions, estimation of coefficients. The motivation of this paper is to generalize the Coefficient Estimates obtained by Attiya, and Aouf et al. by making use of the generalized dif...

In this paper we study the relationships between classes of Ja-cobi polynomials, hypergeometric and analytic univalent functions and obtain bounds for their respected Fekete-Szegö body of coefficients.

In this paper, we introduce a new class of analytic functions of complex order involving a family of generalized differential operators and we discuss the sufficient conditions, estimation of coefficients. The motivation of this paper is to generalize the Coefficient Estimates obtained by Attiya, and Aouf et al. by making use of the generalized dif...

Enough attentions to domains related to conical sections has not been done so far although it deserves more. Making use of the conical domain the authors have defined a new class of starlike and Convex Functions with respect to symmetric points involving the conical domain. Growth and distortion estimates are studied with convolution using domains...

In this present work, authors are focusing to derive the coefficients of the classical Fekete-Szeg¨o for generalized Meixner-Pollaczek polynomials associated with conical domains.

In this paper, we introduce the new subclasses of multivalent analytic functions associated with the Sălăgean operator. The main objective of the present paper is to estimate the Fekete-Szegö coefficients for generalized subclasses of multivalent function defined by Sălăgean operator.

Quasi subordination is an essential concept in the area of complex function theory. It is an remarkable topic which collaborate the concept of both subordination and majorization. In this article, we estimate the Fekete–Szegö Functional with k-th root transform for certain classes of analytic univalent functions using quasi-subordination. The autho...

In this paper, we present few applications of polynomials which will give a flavour of basic principles and behaviours. Moreover, the polynomial introduced by Faber is widely used in enormous areas of mathematical sciences including chemical engineering. Using the concepts of Faber polynomial expansions, we introduce new class of analytic bi-unival...

Domains with conical sections is an underlying concept in the area of complex function theory although is an interesting topic and it deserves more attention. There has been many works focusing towards this area for the past two decades. However, the concept of Hankel determinant has not been studied so far. Exploiting this, we provide an estimate...

In this paper, we obtain certain results for some subclasses of strongly close-to-convex functions, k -starlike functions, k -uniformly convex functions and quasi-convex functions using the Generalized Srivastava-Attiya operator and study their inclusion relationships with integral preserving propteries

In the present paper, we obtain sharp bounds for the Fekete-Szegö coefficient of Janowski λ-spirallike functions with the k th root transform of multivalent functions.

Sigmoid function is an novel concept in the area of univalent function theory. Recently (O. A. Fadipe-Joseph , 2013) introduced and studied the sigmoid function and few classes were discussed in past few years . In this present work, we obtain the first few coeffi-cients of the class and estimates the relevant connection to the famous classical Fek...

The aim of this paper is to establish the coefficient bounds for certain classes of analytic functions associated with q-difference operator. Certain applications of these results for the functions defined through convolution are also obtained.

The aim of this paper is to investigate sharp bound of the Fekete Szeg\"{o} Coefficient for the general class of spirallike functions of universally prestarlike functions using m-th root transformation and involving conical regions.

In this present investigation, we obtain the coefficient bounds using symmetric Toeplitz determinantsT2(2), T2(3), T3(2)andT3(1)for the functions belonging to the subclassMα.

In the present paper, we obtain sharp bounds for the Fekete-Szeg¨ o coefficient of Janowski λ-spirallike functions with the kth root transform of multivalent functions.

In the present work, the authors are focusing to study the best pos-sible upper bound to the second Hankel determinants of the univalent error functions in the open disk using subordination.

In this present work, we obtain certain coefficients of the subclasses of univalent functions and estimates the relevant connection to the famous classical Fekete-Szegö inequality of functions belonging to the class.

Aim of this article is to present some subordination and superordination results, by using an operator, which involves the generalized Fox-Wright function. These results are obtained by investigating some suitable classes of admissible functions. We obtain also some sandwich-type results.

In this paper, we discuss the mapping properties of various subclasses of k-uniformly convex and starlike functions involving the generalized Fox-Wright function.

The aim of this paper is to establish coefficient bounds for certain classes of analytic functions of complex order associated with the q-derivative operator. Some applications of these results for the functions defined through convolution are also obtained.

Using subordination concept, the authors define some new subclasses of analytic functions and obtain the first few coefficient estimates of the class of spirallike function. Also estimates the relevant connection to the famous classical Fekete-Szegö inequality of functions belonging to the class. Results obtained in this paper may motivate further...

A fractional integral is a straightforward generalization of the basic theory of a repeated integral. The earliest such generalization would appear to be Riemann-Liouville fractional order integral. This Riemann-Liouville operator motivates several researchers to construct a few operators. Out of which Erdélyi-Kober operator seems to play a vital r...

In this paper, we obtain certain results for some subclasses of strongly close-to-convex functions, k-starlike functions, k-uniformly convex functions and quasi-convex functions using the Generalized Srivastava-Attiya operator and study their inclusion relationships with integral preserving properties.

In recent years, applications of Bessel functions have been effectively used in the modelling of chemical engineering processes and theory of univalent functions.In this paper, we study a new class of analytic and univalent functions with negative coefficients in the open unit disk defined by Modified Hadamard product with Bessel function. We obtai...

Abstract —In this paper, the main contemplation is to reveal the radius of starlikeness of a certain order of the integral operator in which their functions beongs to the certain classes. Also acquiring the starlikeness conditions for these integral operator and the sufficient condition for a function to be in star starlike with respect to orig...

The aim of this paper is to establish the coefficient estimates for the subclasses of q-starlike and q-convex functions with respect to symmetric points involving q-difference operator. Also certain applications based on these results for subclasses of univalent functions defined by convolution are given.

The aim of this paper is to analysis the sharp upper bound for the second Henkel determinant $|a_2 a_4 − µ a^2_3|$ of the univalent functions defined by Generalised Srivastava Linear Operator.

The aim of this paper is to establish the Fekete-Szegöo Inequality for certain classes of analytic functions which is associated with Srivastava- Attiya integral operator. Certain applications of these results for the functions defined through convolution are also obtained.

In the present work, we propose to investigate the coefficient esti mates for certain subclasses of bi-univalent functions of Ma-Minda type. Some interesting applications of the results presented here are also dis cussed.

The authors aim at finding subordination property and coefficient bounds for functions in the class Wn(α, γ, β) of normalized analytic functions in the open unit disk (inline-equation) and also discuss the special classes which are obtained from the same class.

The aim of this paper is to establish the sharp bound of the Fekete Szegö coefficient function for the subclass U(α, δ, λ, α, β)(φ) of an analytic functions which is associated with Komatu integral operator.

In the present work, we propose to investigate the coefficient estimates for certain subclasses of bi-univalent functions of Ma-Minda type. Some interesting applications of the results presented here are also discussed. Mathematics Subject Classification: 30C45

The aim of this paper is to establish the Fekete-Szeg¨o Inequality for certain classes of analytic functions which is associated with SrivastavaAttiya integral operator. Certain applications of these results for the functions defined through convolution are also obtained.

In recent times, applications of Bessel differential equations have been effectively used in the theory of univalent functions. In this paper we study some subclasses of k-starlike functions, k-uniformly convex functions, and quasi-convex functions involving the Bessel function and derive their inclusion relationships. Further, certain integral pre...

In this paper, we obtained some conditions on the parameters of generalized hypergeometric function and also deals with mapping properties of various subclasses of starlike and uniformly convex functions defined through a generalized hypergeometric function.

The main object of this article is to introduce and investigate an integral operator Lμλ(f) defined, on the various subclasses of the class of normalized analytic functions f in the open unit desk U. Using the techniques of differential subordination, an interesting property of the general integral operator Lμλ (f)is obtained. Some applications of...

The aim of this paper is to gives sharp bound of the Fekete Szegö coefficient functional for the Janowski α-Spirallike functions associated with the kth root transformation. © 2014 S. Annamalai, C. Ramachandran and G. Murugusundaramoorthy.

Let A be the class of all normalized analytic functions f (z) in the open unit disk satisfying f (0) = 0 and f?(0) = 1. Let q 1 and q 2 be univalent in ? with q 1(0) = q 2(0) = 1. We give some applications of first order differential subordination and superordination to obtain sufficient conditions for a normalized analytic functions f with f (0) =...

The object of the present paper is to prove new subordination results for analytic functions defined by the Komatu integral transform. Several results and consequences of the main theorem are also considered. The aim of this paper is to generalize a result obtained by B. A. Frasin [Tamkang J. Math. 42, No. 2, 205–215 (2011; Zbl 1221.30027)].

In our paper, we study a class SRA(λ, β, α, μ, Θ) which consists of analytic and univalent functions with negative coefficients in the open unit disk U = {z:|z| < 1} defined by Modified Hadamard product(or Modified convolution) with Rafid-operator, we obtain coefficient bounds and exterior points for this class.Also Distortion Theorem using Fractio...

In our paper, we study a class SRA(λ, β, α, µ, θ) which consists of analytic and univalent functions with negative coefficients in the open unit disk U = {z : |z| < 1} defined by Hadamard product (or convolution) with Komatu integral operator, we obtain coefficient bounds and exterior points for this class. Also Distortion Theorem using Fractional...

In our paper, we study a class SRA(λ, β, α, μ, θ) which consists of analytic and univalent functions with negative coefficients in the open unit disk U = {z : |z| < 1} defined by Modified Hadamard product(or Modified convolution) with Rafid-operator, we obtain coefficient bounds and exterior points for this class.Also Distortion Theorem using Fract...

In the present investigation, we obtain some sufficient condition for a normalized strongly close-to-star functions in the open disk U = {z ∈ C : |z| < 1} to satisfy the condition − π 2 β ≤ arg f (z) g(z) ≤ π 2 α, 0 ≤ α, β ≤ 1. The aim of this paper is to generalize a result obtained by N.E.Cho and S.Owa. 2010 AMS Subject Classification: Primary 30...

In the present investigation, we consider an unified class of functions of complex order using Hadamard's convolution. We obtain a necessary and sufficient condition for functions to be in these classes.

In this paper, a sharp upper bound for the functional |a3 − µa 2 2 | for functions f ∈ A in the class of function S * (Φ1, Φ2, ϕ) which we call it as the class of Φ2−like functions of type Φ1. Also certain applications of the main result for a class of functions defined by convolution are given. As a special case of the result, the Fekete-Szegö ine...

The main purpose of this paper is to introduce a new class U H(α, β, γ, λ, k), of functions which are analytic in the open disc ∆ = {z ∈ C : |z| < 1}. We obtain various results including characterization, coefficients estimates, distortion and covering theorems, radii of close-to-convexity, starlikeness and convexity for functions belonging to the...

The purpose of the present paper is to derive several Fekete-Szego type coefficient inequalities for certain subclasses of normalized analytic functions f (z) defined in the open unit disk. Various applications of our main results involving (for example) the Owa-Srivastava operator of fractional calculus are also considered. Thus, as one of these a...

In the present investigation, the authors obtain sharp upper bounds for certain coeffi-cient inequalities for linear combination of Mocanu α -convex p− valent functions. The results are extended to functions defined by convolution.

Let f(z) be analytic in the open unit disc Δ:={z∈ℂ:|z|<1}. Let Φ(w) be an analytic function in a domain containing f(Δ),Φ(0)=Φ ' (0)-1=0 and Φ(w)≠0 in f(Δ)-{0}. Suppose that a>0,b≥0,α and η are real numbers such that 0<η≤1,α+η≥0. For 0<β<1, the largest ‘C(,a,b,α,β,η)’ is found such that zf ' (z) Φ(f(z)) α azf ' (z) Φ(f(z))+b1+zf '' (z) f ' (z)-z[Φ(...

The purpose of the present paper is to derive differential Sandwich theorems involving convolution product for certain subclasses of normalized analytic functions in the open unit disk. Relevant connections of the results, which are presented in the paper, with various known results are also considered.

By making use of the familiar Carlson-Shaffer operator,the authors derive derive some subordination and superordination results for certain normalized analytic functions in the open unit disk. Relevant connections ofthe results, which are presented in this paper, with various other known results are also pointed out.

The main purpose of this paper is to introduce a new class UH(q,s,λ,β,k) of functions which are analytic in the open unit disk . We obtain various results including characterization, coefficient estimates, and distortion and covering theorems, for functions belonging to the class UH(q,s,λ,β,k).

Let and be univalent and analytic in the open unit disk We give some applications of first order differential subordination and superordination to obtain sufficient conditions for a normalized analytic functions f to satisfy where is the familiar Dziok-Srivastava operator.

Recommended by Brigitte Forster-Heinlein In the present paper, the authors obtain sharp bounds for certain subclasses of p-valent functions. The results are extended to functions defined by convolution.

In the present investigation, the authors prove several inclu- sion relations associated with the (n, )-neighborhoods of certain subclasses of p-valently analytic functions of complex order, which are introduced here by means of the Hadamard's Convolution. Special cases of some of these inclusion relations are shown to yield many known results.

The main object of this paper is to introduce and investigate a subclass (λ, α, β, k) of normalized analytic functions in the open unit disk Δ, which generalizes the familiar class of uniformly convex functions. The various properties and characteristics for functions belonging to the class (λ, α, β, k) derived here include (for example) a characte...

By using the subordination technique, we obtain a subordination result for a class of meromorphic functions.

In this paper, we consider the class A of the functions f(z) of the form f(z)=z+∑ k=2 ∞ a k z k ,(z∈Δ:={z∈ℂ;|z|<1}), which are analytic in an open disk Δ:={z∈ℂ;|z|<1} and study certain subclass of the class A, for which I a σ f(z)=(1+a) σ z a Γ(σ)∫ 0 z logz t σ-1 t a-1 f(t)dt has some property. Certain inclusion and the closure properties like conv...

In the present investigation, sharp upper bounds of |a 3 -μa 2 2 | for functions f(z)=z+a 2 z 2 +a 3 z 3 +⋯ belonging to certain subclasses of starlike and convex functions with respect to symmetric points are obtained. Also certain applications of the main results for subclasses of functions defined by convolution with a normalized analytic functi...

In the present investigation, we obtain some sufficient condition for a normalized analytic function f(z) defined in the unit disk U={z∈ℂ:|z|<1} to satisfy the condition -π 2β<argzf ' (z) Φ(f(z))<π 2,0<α,β<1, The aim of this paper is to generalize a result obtained by Takahashi and Nanukowa.

The purpose of the present paper is to derive differential Sandwich theorems involving convolution product for certain subclasses of normalized analytic functions in the open unit disk. Relevant connections of the results, which are presented in the paper, with various known results are also considered.