# Shahram NajafzadehPayame Noor University | PNU · Department of Mathematics

Shahram Najafzadeh

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58

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## Publications

Publications (58)

In this work, by considering the Chebyshev polynomial of the first and second kind, a new subclass of univalent functions is defined. We obtain the coefficient estimate, extreme points, and convolution preserving property. Also, we discuss the radii of starlikeness, convexity, and close-to-convexity.
1. Introduction
Let be the open unit disk and b...

Let fi, i 2 {1, 2, . . . ,k}, be an analytic function on the unit disk in the complex plane of the form fi(z) = zn + ai,n+1zn+1 + . . . , n 𝜖 ℕ = {1, 2, . . .}. We consider the following Frasin integral operator:Gnz=∫0znξn−1f1′ξnξn−1α1⋯fk′ξnξn−1αkdξ. We establish a sufficient condition under which this integral operator is n-valent convex and obtai...

UDC 517.5 Let f be an analytic function on the unit disk in the complex plane of the form. We consider the Frasin integral operator as follows: In this paper, we obtain a sufficient condition under which this integral operator is n-valent convex and get other interesting results.

In this paper, we study the radius of convexity of the following integral operators$$I_{n}^{{\gamma_{i} }} \left( {f_{1} , \ldots ,f_{n} } \right) = F\left( z \right) \, : = \mathop \int \limits_{0}^{z} \mathop \prod \limits_{i = 1}^{n} \left( {f_{i}^{'} \left( t \right)} \right)^{{\gamma_{i} }} {\text{d}}t$$ and$$J_{n}^{{\gamma_{i} ,\lambda_{j} }}...

We present a generalization of a result for p-valent functions obtained by Nunokawa and Sokół (Appl Math Comput 22(219): 10768–10776, 2013) and give a few corollaries and examples yielding some classical results on univalent functions.

In this paper, we investigate the problem of stability of integral convolution over the classes of strongly starlike and convex functions with respect to symmetric points and find lower bounds for radius
of stability.

In this paper, we obtain some application of first-order differential subordination, superordination and sandwich-type results involving operator for certain normalized p-valent analytic functions. Further, properties of p-valent functions such as; λ-spirallike and λ-Robertson of complex order are considered.

In this paper, we obtain some application of first-order differential subordination, superordination and sandwich-type results involving operator for certain normalized $p$-valent analytic functions. Further, properties of $p$-valent functions such as; $\lambda$-spirallike and $\lambda$-Robertson of complex order are considered.

The object of the present paper is to study of two certain subclass of analytic functions related with Booth lemniscate which we denote by $\mathcal{BS}(\alpha)$ and $\mathcal{BK}(\alpha)$. Some properties of these subclasses are considered.

In this paper, the problem of stability for certain subclasses of harmonic univalent functions is investigated. Some lower bounds for the radius of stability of these subclasses are found.

In this paper, is proposed the existence and uniqueness of the solution of all fuzzy fractional differential equations, which are equivalent to the fuzzy integral equation. The techniques on L p-spaces are used, defining the L p F ([0, 1]) for 1 ≤ p ≤ ∞, its properties, and using the functional analysis methods. Also the convergence of the method o...

In this paper we investigate the problem of stability for certain subclasses of analytic functions of complex order denoted by S*(A, B, b) and C (A, B, b) and we give the upper and lower bounds of their radius of stability. We also study a stability of geometric properties of a function f under Alexander integral transformation when f is in S*(A, B...

In this paper we investigate the problem of stability for a certain class of p-valent functions in T-neighborhoods and we nd the lower and upper bounds of radius of stability.

K-frames were recently introduced by L. G\v{a}vruta in Hilbert spaces to study atomic systems with respect to bounded linear operator. Also controlled frames have been recently introduced by Balazs, Antoine and Grybos in Hilbert spaces to improve the numerical efficiency of interactive algorithms for inverting the frame operator. In this manuscript...

In the present paper, we will obtain norm estimates of the pre-Schwarzian derivatives for $F_{\lambda,\mu}(z)$, such that \[ F_{\lambda,\mu}(z) = \int_0^z \prod_{i=1}^{n} (f'_i(t))^{\lambda_i}\left( \frac{f_i(t)}{t} \right)^{\mu_i}dt \quad (z\in D),\] where $\lambda_i,\mu_i\in \mathbb{R}$, $\lambda_i=(\lambda_1,\lambda_2,\ldots,\lambda_n$, $\mu_i=(...

We define a new integral operator Fp δ0,..., δm (f1,..., fn) for meromorphic multivalent functions in the punctured open unit disk. The starlikeness condition for this integral operator is determined. Several special cases are also discussed in the form of Corollaries.

In this paper, we consider a subclass S Σ (α, β) of bi-univalent functions defined in the open unit disk D = {z ∈ C : |z| < 1}. Besides, we find upper bounds for the second and third coefficients for functions in this subclass.

K-frames were recently introduced by L. G\v{a}vruta in Hilbert spaces to study atomic systems with respect to bounded linear operator. Also controlled frames have been recently introduced by P. Balazs in Hilbert spaces to improve the numerical efficiency of interactive algorithms for inverting the frame operator. In this manuscript, we will define...

The purpose of this present paper is to derive some inclusion results and coefficient estimates for certain analytic functions with logarithmic coefficients by using Hadamard product. Relevant connections of the results with various known properties are also investigated.

In this paper, by using a differential operator we have defined a new class of meromorphically multivalent functions. Also two useful subclasses of this class involving fixed points are investigated. Important properties of these classes like convex linear combination, coefficient estimates, convex family etc. are found.

In the present paper a certain convolution operator of analytic functions is defined. Moreover, subordination and superordination preserving properties for a class of analytic operators defined on the space of normalized analytic functions in the open unit disk is obtained. We also apply this to obtain sandwich results and generalizations of some k...

By using a linear operator a new class of p-valent meromorphic functions with fixed second coefficients is introduced. Also coefficient estimates, extreme points and convex linear combination are investigated.

By making use of the operators on Hilbert space, the authors in-troduce a new class of univalent functions with a fixed point. Coefficient estimate, distortion bounds and extreme points are obtained. Also the effect of a operator on functions in this class is investigated.

In this paper a new class of meromorphic univalent functions in terms of an integral operator F c (z)=∫ 0 1 cv c f(vz)dv,c≥1, is defined. We find some properties of this new class by using two fixed points.

By using generalized Sălăgean differential operator a new class of univalent holomorphic functions with fixed finitely many coefficients is defined. Coefficient estimates, extreme points, arithmetic mean, and weighted mean properties are investigated.

Using fixed point methods, we prove the generalized Hyers--Ulam--Rassias stability of ternary homomorphisms, and ternary multipliers in ternary Banach algebras for the Jensen--type functional equation $$f(\frac{x+y+z}{3})+f(\frac{x-2y+z}{3})+f(\frac{x+y-2z}{3})= f(x).$$ Comment: 10 pages

By considering a fixed point in unit disk $\Delta$, a new class of univalent convex functions is defined. Coefficient inequalities, integral operator and extreme points of this class are obtained.

In the present paper, we investigate some important properties of a new class of univalent holomorphic functions by using Komatu operator. For example coefficient estimates, extreme points, neighborhoods and partial sums.

The aim of this paper is to prove some inequalities for p-valent meromorphic functions in the punctured unit disk Δ * , and to find important corollaries.

A new class of multivalent holomorphic functions with com- plex order in terms of subordination is introduced. We flnd some prop- erties of this class like, su-cient coe-cient bound, integral operator and Feketo-Szego problem.

The Hyers-Ulam-Rassias stability of the additive type functional equation f(rx+sy)=r+s 2f(x+y)+r-s 2f(x-y), r,s∈ℝ and r≠s, over a unital C * -algebra is investigate.

Making use of the familiar differential subordination structure in this paper, we investigate a new class of p-valent functions with a fixed point w. Some results connected to sharp coefficient bounds, distortion theorem and other important properties are obtained.

Extensions of k-uniformly starlike and convex functions are introduced using an integral operator. Inclusion relations and coefficient bounds for these classes are determined and consequently, some known results are generalized.

In this paper we introduce the class σp*(β) of functions f(z) = Az-p+∑n=p∞(-1)n-1anzn regular and multivalent in the Δ* = {z : 0 < z < 1} and satisfying Re {z ℑ(f(z)) '/ℑ(f(z))} < -β where ℑ is a linear operator. Coefficient inequalities, distortion bounds, weighted mean and arithmetic mean of functions for this class have been obtained.

In the present paper, we investigate some properties of the class ℳ λ (α,β) of analytic univalent functions defined by the Ruscheweyh derivative. Also by using integral operators we find the regions of starlikeness, convexity, and close-to-convexity. Finally, we apply the fractional calculus and neighborhoods to the above mentioned class.

New classes of multivalent meromorphic functions involving hypergeometric and Koebe functions are introduced,we find some properties of these classes e.g. distortion bounds, radii of starlikeness and convexity, extreme points, Hadamard product and verify effect of some integral operator on members of these classes. ISSN (electronic): 1449-5910 We w...

In this paper, we introduce a new class of multivalent func-tions defined by Dziok-Srivastava operator to study some of the interesting properties like coefficient estimates, distortion bounds and to prove the class is closed under convolution product and integral representation.

In this paper, we introduce a new class of multivalent functions defined by convolution and Dziok-Srivastava operator and study some properties of this class e.g. coecient estimates, integral representa- tion, distortion and closure theorems, convolution and integral opera- tor.

New classes of multivalent meromorphic functions involving hypergeometric and Koebe functions are introduced, we find some properties of these classes, e.g. distortion bounds, radii of starlikeness and convexity, extreme points, Hadamard product, and verify the effect of some integral operator on members of these classes.

By considering the functions of the form A z -p +k(z)+ 2 F 1 (a,b;c;z)-∑ k=p+1 2p t k-p-1 z k-p-1 which are meromorphic and multivalent in Δ * with condition |z p+q+1 f (q+1) +Ab λz p+q+1 f (q+1) (z)-Ab+(1+λ)αAb|<β (0≤α<1,0≤1,(q=0orq=2t),b=(p+q)! (p-1)!, we obtain coefficients estimates, distortion bounds, closure theorem, radius of meromorphically...

In this paper we introduce a class of harmonic meromorphic functions in Δ * that are univalent and sense-preserving. Some properties of this class are obtained e.g. coefficient bounds, distortion theorem, extreme points and Hadarmard product.

We define and verify a class of harmonic univalent functions involving Ruscheweyh derivatives of the form f=h+g ¯ and investigate some properties of this class, e.g., necessary and sufficient coefficient conditions, extreme points, distortion bounds and Hadamard product.

For p-valent functions of the form f(z)=z p -∑ k=n+p ∞ a k z k that satisfy the condition z(U z (λ,p) f(z)) ' f t (z)≺p+(γp+(α-γ)(p-η)sinθ)z 1+γz, we find coefficient inequalities, distortion bounds, radii of starlikeness and convexity, and some properties on this class.

By using an integral operator, we introduce a class p-SP ξ (α,β) of parabolic starlike functions in the unit disk and investigate interesting properties of this class.

By using hypergeometric and exponential functions we define a p-valent function of the form f(z)=mz p +∑ k=p+1 2p t k-p-1 z k-p-1 -(e z + 2 F 1 (a,b;c;z)) that satisfies the condition Rez(Q β α f(z)) ' +ηz 2 (Q β α f(z)) '' ηz(Q β α f(z)) ' +(1-η)(Q β α f(z))>γ· We then find sharp coefficient inequalities, quasi-Hadamard product and distortion boun...