ISSN: 2067-239X
ISSN(on-line): 2067-239X

Indexed in:
Mathematical Reviews
Zentralblatt MATH

Front cover

# Volume 9 (2017), Number 2

## On a Certain Subclass of Analytic Functions Deﬁned by Multiplier Transformation and Ruscheweyh Derivative

### Author(s): ALINA ALB LUPAȘ

Abstract: In the present paper we deﬁne a new operator using the multiplier transformation and Ruscheweyh derivative. Denote by $R{I}_{m,\lambda ,l}^{\alpha }$ the operator given by $R{I}_{m,\lambda ,l}^{\alpha }:{\mathsc{𝒜}}_{n}\to {\mathsc{𝒜}}_{n}$, $R{I}_{m,\lambda ,l}^{\alpha }f\left(z\right)=\left(1-\alpha \right){R}^{m}f\left(z\right)+\alpha I\left(m,\lambda ,l\right)f\left(z\right)$, for $z\in U$, where ${R}^{m}f\left(z\right)$ denote the Ruscheweyh derivative, $I\left(m,\lambda ,l\right)f\left(z\right)$ is the multiplier transformation and ${\mathsc{𝒜}}_{n}=\left\{f\in \mathsc{ℋ}\left(U\right):f\left(z\right)=z+{a}_{n+1}{z}^{n+1}+\dots ,\phantom{\rule{1em}{0ex}}z\in U\right\}$ is the class of normalized analytic functions. A certain subclass, denoted by ${\mathsc{ℛ}\mathsc{ℐ}}_{m}\left(\delta ,\lambda ,l,\alpha \right)$, of analytic functions in the open unit disc is introduced by means of the new operator. By making use of the concept of differential subordination we will derive various properties and characteristics of the class ${\mathsc{ℛ}\mathsc{ℐ}}_{m}\left(\delta ,\lambda ,l,\alpha \right)$. Also, several diﬀerential subordinations are established regarding the operator $R{I}_{m,\lambda ,l}^{\alpha }$.

## Approximation of Fuzzy Numbers by Max-Product Operators

### Author(s): GEORGE A. ANASTASSIOU

Abstract: Here we study quantitatively the approximation of fuzzy numbers by fuzzy approximators generated by the Max-product operators of Bernstein type and Meyer-Köning and Zeller type.

## Global Asymptotic Stability of Nonlinear Neutral Diﬀerential Equations With Inﬁnite Delay

### Author(s): ABDELOUAHEB ARDJOUNI and AHCENE DJOUDI

Abstract: This paper is mainly concerned the global asymptotic stability of the zero solution of a class of nonlinear neutral diﬀerential equations in ${C}^{1}$. By converting the nonlinear neutral diﬀerential equation into an equivalent integral equation, our main results are obtained via the Banach contraction mapping principle. Finally, an example is given to illustrate our results.

## Results on Certain Subclasses of Analytic Functions Deﬁned by a Derivative Operator

### Author(s): ABDUSSALAM EGHBIQ and MASLINA DARUS

Abstract: In this paper, we introduce and study the classes ${S}^{\alpha ,n,\beta }\left(m,l,q,\lambda \right)$ and $T{S}^{\alpha ,n,\beta }\left(m,l,q,\lambda \right)$ deﬁned by a generalised derivative operator ${D}^{\alpha ,n}\left(m,l,q,\lambda \right)$. Coefficient inequalities are obtained for the classes ${S}^{\alpha ,n,\beta }\left(m,l,q,\lambda \right)$ and $T{S}^{\alpha ,n,\beta }\left(m,l,q,\lambda \right)$. Further, growth and distortion, extreme points, and inclusion are also given for the class $T{S}^{\alpha ,n,\beta }\left(m,l,q,\lambda \right)$.

## New Inequalities of the Type of Hadamard’s Through $s-\left(\alpha ,m\right)$ Co-Ordinated Convex Functions

Abstract: This monograph is associated with the renowned Hermite-Hadamard’s integral inequality of $2$-variables on the co-ordinates. In this article we established several inequalities of the type of Hadamard’s for the mappings whose absolute values of second order partial derivatives are $s-\left(\alpha ,m\right)$-convex mappings.
## Coefficient Properties Involving the Generalized $\mathsc{𝒦}-$Mittag-Leffler Functions
Abstract: In this article we investigate the Fekete-Szegö problem for the integral operator associated with the most generalized $\mathsc{𝒦}-$ Mittag-Leffler function. Our results will focus on some of the subclasses of starlike and convex functions.