# 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 $R{I}_{m,\lambda ,l}^{\alpha}:{\mathcal{\mathcal{A}}}_{n}\to {\mathcal{\mathcal{A}}}_{n}$,
$R{I}_{m,\lambda ,l}^{\alpha}f\left(z\right)=\left(1-\alpha \right){R}^{m}f\left(z\right)+\alpha I\left(m,\lambda ,l\right)f\left(z\right)$, 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 ${\mathcal{\mathcal{A}}}_{n}=\left\{f\in \mathcal{\mathscr{H}}\left(U\right):f\left(z\right)=z+{a}_{n+1}{z}^{n+1}+\dots ,\phantom{\rule{1em}{0ex}}z\in U\right\}$ is the class of normalized analytic functions. A certain subclass, denoted by
${\mathcal{\mathcal{R}}\mathcal{\mathcal{I}}}_{m}\left(\delta ,\lambda ,l,\alpha \right)$, 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 ${\mathcal{\mathcal{R}}\mathcal{\mathcal{I}}}_{m}\left(\delta ,\lambda ,l,\alpha \right)$. 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

### Author(s): MUHAMMAD MUDDASSAR, MUHAMMAD IQBAL BHATTI and FARKHANDA YASIN

**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 $\mathcal{\mathcal{K}}-$Mittag-Leffler Functions

### Author(s): HAMEED UR REHMAN, MASLINA DARUS and JAMAL SALAH

**Abstract:** In this article we investigate the Fekete-Szegö problem for the integral operator associated with the most generalized
$\mathcal{\mathcal{K}}-$
Mittag-Leffler function. Our results will focus on some of the subclasses of starlike and convex functions.