# Volume 10 (2018), Number 1

## Some Properties of Certain Subclasses of Analytic Functions Associated with Generalized Differential Operator Involving Mittag-Leﬄer Function

### Author(s): SUHILA ELHADDAD and MASLINA DARUS

**Abstract:** A subclass in the open unit disc of analytic functions is introduced in this paper.
This subclass ${\mathcal{\mathcal{S}}}_{\mathit{\vartheta}}^{m,\delta}\left(\lambda ,\alpha ,\beta ,A,B\right)$ is mainly deﬁned by generalized differential Operator.
Some interesting properties of this class are also obtained.

## Existence, Interval of Existence and Uniqueness of Solutions for Nonlinear Implicit Caputo Fractional Differential Equations

### Author(s): MOUSSA HAOUES, ABDELOUAHEB ARDJOUNI and AHCENE DJOUDI

**Abstract:** In this paper, we use the contraction mapping principle to obtain the existence, interval
of existence and uniqueness of solutions for nonlinear implicit Caputo fractional differential equations.
We also use the generalization of Gronwall’s inequality to show the estimate of the solutions.
The results obtained here extend the work of Dong, Feng and Jiang in [6].

## On Weighted Ostrowski Grüss Inequality with Applications

### Author(s): NAZIA IRSHAD and ASIF R. KHAN

**Abstract:** The purpose of present article is to obtain weighted Ostrowski Grüss type inequality for
differentiable functions by using weighted Korkine’s identity. We also discussed its applications
into probability density function and numerical quadrature rules.

## Ishikawa Iteration With Errors for Nearly Weak Uniformly $L$-Lipschitzian Mappings

### Author(s): ADESANMI ALAO MOGBADEMU

**Abstract:** In this paper, we discuss a new class of nearly weak uniformly
$L$-Lipschitzian mappings
and prove some strong convergence results of the modiﬁed Ishikawa iteration with errors in real Banach spaces.
Our results are new extensions of some well-known results from the existing literature (see, e.g., [2], [4], [6]
and many others). An open problem is posed.

## Second and Third Hankel Determinant for a Class Deﬁned by Generalized Polylogarithm Functions

### Author(s): MOHD NAZRAN MOHAMMED PAUZI, MASLINA DARUS and SAIBAH SIREGAR

**Abstract:** By making use of ${\U0001d507}_{\lambda}^{m}f\left(z\right)$,
the generalized Polylogarithms derivative operator introduced by Al-Saqsi and Darus [4] deﬁned by

$${\U0001d507}_{\lambda}^{m}f\left(z\right)=z+\sum _{n=2}^{\infty}\frac{{n}^{m}\left(n+\lambda -1\right)!}{\lambda !\left(n-1\right)!}{a}_{n}{z}^{n},$$ |

## On a Certain Subclass of Uniformly Convex Functions Deﬁned by Bessel Functions

### Author(s): P. THIRUPATHI REDDY and B. VENKATESWARLU

**Abstract:** The aim of the present paper is to investigate some characterization for generalized Bessel
functions of ﬁrst kind is to be subclass of analytic functions. Furthermore we studied coefficient estimates,
radius of starlikeness, convexity, close - to - convexity, convex linear combinations for the class
$UB\left(\gamma ,c\right)$. Finally we proved Integral means inequalities for the class.