# Volume 3 (2011), Number 1

## On a Certain Subclass of Analytic Functions Involving Differential Operators

### Author(s): AFAF ABUBAKER AND MASLINA DARUS

**Abstract:** In this paper we introduce a new subclass of normalized
analytic functions in the open unit disc which is defined by a certain
differential operator. A coefficient inequality, distortion Theorems and
extreme points of differential operator for this class are given. We also
discuss the boundedness properties associated with partial sums of functions
in the class $T{S}_{\lambda ,\delta}^{\sigma ,s}(\beta ,\gamma ,n)$.

## A Companion of Ostrowski's Inequality with Applications

### Author(s): MOHAMMAD WAJEEH ALOMARI

**Abstract:** An inequality for a companion of Ostrowski's integral
inequality is proved. Applications to a composite quadrature rule and to
probability density functions are considered.

## Some Differential Equations of First Order with Mixed Modified Arguments and with a Parameter

### Author(s): MARIA DOBRIČšOIU

**Abstract:** In this paper we study the solution of a generalization
of a type of differential equation with mixed modified argument and with a
parameter. Using an observation from V.A. Ilea [6] we present two result
regarding the existence and uniqueness and the data dependence of the
solution of this differential equation. An example is also given here.

## Growth and Weighted Polynomial Approximation of Analytic Functions

### Author(s): DEVENDRA KUMAR

**Abstract:** Let ${H}_{R}$ be the class of functions analytic in ${G}_{R}$ but not in ${G}_{{R}^{\prime}}$ if $R<{R}^{\prime}$, ${G}_{{R}_{o}}=\text{int}\text{\hspace{0.17em}}{S}_{{R}_{o}}$, $0<{R}_{o}<R<1$ and ${S}_{{R}_{o}}=\{z\in \u2102:|z{e}^{1-z}|={R}_{o},\text{\hspace{0.17em}}|z|\le 1\}$.
This paper deals with the characterization of rate of decay of weighted approximation
error on ${S}_{{R}_{o}}$, in terms of order and type of $f\in {H}_{R}$.

## A Generalized Goldbach (Descartes) Binary Problem

### Author(s): A. PERETTI AND M. BAICA

**Abstract:** In this paper the authors will introduce a Diophantine
Equation which can be considered as the generalized Descartes (misnamed Goldbach)
binary problem. The authors do not solve the problem but give some important hints
which could lead to the solution of this problem. Also we should not be surprised
if it will take again more than 360 years until a complete solution will be given
to our generalized conjecture.

## Certain Subclass of Analytic Functions Associated with Caputo's Fractional Differentiation

### Author(s): JAMAL SALAH AND MASLINA DARUS

**Abstract:** In this paper, we define a class ${T}_{\eta ,\lambda}\left(\alpha ,\beta ,A,B\right)$ of analytic functions involving
the integral operator given by the authors. Several results like characterization
property, distortion theorem and other interesting properties of the same class
are provided.

## On Uniform Exponential Stability of Variational Difference Equations in Banach Spaces

### Author(s): MIHAELA AURELIA TOMESCU

**Abstract:** In this paper we study the uniform exponential stability
property for variational difference equations in Banach spaces. Characterizations
of this concept are given. The obtained results can be considered as variants of
the classical results due to E.Barbashin ([1]) and R.Datko ([2]) for variational
difference equations.

## Oscillation of a Class of Two-variables Functional Equations with Mix Nonlinear Type

### Author(s): WENGUI YANG

**Abstract:** In this study we will establish some sufficient conditions of
oscillation of a class of two-variables functional equations with mix nonlinear type.
As applications, the two-variables functional equations with several nonlinear terms
are also considered.