# Volume 4 (2012), Number 2

## A Generalization of Companion Inequality of Ostrowski's Type for Mappings Whose First Derivatives Are Bounded and Applications in Numerical Integration

### Author(s): MOHAMMAD W. ALOMARI

**Abstract:** An inequality for a companion of Ostrowski's integral inequality
is proved. Application to a composite quadrature rule is considered.

## Growth of Universal Entire Harmonic Functions

### Author(s): DEVENDRA KUMAR AND SACHIN KUMAR GUPTA

**Abstract:** In this paper we obtained some bounds on growth parameters order
and type of $J$
-universal entire harmonic functions on ${\mathbb{R}}^{N}$. The results are expressed
in terms of the derivatives of function at origin on ${\mathbb{R}}^{N}$.

## A Class of Nonlinear Integral Equations

### Author(s): MARIA DOBRIČšOIU

**Abstract:** Using *the Contraction Principle* and
*the General Data Dependence Theorem*, several results of existence and uniqueness
and of continuous dependence of data of the solution of a class of integral equations with
modified argument from physics, that is a mathematical model reference with to the turbo-reactors
working: $$x(t)={\displaystyle {\int}_{a}^{b}K}(t,s)\xb7h(s,x(s),x(a),x(b))ds+f(t),t\in [a,b],$$ where $a,b\in \mathbb{R}$,
$a<b$,
$K:[a,b]\times [a,b]\to \mathbb{R}$,
$h:[a,b]\times {\mathbb{R}}^{3}\to \mathbb{R}$,
$f:[a,b]\to \mathbb{R}$ and $x:[a,b]\to \mathbb{R}$ are given. Also, an example is given.

## New Ostrowski Type Inequalities for Co-ordinated Convex Functions

### Author(s): MUHAMMAD AMER LATIF, SABIR HUSSAIN AND SEVER S. DRAGOMIR

**Abstract:** In this paper some new Owstroski type inequalites for co-ordinated
convex functions are obtained.

## Antiperiodic Solutions for Shunting Inhibitory Cellular Neural Networks with Nonlinear Behaved Functions and Mixed Delays

### Author(s): WENGUI YANG AND QINGBO ZHAO

**Abstract:** In this paper, a class of shunting inhibitory cellular neural networks
(SICNNs) with nonlinear behaved functions and mixed delays are are considered. Sufficient
conditions for the existence and globally exponentially stability of the antiperiodic solutions
are established, which are new and complement previously known results. An example is employed
to illustrate our feasible results.