An Existence Theorem for Some Nonlinear Volterra-Fredholm Integral Equations in the Space of Continuous Tempered Functions

Abstract

The aim of the present paper is to study the existence and asymptotic behavior of the solutions of some functional integral equations which contain a number of classical nonlinear integral equations as special cases. The main tools used in our considerations are the concept of a measure of noncompactness and the classical Schauder fixed point principle. The investigations of the paper are placed in the space of continuous and tempered functions on the real half-line. The applicability of the results is illustrated by examples.

Keywords:

• Measure of noncompactness
• nonlinear integral equation
• Schauder fixed-point theorem
• space of continuous tempered functions

2010 MATHEMATICS SUBJECT CLASSIFICATION:

• Primary: 45G10
• 47H08
• Secondary: 47H10
• 45M99

Acknowledgement

The author would like to express his gratitude to Professor Zuhair NASHED, the editor-in-chief of Numerical Functional Analysis and Optimization, for his sincere interest in the evaluation process of the paper. Also, he thanks to the reviewers for their comments and suggestions.