Positive Solution of a Quadratic Integral Equation Using Generalization of Darbo’s Fixed Point Theorem

Abstract

The objective of this article is to establish a fixed point theorem using different class of control functions, which is a generalization of Darbo’s fixed point theorem (DFPT) and its various versions obtained by several authors. Using this result we obtain existence of at least one positive solution for a quadratic integral equation of Fredholm type.

Keywords:

• Fixed point
• measures of non-compactness
• positive solutions
• quadratic integral equation

2010 MATHEMATICS SUBJECT CLASSIFICATION:

• 47H30
• 46E10
• 34A08
• 46E15