Quadratic Integral Equations in Reflexive Banach Space

Discussiones Mathematicae Diﬀerential Inclusions, Control and Optimization 30 (2010 ) 61–69 doi:10.7151/dmdico.1112

QUADRATIC INTEGRAL EQUATIONS IN REFLEXIVE BANACH SPACE

Hussein A.H. Salem

Faculty of Sciences Taibah University, Yanbu Saudi Arabia and Department of Mathematics Faculty of Sciences Alexandria University, Egypt e-mail: [email protected]

Abstract This paper is devoted to proving the existence of weak solutions to some quadratic integral equations of fractional type in a reflexive Banach space relative to the weak topology. A special case will be considered. Keywords and phrases: Pettis integral, fractional calculus, fixed point theorem, quadratic integral equation. 2000 Mathematics Subject Classification: 26A33.

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Received 5 January 2009