Kattar Enada Bensatal, Abdelkrim Salim, Mouffak Benchohra

Measure of Weak Noncompactness and Integro-Differential Equations with Finite Delay

abstract:
This paper discusses the existence of solutions for integro-differential equations via resolvent operators in Banach space. Our approach is based on a M\"{o}nch'{s} type fixed point theorem with measure of weak noncompactness. An example is given to show the application of our result.

Mathematics Subject Classification: 45J05, 47H10, 34G20, 37C25, 54H25, 58C30, 35D30

Key words and phrases: Integro-differential equation, resolvent operator, fixed point theorem, Pettis integral, measure of weak noncompactness, weak solution