Fixed Point Index for Simulation Mappings and Applications

Abstract

In this paper, we construct the fixed point index for a class of contractive mapping defined by a simulation mapping and a measure of noncompact-ness noted by Zµ− contraction maps. Then we establish some fixed point theorem for this mapping of the Krasnoselskii type. An Application to the integral equation is presented to support the results.

Keywords

• fixed point index
• fixed point
• leary-shauder boundary condition
• measure of non compactness
• contractive mappings
• krasnoselskii fixed point theorem
• primary 47h07, 47h08
• secondary 47h09, 47h10