Fixed point theorems for convex-power condensing operators in Banach algebra

Abstract

We introduce the concept of a convex-power condensing mapping $A\cdot B+C$ in a Banach algebra relative to a measure of noncompactness as a generalization of condensing and convex-power condensing mappings. We present new fixed point theorems, and we apply these results to investigate the existence of solutions for a nonlinear hybrid integral equation of Volterra type.