Some noncompact types of fixed point results in the generalized Banach spaces with respect to the G–weak topology contexts and applications

Abstract

This research deals with Krasnoselskii’s fixed point theorem where the entries operators do not need to be G-weakly compact and contraction. These results were obtained by using the so-called generalized measure of weak noncompactness and some user-friendly lemmas. Moreover, these gained fixed point results are applied to study the existence of solutions of a coupled system for integral equations in the generalized Banach space $\mathcal{{ C }} ( [0,1], E_{1} )\times \mathcal{{ C }} ( [0,1], E_{2} ) $ C ( [ 0 , 1 ] , E 1 ) × C ( [ 0 , 1 ] , E 2 ) .