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

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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 ) .

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