Applicability of Petryshyn’s Fixed Point Theorem on the Existence of a Solution to Weakly Singular Integral Equations

Abstract

Various approach have been introduced for the existence of solutions for integral equations but, for the most part, researchers
have deal with the Darbo fixed point theorem as an extension of Schauder theorem. Under certain hypotheses, we establish the existenceof solution for weakly singular integral equations by employing the generalization of Darbos fixed point theorem and measures of noncompactness in Banach space. Finally, some examples are given and with the help of MATLAB R2018a parameters is finding.