Existence of solutions to nonlinear functional-integral equations via the measure of noncompactness
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The purpose of this work is to present two new notions of \(\mu \)-set contraction of a bounded subset of a Banach space and establish some fixed point and coupled fixed point results in the direction of Darbo (Rend Sem Math Univ Padova 4:84–92, 1995). We apply our work to get existence of solutions to nonlinear functional-integral equations followed by an illustration. Our work generalizes many existing results in the literature.
KeywordsFixed point coupled fixed point measure of noncompactness functional-integral equation
Mathematics Subject Classification34A08 54H25 47H10
The authors express their gratitude to the referees for careful reading of the manuscript. The first author is thankful to the United States-India Education Foundation, New Delhi, India, and IIE/CIES, Washington, DC, USA, for Fulbright-Nehru PDF Award (no. 2052/FNPDR/2015).