MMN-1202
Some generalizations of Darbo fixed point theorem and its application
R. Arab;Abstract
Recently, B. Samet et al. (Fixed Point Theory and Appl. 2013:5, 2013, doi:10.1186/1687-1812-2013-5) has introduced the concept of new contraction mappings and obtained results on the fixed point for nonlinear contractive mappings in a metric space. In the present paper, we introduce the concept of a new contraction via the measure of non-compactness on a Banach space, obtain few generalizations of Darbo fixed point theorem and extend some recent results of Aghajani et al. We also show the applicability of obtained results to the theory of integral equations.
Vol. 18 (2017), No. 2, pp. 595-610