A New Version of Schauder and Petryshyn Type Fixed Point Theorems in S-Modular Function Spaces

Abstract

de la Sen, manuel/0000-0001-9320-9433; EGE, OZGUR/0000-0002-3877-2714; Ramezani, Maryam/0000-0002-5593-1924WOS: 000516823700015In this paper, using the conditions of Taleb-Hanebaly's theorem in a modular space where the modular is s-convex and symmetric with respect to the ordinate axis, we prove a new generalized modular version of the Schauder and Petryshyn fixed point theorems for nonexpansive mappings in s-convex sets. Our results can be applied to a nonlinear integral equation in Musielak-Orlicz space Lp where 0<p <= 1 and 0<s <= p.Spanish GovernmentSpanish Government; European Fund of Regional Development FEDEREuropean Union (EU) [RTI2018-094336-B-I00]; Basque GovernmentBasque Government [IT1207-19]The authors thank the Spanish Government and the European Fund of Regional Development FEDER for Grant RTI2018-094336-B-I00 (MCIU/AEI/FEDER, UE) and the Basque Government for Grant IT1207-19. We would like to express our gratitude to the anonymous referees for their helpful suggestions and corrections

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