Algorithm for Two Generalized Nonexpansive Mappings in Uniformly Convex Spaces

Gabriela Ioana Usurelu, Teodor Turcanu and Mihai Postolache
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Gabriela Ioana Usurelu: Department of Mathematics and Informatics, University Politehnica of Bucharest, 060042 Bucharest, Romania
Teodor Turcanu: Department of Mathematics and Informatics, University Politehnica of Bucharest, 060042 Bucharest, Romania
Mihai Postolache: Department of Mathematics and Informatics, University Politehnica of Bucharest, 060042 Bucharest, Romania

Mathematics, 2022, vol. 10, issue 3, 1-18

Abstract: In this paper, we study the common fixed-point problem for a pair of García-Falset mapping and ( α , β ) -generalized hybrid mapping in uniformly convex Banach spaces. For this purpose, we construct a modified three-step iteration by properly including together these two types of mappings into its formula. Under this modified iteration, a necessary and sufficient condition for the existence of a common fixed point as well as weak and strong convergence outcomes are phrased under some additional conditions.

Keywords: García-Falset mapping; condition ( E ); Suzuki mapping; condition ( C ); ( ? , ? )-generalized hybrid mappings; common fixed point; iteration (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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