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Algorithm for Two Generalized Nonexpansive Mappings in Uniformly Convex Spaces

Author

Listed:
  • 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
    Gheorghe Mihoc-Caius Iacob Institute of Mathematical Statistics and Applied Mathematics, Romanian Academy, 050711 Bucharest, Romania
    Business School, Sichuan University, Chengdu 610064, China)

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.

Suggested Citation

  • Gabriela Ioana Usurelu & Teodor Turcanu & Mihai Postolache, 2022. "Algorithm for Two Generalized Nonexpansive Mappings in Uniformly Convex Spaces," Mathematics, MDPI, vol. 10(3), pages 1-18, January.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:3:p:318-:d:729439
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