A Mean Convergence Theorem without Convexity for Finite Commutative Nonlinear Mappings in Reflexive Banach Spaces

Lawal Yusuf Haruna, Bashir Ali, Yekini Shehu and Jen-Chih Yao
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Lawal Yusuf Haruna: Department of Mathematical Sciences, Kaduna State University, Kaduna P.M.B. 2339, Nigeria
Bashir Ali: Department of Mathematical Sciences, Bayero University, Kano 700006, Nigeria
Yekini Shehu: College of Mathematics and Computer Science, Zhejiang Normal University, Jinhua 321004, China
Jen-Chih Yao: Research Center for Interneural Computing, China Medical University Hospital, China Medical University, Taichung 40402, Taiwan

Mathematics, 2022, vol. 10, issue 10, 1-20

Abstract: This paper investigates the Bregman version of the Takahashi-type generic 2-generalized nonspreading mapping which includes the generic 2-generalized Bregman nonspreading mapping as a special case. Relative to the attractive points of nonlinear mapping, the Baillon-type nonlinear mean convergence theorem for finite commutative generic 2-generalized Bregman nonspreading mappings without the convexity assumption is proved in the setting of reflexive Banach spaces. Using this result, some new and well-known nonlinear mean convergence theorems for the finite generic generalized Bregman nonspreading mapping, the 2-generalized Bregman nonspreading mapping and the normally 2-generalized hybrid mapping, among others, are established. Our results extend and generalize many corresponding ones announced in the literature.

Keywords: attractive point; nonlinear mean convergence; generic 2-generalized Bregman nonspreading mapping; generic 2-generalized nonspreading mapping; normally 2-generalized hybrid mapping (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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