Generalized viscosity approximation method for minimization and fixed point problems of quasi-pseudocontractive mappings in Hadamard spaces

H. A. Abass, A. A. Mebawondu, K. O. Aremu, O. K. Oyewole*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

In this paper, we introduce a generalized viscosity method which includes a sequence of contractive mappings for approximating solutions of fixed point problem of finitely many resolvents of a lower semi-continuous function together with a fixed point problem of countable infinite family of L-Lipschitzian and quasi-pseudocontractive mappings in Hadamard spaces. We establish a strong convergence result without imposing a compactness condition of the proposed algorithm to an element in the intersection of the set of solutions of fixed point problem of finitely many resolvents of a lower semi-continuous function and fixed point problem of countable infinite family of quasi-pseudocontractive mappings. We display a numerical example to show the applicability of our main result. Our results complement and extend many recent results in literature.

Original languageEnglish
JournalAsian-European Journal of Mathematics
DOIs
Publication statusAccepted/In press - 2022
Externally publishedYes

Keywords

  • CAT(0) spaces
  • Quasi-pseudocontractive mapping
  • fixed point problem
  • generalized viscosity
  • minimization problem

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