Nonlinear Functional Analysis and Applications

Kyungnam University, Department of Mathematics Eduaction (경남대학교 수학교육과)
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APPROXIMATING FIXED POINTS FOR GENERALIZED 𝛼-NONEXPANSIVE MAPPING IN CAT(0) SPACE VIA NEW ITERATIVE ALGORITHM

  • Samir Dashputre (Department of Mathematics, Shahid Durwasha Nishad Govt. College) ;
  • Rakesh Tiwari (Department of Mathematics, Govt. V.Y.T. PG Autonomous College) ;
  • Jaynendra Shrivas (Department of Mathematics, Govt. V.Y.T. PG Autonomous College)
  • Received : 2023.05.09
  • Accepted : 2023.09.08
  • Published : 2024.03.15
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Abstract

In this paper, we provide certain fixed point results for a generalized 𝛼-nonexpansive mapping, as well as a new iterative algorithm called SRJ-iteration for approximating the fixed point of this class of mappings in the setting of CAT(0) spaces. Furthermore, we establish strong and ∆-convergence theorem for generalized 𝛼-nonexpansive mapping in CAT(0) space. Finally, we present a numerical example to illustrate our main result and then display the efficiency of the proposed algorithm compared to different iterative algorithms in the literature. Our results obtained in this paper improve, extend and unify results of Abbas et al. [10], Thakur et al. [22] and Piri et al. [19].

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References

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