Korean Journal of Mathematics

The Kangwon-Kyungki Mathematical Society (강원경기수학회)
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ITERATIVE PROCESS FOR FINDING FIXED POINTS OF QUASI-NONEXPANSIVE MULTIMAPS IN CAT(0) SPACES

  • Pitchaya Kingkam (Department of Mathematics, Faculty of Science, Lampang Rajabhat University) ;
  • Jamnian Nantadilok (Department of Mathematics, Faculty of Science, Lampang Rajabhat University)
  • Received : 2022.09.20
  • Accepted : 2023.02.24
  • Published : 2023.03.30
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Abstract

Let 𝔼 be a CAT(0) space and K be a nonempty closed convex subset of 𝔼. Let T : K → 𝓟(K) be a multimap such that F(T) ≠ ∅ and ℙT(x) = {y ∈ Tx : d(x, y) = d(x, Tx)}. Define sequence {xn} by xn+1 = (1 - α)𝜈n⊕αwn, yn = (1 - β)un⊕βwn, zn = (1-γ)xn⊕γun where α, β, γ ∈ [0; 1]; un ∈ ℙT (xn); 𝜈n ∈ ℙT (yn) and wn ∈ ℙT (zn). (1) If ℙT is quasi-nonexpansive, then it is proved that {xn} converges strongly to a fixed point of T. (2) If a multimap T satisfies Condition(I) and ℙT is quasi-nonexpansive, then {xn} converges strongly to a fixed point of T. (3) Finally, we establish a weak convergence result. Our results extend and unify some of the related results in the literature.

Keywords

Acknowledgement

This research work is supported by Faculty of Science, Lampang Rajabhat University

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