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IJMSI 2024, 19(1): 135-148 |
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Ullah K, Abbas M, Ahmad J, Ahmad F. Approximating Fixed Points of Operators Satisfying the ($B_{gamma,mu}$) Condition. IJMSI 2024; 19 (1) :135-148
URL: http://ijmsi.ir/article-1-1714-en.html
URL: http://ijmsi.ir/article-1-1714-en.html
Abstract:
Suppose C is any nonempty subset of a Banach space X. A mapping T : C → C is said to satisfy condition (Bγ,µ) if there exists γ ∈ [0, 1] and µ ∈ [0, 1 /2 ] with 2µ ≤ γ such that for each two elements x, y ∈ C,
γ||x - T x|| ≤ ||x - y|| + µ||y - T y||
implies ||T x - T y|| ≤ (1 - γ)||x - y|| + µ(||x - T y|| + ||y - T x||).
In this research, we suggest some convergence results for these mappings under a up-to-date iterative process in a Banach space setting. Our results are new and improve some known results of the literature.
Keywords: Condition $(B_{gamma, mu})$, Condition (I), Convergence result, K* iteration, Banach space.
Type of Study: Research paper |
Subject:
General
References
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