Fixed Point Approximation for Asymptotically Nonexpansive Type Mappings in Uniformly Convex Hyperbolic Spaces

Kang, Shin Min; Dashputre, Samir; Malagar, Bhuwan Lal; Kwun, Young Chel

doi:10.1155/2015/510798

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2024

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“…Many researchers attracted in the direction of approximating the fixed points of nonexpansive mapping and its generalized form [4,5,9,14,16,17,19,20,21,30] in a hyperbolic space.…”

Section: Preliminariesmentioning

confidence: 99%

On fixed point convergence results for class of nonexpansivemappings in hyperbolic spaces via PJ iteration process

Shrivas,

Verma,

Chandraker

2024

IJAMR

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In this paper, we provide certain fixed point results for a mean nonexpansive mapping, as well as a new iterative algorithm called PJ-iterationfor approximating the fixed point of this class of mappings in the setting of hyperbolic spaces. Furthermore, we establish strong and∆-convergence theorem for mean nonexpansive mapping in hyperbolic space. Finally, we present a numerical example to illustrate ourmain result and then display the efficiency of the proposed algorithm compared to different iterative algorithms in the literature. Our resultsobtained in this paper improve, extend and unify some related results in the literature.

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“…Many researchers attracted in the direction of approximating the fixed points of nonexpansive mapping and its generalized form [4,5,9,14,16,17,19,20,21,30] in a hyperbolic space.…”

Section: Preliminariesmentioning

confidence: 99%