Fixed point approximation of Picard normal S-iteration process for generalized nonexpansive mappings in hyperbolic spaces

Imdad, Mohammad; Dashputre, Samir

doi:10.1007/s40096-016-0187-8

Cited by 11 publications

(4 citation statements)

References 22 publications

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“…Proposition 2.1. [11] Let {x n } be a sequence in X and C be a nonempty subset of X. Suppose that T : C → C is any nonlinear mapping and the sequence {x n } is Fejer monotone with respect to C, then we have the following:…”

Section: Preliminariesmentioning

confidence: 99%

Convergence of Thakur Iteration Scheme for Mean Nonexpansive Mappings in Hyperbolic Spaces

Sahu,

Banerjee

2024

Electronic Journal of Mathematical Analysis and Applications

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The purpose of this paper, we modify the Thakur iteration process into hyperbolic metric spaces where the symmetry condition is satisfied and establish strong and ∆-convergence theorems for mean nonexpansive mappings in uniformly convex hyperbolic spaces. We provide an example of mean nonexpansive mapping which is not nonexpansive mapping. Using this example and some numerical texts, we infer empirically that the Thakur iteration process converges faster than the Abbas, Agarwal, Noor, Ishikawa and Mann iteration process.2010 Mathematics Subject Classification. 47H09, 47H10 47H20.

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Section: Preliminariesmentioning

confidence: 99%

Convergence of Thakur Iteration Scheme for Mean Nonexpansive Mappings in Hyperbolic Spaces

Sahu,

Banerjee

2024

Electronic Journal of Mathematical Analysis and Applications

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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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“…Lemma 3 (see [18]). Let D be a nonempty closed convex subset of a complete uniformly convex hyperbolic space X with a monotone modulus of uniform convexity η.…”

mentioning

confidence: 99%

“…It follows from(18) and(19) that d(x n+1 , q) ≤ d(z n , q). By taking lim inf as n ⟶ ∞ on both sides, we obtain that…”

mentioning

confidence: 99%

Fixed-Point Approximations of Generalized Nonexpansive Mappings via Generalized M-Iteration Process in Hyperbolic Spaces

Chuadchawna

Farajzadeh

Kaewcharoen

2020

International Journal of Mathematics and Mathematical Sciences

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In this paper, we propose the generalized M-iteration process for approximating the fixed points from Banach spaces to hyperbolic spaces. Using our new iteration process, we prove Δ-convergence and strong convergence theorems for the class of mappings satisfying the condition Cλ and the condition E which is the generalization of Suzuki generalized nonexpansive mappings in the setting of hyperbolic spaces. Moreover, a numerical example is given to present the capability of our iteration process and the solution of the integral equation is also illustrated using our main result.

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Fixed point approximation of Picard normal S-iteration process for generalized nonexpansive mappings in hyperbolic spaces

Cited by 11 publications

References 22 publications

Convergence of Thakur Iteration Scheme for Mean Nonexpansive Mappings in Hyperbolic Spaces

Convergence of Thakur Iteration Scheme for Mean Nonexpansive Mappings in Hyperbolic Spaces

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

Fixed-Point Approximations of Generalized Nonexpansive Mappings via Generalized M-Iteration Process in Hyperbolic Spaces

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