Convergence results for Górnicki type contractive mapping in CAT(0) spaces

Godwin Chidi Ugwunnadi; Abdul Rahim Khan; Austine Efut Ofem

doi:10.1007/s41478-024-00864-8

Convergence results for Górnicki type contractive mapping in CAT(0) spaces

Godwin Chidi Ugwunnadi^*, Abdul Rahim Khan, Austine Efut Ofem

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

Abstract

This article presents new existence and uniqueness results for a nonlinear mapping in CAT(0) spaces. We prove these results without the necessity of stringent conditions, which are usually imposed on the mapping. We also prove the Δ-convergence and strong convergence results for the Ishikawa iterative method of the considered nonlinear mapping. Finally, we apply one of the results to obtain a solution of a nonlinear integral equation.

Original language	English
Pages (from-to)	825-838
Number of pages	14
Journal	Journal of Analysis
Volume	33
Issue number	2
DOIs	https://doi.org/10.1007/s41478-024-00864-8
Publication status	Published - Apr 2025
Externally published	Yes

Keywords

CAT(0) space
Fixed point
Górnicki type contractive mapping
Ishikawa iteration
Nonlinear integral equations
Δ-convergence

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10.1007/s41478-024-00864-8

Cite this

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title = "Convergence results for G{\'o}rnicki type contractive mapping in CAT(0) spaces",

abstract = "This article presents new existence and uniqueness results for a nonlinear mapping in CAT(0) spaces. We prove these results without the necessity of stringent conditions, which are usually imposed on the mapping. We also prove the Δ-convergence and strong convergence results for the Ishikawa iterative method of the considered nonlinear mapping. Finally, we apply one of the results to obtain a solution of a nonlinear integral equation.",

keywords = "CAT(0) space, Fixed point, G{\'o}rnicki type contractive mapping, Ishikawa iteration, Nonlinear integral equations, Δ-convergence",

author = "Ugwunnadi, \{Godwin Chidi\} and Khan, \{Abdul Rahim\} and Ofem, \{Austine Efut\}",

note = "Publisher Copyright: {\textcopyright} The Author(s), under exclusive licence to The Forum D{\textquoteright}Analystes 2024.",

year = "2025",

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doi = "10.1007/s41478-024-00864-8",

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T1 - Convergence results for Górnicki type contractive mapping in CAT(0) spaces

AU - Ugwunnadi, Godwin Chidi

AU - Khan, Abdul Rahim

AU - Ofem, Austine Efut

N1 - Publisher Copyright: © The Author(s), under exclusive licence to The Forum D’Analystes 2024.

PY - 2025/4

Y1 - 2025/4

N2 - This article presents new existence and uniqueness results for a nonlinear mapping in CAT(0) spaces. We prove these results without the necessity of stringent conditions, which are usually imposed on the mapping. We also prove the Δ-convergence and strong convergence results for the Ishikawa iterative method of the considered nonlinear mapping. Finally, we apply one of the results to obtain a solution of a nonlinear integral equation.

AB - This article presents new existence and uniqueness results for a nonlinear mapping in CAT(0) spaces. We prove these results without the necessity of stringent conditions, which are usually imposed on the mapping. We also prove the Δ-convergence and strong convergence results for the Ishikawa iterative method of the considered nonlinear mapping. Finally, we apply one of the results to obtain a solution of a nonlinear integral equation.

KW - CAT(0) space

KW - Fixed point

KW - Górnicki type contractive mapping

KW - Ishikawa iteration

KW - Nonlinear integral equations

KW - Δ-convergence

UR - https://www.scopus.com/pages/publications/105003010750

U2 - 10.1007/s41478-024-00864-8

DO - 10.1007/s41478-024-00864-8

M3 - Article

AN - SCOPUS:105003010750

SN - 0971-3611

VL - 33

SP - 825

EP - 838

JO - Journal of Analysis

JF - Journal of Analysis

IS - 2

ER -

Convergence results for Górnicki type contractive mapping in CAT(0) spaces

Abstract

Keywords

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