ON ENRICHED SUZUKI NONEXPANSIVE MAPPINGS IN P-UNIFORMLY CONVEX METRIC SPACES

K. O. Aremu; A. O. Ayigoro; M. S. Abubakar

doi:10.28924/2291-8639-23-2025-242

ON ENRICHED SUZUKI NONEXPANSIVE MAPPINGS IN P-UNIFORMLY CONVEX METRIC SPACES

K. O. Aremu^*, A. O. Ayigoro, M. S. Abubakar

^*Corresponding author for this work

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

Abstract

This paper introduces and defines the concept of enriched Suzuki nonexpansive mappings T in p-uniformly convex metric spaces, thereby extending earlier results established in Hadamard spaces. We show that the τ-averaged mapping T_τ preserves the fixed points of T. In addition, we prove that T_τ is quasi-nonexpansive and that the sequence generated by the Mann iteration converges to a fixed point of both T and its averaged counterpart T_τ . We further establish both ∆-convergence and strong convergence of the Mann iteration sequence for the τ-averaged mapping. Additionally, we present an illustrative example of an enriched Suzuki nonexpansive mapping within p-uniformly convex metric spaces.

Original language	English
Article number	242
Journal	International Journal of Analysis and Applications
Volume	23
DOIs	https://doi.org/10.28924/2291-8639-23-2025-242
Publication status	Published - 2025
Externally published	Yes

Keywords

Mann iteration
convergence
enriched Suzuki mapping
fixed point
p-uniformly convex metric space

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10.28924/2291-8639-23-2025-242

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title = "ON ENRICHED SUZUKI NONEXPANSIVE MAPPINGS IN P-UNIFORMLY CONVEX METRIC SPACES",

abstract = "This paper introduces and defines the concept of enriched Suzuki nonexpansive mappings T in p-uniformly convex metric spaces, thereby extending earlier results established in Hadamard spaces. We show that the τ-averaged mapping Tτ preserves the fixed points of T. In addition, we prove that Tτ is quasi-nonexpansive and that the sequence generated by the Mann iteration converges to a fixed point of both T and its averaged counterpart Tτ . We further establish both ∆-convergence and strong convergence of the Mann iteration sequence for the τ-averaged mapping. Additionally, we present an illustrative example of an enriched Suzuki nonexpansive mapping within p-uniformly convex metric spaces.",

keywords = "Mann iteration, convergence, enriched Suzuki mapping, fixed point, p-uniformly convex metric space",

author = "Aremu, \{K. O.\} and Ayigoro, \{A. O.\} and Abubakar, \{M. S.\}",

note = "Publisher Copyright: {\textcopyright} 2025 the author(s).",

year = "2025",

doi = "10.28924/2291-8639-23-2025-242",

language = "English",

volume = "23",

journal = "International Journal of Analysis and Applications",

issn = "2291-8639",

publisher = "Semnan University, Center of Excellence in Nonlinear Analysis and Applications",

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T1 - ON ENRICHED SUZUKI NONEXPANSIVE MAPPINGS IN P-UNIFORMLY CONVEX METRIC SPACES

AU - Aremu, K. O.

AU - Ayigoro, A. O.

AU - Abubakar, M. S.

PY - 2025

Y1 - 2025

N2 - This paper introduces and defines the concept of enriched Suzuki nonexpansive mappings T in p-uniformly convex metric spaces, thereby extending earlier results established in Hadamard spaces. We show that the τ-averaged mapping Tτ preserves the fixed points of T. In addition, we prove that Tτ is quasi-nonexpansive and that the sequence generated by the Mann iteration converges to a fixed point of both T and its averaged counterpart Tτ . We further establish both ∆-convergence and strong convergence of the Mann iteration sequence for the τ-averaged mapping. Additionally, we present an illustrative example of an enriched Suzuki nonexpansive mapping within p-uniformly convex metric spaces.

AB - This paper introduces and defines the concept of enriched Suzuki nonexpansive mappings T in p-uniformly convex metric spaces, thereby extending earlier results established in Hadamard spaces. We show that the τ-averaged mapping Tτ preserves the fixed points of T. In addition, we prove that Tτ is quasi-nonexpansive and that the sequence generated by the Mann iteration converges to a fixed point of both T and its averaged counterpart Tτ . We further establish both ∆-convergence and strong convergence of the Mann iteration sequence for the τ-averaged mapping. Additionally, we present an illustrative example of an enriched Suzuki nonexpansive mapping within p-uniformly convex metric spaces.

KW - Mann iteration

KW - convergence

KW - enriched Suzuki mapping

KW - fixed point

KW - p-uniformly convex metric space

UR - https://www.scopus.com/pages/publications/105019945198

U2 - 10.28924/2291-8639-23-2025-242

DO - 10.28924/2291-8639-23-2025-242

M3 - Article

AN - SCOPUS:105019945198

SN - 2291-8639

VL - 23

JO - International Journal of Analysis and Applications

JF - International Journal of Analysis and Applications

M1 - 242

ER -

ON ENRICHED SUZUKI NONEXPANSIVE MAPPINGS IN P-UNIFORMLY CONVEX METRIC SPACES

Abstract

Keywords

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