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Mathematics
Volume 13
Issue 24
10.3390/math13243975
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This is an early access version, the complete PDF, HTML, and XML versions will be available soon.
Article

Optimal Pair of Fixed Points of Noncyclic Chatterjea-Type Mappings in Busemann Convex Spaces

by
Moosa Gabeleh
1,2,*,
Morteza Hassanvand
3 and
Maggie Aphane
1
1
Department of Mathematics and Applied Mathematics, Sefako Makgatho Health Sciences University, Ga-Rankuwa, Pretoria 0204, South Africa
2
Department of Mathematics, Faculty of Basic Sciences, Ayatollah Boroujerdi University, Boroujerd 69199-69737, Iran
3
Department of Pure Mathematics, Faculty of Mathematics and Statistics, University of Isfahan, Isfahan 81746-73441, Iran
*
Author to whom correspondence should be addressed.
Mathematics 2025, 13(24), 3975; https://doi.org/10.3390/math13243975
Submission received: 20 November 2025 / Revised: 8 December 2025 / Accepted: 9 December 2025 / Published: 13 December 2025
(This article belongs to the Special Issue Advanced Theories and Novel Methods for Nonlinear Analysis, Optimization and Applications)
Versions Notes

Abstract

We introduce and study a new class of noncyclic Chatterjea-type C-nonexpansive mappings in geodesic spaces. We establish a notable existence theorem for best proximity pairs by employing the pivotal geometric property of proximal normal structure within the framework of reflexive Busemann convex spaces. Moreover, we investigate minimal invariant sets associated with these mappings and derive a generalization of the Goebel–Karlovitz lemma. Our main contribution extends this fundamental result to geodesic spaces with property UC, thereby providing a significant generalization of the classical theorem for the case of Chatterjea-type C-nonexpansive mappings.
Keywords: best proximity pairs; Busemann convex spaces; CAT(0) spaces; property UC; proximal normal structure best proximity pairs; Busemann convex spaces; CAT(0) spaces; property UC; proximal normal structure

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MDPI and ACS Style

Gabeleh, M.; Hassanvand, M.; Aphane, M. Optimal Pair of Fixed Points of Noncyclic Chatterjea-Type Mappings in Busemann Convex Spaces. Mathematics 2025, 13, 3975. https://doi.org/10.3390/math13243975

AMA Style

Gabeleh M, Hassanvand M, Aphane M. Optimal Pair of Fixed Points of Noncyclic Chatterjea-Type Mappings in Busemann Convex Spaces. Mathematics. 2025; 13(24):3975. https://doi.org/10.3390/math13243975

Chicago/Turabian Style

Gabeleh, Moosa, Morteza Hassanvand, and Maggie Aphane. 2025. "Optimal Pair of Fixed Points of Noncyclic Chatterjea-Type Mappings in Busemann Convex Spaces" Mathematics 13, no. 24: 3975. https://doi.org/10.3390/math13243975

APA Style

Gabeleh, M., Hassanvand, M., & Aphane, M. (2025). Optimal Pair of Fixed Points of Noncyclic Chatterjea-Type Mappings in Busemann Convex Spaces. Mathematics, 13(24), 3975. https://doi.org/10.3390/math13243975

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