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

Author

Listed:
  • Moosa Gabeleh

    (Department of Mathematics and Applied Mathematics, Sefako Makgatho Health Sciences University, Ga-Rankuwa, Pretoria 0204, South Africa
    Department of Mathematics, Faculty of Basic Sciences, Ayatollah Boroujerdi University, Boroujerd 69199-69737, Iran)

  • Morteza Hassanvand

    (Department of Pure Mathematics, Faculty of Mathematics and Statistics, University of Isfahan, Isfahan 81746-73441, Iran)

  • Maggie Aphane

    (Department of Mathematics and Applied Mathematics, Sefako Makgatho Health Sciences University, Ga-Rankuwa, Pretoria 0204, South Africa)

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.

Suggested Citation

  • Moosa Gabeleh & Morteza Hassanvand & Maggie Aphane, 2025. "Optimal Pair of Fixed Points of Noncyclic Chatterjea-Type Mappings in Busemann Convex Spaces," Mathematics, MDPI, vol. 13(24), pages 1-26, December.
    • Handle: RePEc:gam:jmathe:v:13:y:2025:i:24:p:3975-:d:1817243
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