A Common Fixed Point Theorem for Vicinal Mappings on Geodesic Spaces

Kajimura, Takuto; Kimura, Yasunori

doi:10.3390/axioms15040276

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A Common Fixed Point Theorem for Vicinal Mappings on Geodesic Spaces

by

Takuto Kajimura

and

Yasunori Kimura

^*

Department of Information Science, Toho University, Miyama, Funabashi 274-8510, Chiba, Japan

^*

Author to whom correspondence should be addressed.

Axioms 2026, 15(4), 276; https://doi.org/10.3390/axioms15040276

Submission received: 16 January 2026 / Revised: 2 April 2026 / Accepted: 8 April 2026 / Published: 10 April 2026

(This article belongs to the Special Issue Numerical Analysis and Applied Mathematics, 2nd Edition)

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Abstract

In 2024, Kimura proposed the modified shrinking method without assuming the existence of a common fixed point for a family of nonexpansive mappings defined on a complete geodesic space with a nonpositive upper curvature bound. In this paper, we discuss this method for vicinal mappings in an admissible complete geodesic space whose upper curvature bound is an arbitrary real number. Moreover, we investigate the convex minimization problem by using the main result and a resolvent for convex functions.

Keywords: geodesic space; vicinal mapping; fixed point; resolvent

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MDPI and ACS Style

Kajimura, T.; Kimura, Y. A Common Fixed Point Theorem for Vicinal Mappings on Geodesic Spaces. Axioms 2026, 15, 276. https://doi.org/10.3390/axioms15040276

AMA Style

Kajimura T, Kimura Y. A Common Fixed Point Theorem for Vicinal Mappings on Geodesic Spaces. Axioms. 2026; 15(4):276. https://doi.org/10.3390/axioms15040276

Chicago/Turabian Style

Kajimura, Takuto, and Yasunori Kimura. 2026. "A Common Fixed Point Theorem for Vicinal Mappings on Geodesic Spaces" Axioms 15, no. 4: 276. https://doi.org/10.3390/axioms15040276

APA Style

Kajimura, T., & Kimura, Y. (2026). A Common Fixed Point Theorem for Vicinal Mappings on Geodesic Spaces. Axioms, 15(4), 276. https://doi.org/10.3390/axioms15040276

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A Common Fixed Point Theorem for Vicinal Mappings on Geodesic Spaces

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