Fixed Point Theorem for Interpolative Contraction of Reich-Rus-Ciri´c type Mappings in CAT(0) Spaces

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DOI: https://doi.org/10.28924/2291-8639-24-2026-42
Published: Feb 19, 2026
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Natthaphon Artsawang, Cholatis Suanoom, Anteneh Getachew Gebrie, Fixed Point Theorem for Interpolative Contraction of Reich-Rus-Ciri´c type Mappings in CAT(0) Spaces, Int. J. Anal. Appl., 24 (2026), 42.

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Natthaphon Artsawang, Cholatis Suanoom, Anteneh Getachew Gebrie

Abstract

In this paper, we present a new fixed point theorem for mappings defined on complete CAT(0) spaces. Specifically, we introduce an enhanced version of the Suzuki-type interpolative Reich–Rus–Čirić contraction that incorporates a geodesic iteration condition reflecting the nonpositive curvature structure of CAT(0) spaces. Our main result ensures the existence and uniqueness of a fixed point under suitable contractive conditions and orbital admissibility. The proof relies heavily on the convexity properties of the metric in CAT(0) spaces and the geometrical behavior of iterative sequences along geodesics. This contributes to the ongoing development of fixed point theory in nonlinear and curved metric settings.

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