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DOI: 10.23952/jnfa.2025.18
Received September 15, 2024; Accepted December 15, 2024; Published June 23, 2025
Abstract. This paper introduces a metric version of Goebel’s definition for uniformly non-square Banach spaces. We show that such spaces with a PDFcharacteristic of convexity strictly less than one possess the uniform normal structure property. This property implies property (R), which in turn is equivalent to reflexivity in Banach spaces. As an application, we explore conditions for finding fixed points of a continuous mapping of uniformly k-Lipschitzian type on a complete bounded uniformly non-square metric space.
How to Cite this Article:
S. Shukri, Some fixed point results on uniformly non-square metric spaces, J. Nonlinear Funct. Anal. 2025 (2025) 18.