Presymmetric w -Distances on Metric Spaces

Salvador Romaguera () and Pedro Tirado
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Salvador Romaguera: Instituto Universitario de Matemática Pura y Aplicada, Universitat Politècnica de València, 46022 Valencia, Spain
Pedro Tirado: Instituto Universitario de Matemática Pura y Aplicada, Universitat Politècnica de València, 46022 Valencia, Spain

Mathematics, 2024, vol. 12, issue 2, 1-11

Abstract: In an outstanding article published in 2008, Suzuki obtained a nice generalization of the Banach contraction principle, from which a characterization of metric completeness was derived. Although Suzuki’s theorem has been successfully generalized and extended in several directions and contexts, we here show by means of a simple example that the problem of achieving, in an obvious way, its full extension to the framework of w -distances does not have an emphatic response. Motivated by this fact, we introduce the concept of presymmetric w -distance on metric spaces. We also give some properties and examples of this new structure and show that it provides a reasonable setting to obtain a real and hardly forced w -distance generalization of Suzuki’s theorem. This is realized in our main result, which consists of a fixed point theorem that involves presymmetric w -distances and certain contractions of Suzuki-type. We also discuss the relationship between our main result and the well-known w -distance full generalization of the Banach contraction principle, due to Suzuki and Takahashi. Connected to this approach, we prove another fixed point result that compares with our main result through some examples. Finally, we state a characterization of metric completeness by using our fixed point results.

Keywords: metric space; presymmetric w-distance; basic p-contraction of Suzuki-type; p-contractive self map; fixed point (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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