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Basic Contractions of Suzuki-Type on Quasi-Metric Spaces and Fixed Point Results

Author

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  • Salvador Romaguera

    (Instituto Universitario de Matemática Pura y Aplicada-IUMPA, Universitat Politècnica de València, 46022 Valencia, Spain)

Abstract

This paper deals with the question of achieving a suitable extension of the notion of Suzuki-type contraction to the framework of quasi-metric spaces, which allows us to obtain reasonable fixed point theorems in the quasi-metric context. This question has no an easy answer; in fact, we here present an example of a self map of Smyth complete quasi-metric space (a very strong kind of quasi-metric completeness) that fulfills a simple and natural contraction of Suzuki-type but does not have fixed points. Despite it, we implement an approach to obtain two fixed point results, whose validity is supported with several examples. Finally, we present a general method to construct non- T 1 quasi-metric spaces in such a way that it is possible to systematically generate non-Banach contractions which are of Suzuki-type. Thus, we can apply our results to deduce the existence and uniqueness of solution for some kinds of functional equations which is exemplified with a distinguished case.

Suggested Citation

  • Salvador Romaguera, 2022. "Basic Contractions of Suzuki-Type on Quasi-Metric Spaces and Fixed Point Results," Mathematics, MDPI, vol. 10(21), pages 1-13, October.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:21:p:3931-:d:950886
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    Cited by:

    1. Delbianco Fernando & Tohmé Fernando, 2023. "What is a relevant control?: An algorithmic proposal," Asociación Argentina de Economía Política: Working Papers 4643, Asociación Argentina de Economía Política.

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