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First Results in Suprametric Spaces with Applications

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Abstract

We introduce the concept of suprametric space and study some basic properties of its topology. Then we show that certain contraction maps in suprametric spaces have a unique fixed point either the space is complete or it contains a nonempty \(\omega \)-limit set. Next, we construct three suprametrics in partially ordered vector spaces, and utilize them to derive several fixed point theorems. Finally, we apply the obtained results to investigate the existence of solutions to some nonlinear integral and matrix equations.

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  1. Département de Mathématiques, Université de Tunis, École Nationale Supérieure d’Ingénieurs de Tunis, 1008 Montfleury, Tunis, Tunisia

    Maher Berzig

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  1. Maher Berzig
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Berzig, M. First Results in Suprametric Spaces with Applications. Mediterr. J. Math. 19, 226 (2022). https://doi.org/10.1007/s00009-022-02148-6

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