Discontinuity at the fixed point in suprametric spaces

Nicola Fabiano; Sedigheh Barootkoob; Hossein Lakzian

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arXiv · 2605.06694

Discontinuity at the fixed point in suprametric spaces

Nicola Fabiano·Sedigheh Barootkoob·Hossein Lakzian

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Abstract

The aim of this paper is to generalize some fixed point theorems in the class of convex contraction of order $m$ on a complete suprametric space. Then, we will prove that the class of convex contraction of order m is strong enough to generate a fixed point on a complete suprametric spaces but do not force the mapping to be continuous at the fixed point, and it can be replaced by relatively weaker conditions of $k$-continuity or $T$-orbitally lower semi-continuous. On this way a new and distinct solution to the open problem of Rhoades (Contemp Math 72:233-245,1988) is found. In sequel, we will prove some fixed point results in the setting suprametric spaces which are generalizations of the results regarding Sehgal, \'Ciri\'c and Fisher's quasi-contraction. Some examples and application will be approved our results.

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BibTeX RIS

Nicola Fabiano, Sedigheh Barootkoob, Hossein Lakzian. 2026-05-03. Discontinuity at the fixed point in suprametric spaces. https://arxiv.org/abs/2605.06694

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