Fixed points for three point generalized orbital triangular contractions

Cristina Maria Pacurar; Ovidiu Popescu

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arXiv · 2404.15682

Fixed points for three point generalized orbital triangular contractions

Cristina Maria Pacurar·Ovidiu Popescu

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Abstract

In this paper we introduce and study new classes of mappings in metric spaces. The main class of mappings is called generalized orbital triangular contractions and it generalizes some existing results (such as Banach contractions, mappings contracting perimeters of triangles). We prove that these contractions are not necessarily continuous and have a unique fixed point under certain conditions. Moreover, we extend our class to generalized orbital triangular Kannan contractions and generalized orbital triangular Chatterjea contractions.

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Cristina Maria Pacurar, Ovidiu Popescu. 2024-04-24. Fixed points for three point generalized orbital triangular contractions. https://arxiv.org/abs/2404.15682

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