CCM-spaces and fixed point results of R-contractive mappings

Abstract

In this paper, we obtain existence results in CCM (Complete Cone Metric) spaces and a fixed point theorem for R-contractive mappings. These results generalize and extend several well-known results existing in the literature.

AMS subject classifications: 46J10; 46J15; 47H10

1. Introduction and Preliminaries

Banach contraction principle is the first and foremost theorem in the fixed point theory. Huang and Zhang [3] generalized the metric space into cone metric space, where the set of real numbers is replaced by an ordered Banach space and obtained some fixed point results in CMS (Cone Metric Space). Later on many mathematicians have been working in this area of results, they extended the results in different ways with different types of contractive conditions (see for e.g. [1, 2, 5–17]). Beiranvand, Moradi, et al. [2] introduced the class of T-contraction and T-contractive functions, extending the Banach contraction principle and Edelstein's fixed point theorems. S. Moradi [6] introduced the T-Kannan contractive mapping. The main aim of this paper is to analyze the existence of fixed point theorems of R-contractive condition. Our result is a generalization results of [5].

This page shows an excerpt of the introduction. The full text, including the theorems, proofs and examples, is available in the PDF.

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Prudhvi, K. (2026). CCM-spaces and fixed point results of R-contractive mappings. Asia Mathematika, 10(2), 67–71. https://doi.org/10.5281/zenodo.23087028

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