BEST PROXIMITY AND FIXED POINT OUTCOMES IN METRIC SPACES FOR THE PROXIMAL CONTRACTION OF $\alpha_{0}-(\psi_0, g_0)$

Print ISSN: 0972-7752 | Online ISSN: 2582-0850 | Total Downloads : 56

Volume : 19 , Issue : 3
DOI: https://doi.org/10.56827/SEAJMMS.2023.1903.12
Author :
Rashmi Sharma (Department of Mathematics, GNA University, Phagwara, Punjab, INDIA)
Manoj Kumar (Department of Mathematics, Baba Mastnath University, Rohtak, Haryana, INDIA)

Abstract

In this paper, we introduce new notions of $\alpha_{0}-(\psi_0, g_0)$ - proximal contraction of Type-I and Type-II and modified $\alpha_{0}-(\psi_0, g_0)$ - proximal contraction. In the setting of these notions, we prove certain fixed point theorems in metric space. Additionally, a few applications are provided to show how the results can be used.

Keywords and Phrases

Best proximity point, metric space, fixed point, proximal generalized contraction.

A.M.S. subject classification

46N40, 46T99, 47H10, 54H25.

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