Certain Fixed Point Results On 𝔄-Metric Space Using Banach Orbital Contraction and Asymptotic Regularity-Reference-Cited by-同舟云学术

Certain Fixed Point Results On 𝔄-Metric Space Using Banach Orbital Contraction and Asymptotic Regularity

Published:2023-03-30 Issue:2 Volume:73 Page:485-500
ISSN:1337-2211
Container-title:Mathematica Slovaca
language:en
Short-container-title:

Author:

Roy Kushal¹,Dey Debashis²,Saha Mantu¹

Affiliation:

1. * Department of Mathematics, The University of Burdwan , Purba Bardhaman-713104 , West Bengal , INDIA

2. ** Sudpur High School(H.S) , Purba Bardhaman-713150 , West Bengal , INDIA

Abstract

ABSTRACT In this paper, we investigate the existence of φ-fixed point for Banach orbital contraction over 𝔄-metric space. Also a fixed point result has been established via asymptotic regularity property over such generalized metric space. Our fixed point theorems have also been applied to the fixed circle problem. Moreover, we give some new solutions to the open problem raised by Özgür and Taş on the geometric properties of φ-fixed points of self-mappings and the existence and uniqueness of φ-fixed circles and φ-fixed discs for various classes of self-mappings.

Publisher

Walter de Gruyter GmbH

Subject

General Mathematics

Link

https://www.degruyter.com/document/doi/10.1515/ms-2023-0036/pdf

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