On unique and nonunique fixed points and fixed circles in \(\mathcal{M}_v^b\)-metric space and application to cantilever beam problem
type: Item
instance of: scholarly article
title: On unique and nonunique fixed points and fixed circles in \(\mathcal{M}_v^b\)-metric space and application to cantilever beam problem
zbMATH Open document ID: 1498.54072
DOI: 10.1155/2021/6681044
author: Meena Joshi
author: Anita Tomar
author: Hossam A. Nabwey
author: Reny George
published in: Journal of Function Spaces
publication date: 2021-05-04T00:00:00Z
review text: Summary: We introduce \(\mathcal{M}_v^b\)-metric to generalize and improve \(\mathcal{M}_v\)-metric and unify numerous existing distance notions. Further, we define topological notions like open ball, closed ball, convergence of a sequence, Cauchy sequence, and completeness of the space to discuss topology on \(\mathcal{M}_v^b\)-metric space and to create an environment for the survival of a unique fixed point. Also, we introduce a notion of a fixed circle and a fixed disc to study the geometry of the set of nonunique fixed points of a discontinuous self-map and establish fixed circle and fixed disc theorems. Further, we verify all these results by illustrative examples to demonstrate the authenticity of the postulates. Towards the end, we solve a fourth order differential equation arising in the bending of an elastic beam.
Mathematics Subject Classification ID: 54H25
Mathematics Subject Classification ID: 54E40
zbMATH DE Number: 7343386
zbMATH Keywords: \(\mathcal{M}_v^b\)-metric space
zbMATH Keywords: fixed circle theorem
zbMATH Keywords: fixed disc theorem
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2021/6681044
OpenAlex ID: W3133501561
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description: scientific article; zbMATH DE number 7343386