On Unique and Nonunique Fixed Points and Fixed Circles in Mvb-Metric Space and Application to Cantilever Beam Problem. (8th March 2021)

• Record Type: Journal Article
• Authors: Joshi, Meena; Tomar, Anita; Nabwey, Hossam A.; George, Reny
• Other Names: Isik Huseyin Academic Editor.
• Is Part Of: Journal of function spaces. Volume 2021(2021)
• Publication Date: 2021-03-08
• Subjects: Function spaces -- Periodicals; 515.7305
• DOI: 10.1155/2021/6681044
• Languages: English
• ISSNs: 2314-8896

Abstract

Abstract : We introduce M v b -metric to generalize and improve 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 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.