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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.

journal of function spaces

On Unique and Nonunique Fixed Points and Fixed Circles in <math xmlns="http://www.w3.org/1998/Math/MathML" id="M1"> <msubsup> <mrow> <mi mathvariant="script">M</mi> </mrow> <mrow> <mi>v</mi> </mrow> <mrow> <mi>b</mi> </mrow> </msubsup> </math>-Metric Space and Application to Cantilever Beam Problem

On Unique and Nonunique Fixed Points and Fixed Circles in M v b -Metric Space and Application to Cantilever Beam Problem

On Unique and Nonunique Fixed Points and Fixed Circles in $M_{v}^{b}$ -Metric Space and Application to Cantilever Beam Problem