Fixed point and a Cantilever beam problem in a partial b-metric space

Abstract

We determine the common fixed point of two maps satisfying Hardy-Roger type contraction in a complete partial b-metric space without exploiting any variant of continuity or commutativity, which is indispensable in analogous results. Towards the end, we give examples and an application to solve a Cantilever beam problem employed in the distortion of an elastic beam in equilibrium to substantiate the utility of these improvements.

Keywords

• fixed point
• commutativity
• continuity
• partial-b-metric spaces
• 54h25
• 47h10