Fixed Points for (<i>ξ</i>,<i>ω</i>)-Weakly Cyclic Type Generalized Contraction Condition in Metric Spaces with an Application

Abstract

In the present work, we have introduced a new type of (ξ,ω)-weakly cyclic generalized contraction in the setting of metric spaces and established some fixed-point results. Fixed-point results are useful in establishing the existence of unique solution to differential equations. We have supplemented the derived results with suitable non-trivial examples with an application to the Boundary Value Problem, generalizing some known results. The analytical result has been verified with numerical simulation.

Keywords

• fixed point
• cyclic representation
• altering distance function
• (ξ,ω)-weakly cyclic generalized contraction
• boundary value problem