Author(s): Sanyogita

Abstract: The objective of this work is to illustrate a new concept to examine the existence of fixed points for multivalued F-contraction in the. In this generalize approach, we present the idea of multivalued F-contraction and also proved corresponding fixed point theorems in overall modular metric space with some specific assumption. We justify fixed point theorems for F-contractions of Hardy–Rogers type involving self-mappings characterized on metric spaces as well as ordered metric spaces. Then we implement our findings to create the existence of solutions for non-linear integral equations of certain type. An example as well as its application to multistage decision processes are illustrated to describe the usability of the derived theorems.

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