Fixed Point Results of Dynamic Process Dˇϒ,μ0 through FIC‐Contractions with Applications

Abstract

This article constitutes the new fixed point results of dynamic process D(ϒ, μ0) through FIC-integral contractions of the Ciric kind and investigates the said contraction to iterate a fixed point of set-valued mappings in the module of metric space. To do so, we use the dynamic process instead of the conventional Picard sequence. The main results are examined by tangible nontrivial examples which display the motivation for such investigation. The work is completed by giving an application to Liouville‐Caputo fractional differential equations.

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“…Ćirić [3] demonstrated that fixed points exist uniquely for generalized contraction mappings in a metric space, provided that the mapping exhibits orbital continuity. Ali et al [4] discussed the dynamic process through integral contractions of the Ćirić kind. Anevska et al [5] provided proofs for some fixed-point results in 2-Banach spaces.…”

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“…In 2002, Branciari [1] analyzed the existence of FPs for mappings defined on complete MS and focused on a general contraction of integral-type. For additional information, refer to [2,3]. Nadler [4] introduced a novel approach to FP theorems, contributing to the expansion of the BCP and incorporating multivalued mappings within complete MS.…”