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The purpose of this work is to introduce a new class of implicit relation and implicit type contractive condition in metric spaces under  w -distance functional. Further, we derive fixed point results under a new class of contractive condition followed by three suitable examples. Next, we discuss results about weak well-posed property, weak limit shadowing property, and generalized  w -Ulam-Hyers stability of the mappings of a given type. Finally, we obtain sufficient conditions for the existence of solutions for fractional differential equations as an application of the main result.

journal of function spaces

An Implicit Relation Approach in Metric Spaces under <math xmlns="http://www.w3.org/1998/Math/MathML" id="M1"> <mi>w</mi> </math>-Distance and Application to Fractional Differential Equation

An Implicit Relation Approach in Metric Spaces under w -Distance and Application to Fractional Differential Equation

An Implicit Relation Approach in Metric Spaces under $w$ -Distance and Application to Fractional Differential Equation