On Modified Interpolative Almost e-Type Contraction in Partial Modular b-Metric Spaces

Abstract

The current study attempts to identify a new generalized metric space structure, referred to as partial modular b-metric, that extends both partial modular metric space via b-metric space and explains the topological aspects of the new space implementing examples. In addition, a new contraction mapping referred to as modified interpolative almost e-type contraction is determined, which is an interpretation of interpolative contraction bestowed with almost contraction and e-contraction as well as a simulation function and a fixed point theorem that encompass such mappings in the context of partial modular b-metric space is demonstrated. In conclusion, an example and an application that endorse the main theorem's outcomes are offered.