Fixed Point Results on Partial Modular Metric Space

Abstract

In the present paper, we refine the notion of the partial modular metric defined by Hosseinzadeh and Parvaneh to eliminate the occurrence of discrepancies in the non-zero self-distance and triangular inequality. In support of this, we discuss non-trivial examples. Finally, we prove a common fixed-point theorem for four self-mappings in partial modular metric space and an application to our result; the existence of a solution for a system of Volterra integral equations is discussed.

On Modified Interpolative Almost E−Type Contraction in Partial Modular b−Metric Spaces

“…In conclusion, according to the attractiveness of b−metric, partial metric, and modular metric spaces, we derive a new generalized metric space structure referred to as partial modular b−metric space, which improves the results of the work of Das et al [11] and Hosseinzadeh and Parvaneh [10]. Furthermore, we describe certain key topological properties and provide instances to back them up.…”

“…If we assume κ z ≤ κ z+1 , then, we deduce that κ z − κ z+1 = κ z+1 − κ z , thereby, from (11), we achieve that…”

“…In addition, Hosseinzadeh and Parvaneh [10] developed an innovative generalized metric function entitled partial modular metric space and provided some new insights on this space, considering modular metric and partial metric functions. However, to remove inconsistency in non-zero self-distance and triangular inequality, Das et al [11] modified the notion of partial modular metric in 2022.…”

“…Subsequently, the notation of the partial modular metric function was redefined by Das et al [11] in 2022 by considering the below conditions instead of the ( 1 ) and ( 4 ) of Definition 3:…”

“…We utilize the definition of partial modular metric as defined by Das et al [11] throughout the study.…”