On Modified Interpolative Almost <inline-formula><math display="inline"><semantics><mrow><mi mathvariant="script">E</mi><mo>−</mo></mrow></semantics></math></inline-formula>Type Contraction in Partial Modular <inline-formula><math display="inline"><semantics><mrow><mi>b</mi><mo>−</mo></mrow></semantics></math></inline-formula>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.

Keywords

• interpolative contraction
• simulation function
• b − metric space%22%2C%22default_operator%22%3A%22AND%22%7D%7D%7D"> partial modular <named-content content-type="inline"><inline-formula> <mml:math id="mm10003"> <mml:semantics> <mml:mrow> <mml:mi>b</mml:mi> <mml:mo>−</mml:mo> </mml:mrow> </mml:semantics> </mml:math> </inline-formula></named-content>metric space