C*-Algebra Valued Modular G-Metric Spaces with Applications in Fixed Point Theory

This article introduces a new type of C*-algebra valued modular G-metric spaces that is more general than both C*-algebra valued modular metric spaces and modular G-metric spaces. Some properties are also discussed with examples. A few common fixed point results in C*-algebra valued modular G-metric spaces are discussed using the “C*-class function”, along with some suitable examples to validate the results. Ulam–Hyers stability is used to check the stability of some fixed point results. As applications, the existence and uniqueness of solutions for a particular problem in dynamical programming and a system of nonlinear integral equations are provided.

(φ, ψ)-Contractıon Condition for Multivalued Mappings in Complete Modular Metric Spaces

In this paper we investigated (φ, ψ)-contractıon condition for multivalued type mappings in complete modular metric spaces. Our results are more general than metric versions of these type mappings.