AN EMPIRICAL STUDY OF FIXED POINT THEOREMS IN A NEW TYPE OF MODULAR METRIC SPACES

ABSTRACT

In this paper, we will considering both a modular metric space and a generalized metric space in the sense of Jleli and Samet, we analyze a new concept of generalized modular metric space. Generalizations of standard metric spaces are interesting because they allow for some deep understanding of the classical results obtained in metric spaces.Then we proceed to prove the Banach contraction principle (BCP) and ciric’s fixed point theorem for quasicontraction mappings in this new space. To prove ciric’s fixed point theorem in this new space, we take the contraction constant , where C is as given in Definition 1.1.1.In this paper, we also investigate a new concept of generalized modular metric space. Then we present some examples showing that the generalized modular metric space includes some kind of metric structures. Finally, we also study some fixed point results for both contraction and quasicontraction type mappings on generalized modular metric spaces.

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