A generalized metric space and related fixed point theorems

Abstract

We introduce a new concept of generalized metric spaces for which we extend some well-known fixed point results including Banach contraction principle,Ćirić's fixed point theorem, a fixed point result due to Ran and Reurings, and a fixed point result due to Nieto and Rodríguez-López. This new concept of generalized metric spaces recover various topological spaces including standard metric spaces, b-metric spaces, dislocated metric spaces, and modular spaces. MSC: 54H25; 47H10

New Fixed Point Tools in Non-metrizable Spaces

“…In the following we describe another generalization of the standard notion of metric given by Jleli and Samet in [9] which extends some other generalized metric structures such as: b-metric spaces introduced by Bakhtin [2] and dislocated metric defined by Hitzler and Seda in [6]. In these spaces several fixed point results are improved.…”

Fixed Point Theorems for Weak K-Quasi Contractions on a Generalized Metric Space with Partial Order

“…We Jleli and Samet [13] extended Banach contraction principle to generalized metric spaces as follo ws. …”

“…Several authors have studied fixed point theory extensively, [see 2,6,11,14]. Co mbin ing several generalizations of metric spaces Jleli and Samet [13] obtained a new generalizat ion in 2015. They termed it as a generalized metric space.…”

Fixed point theorems for contractive mappings and Ciric-Maiti-Pal orbit mappings of contractive type in re-defined generalized metric spaces

“…The first author also introduced the concepts of qpb-cyclic-Banach contraction mapping, qpb-cyclic-Kannan mapping and qpb-cyclic-quasi-contraction mapping and established the existence and uniqueness of fixed point theorems for these mappings in quasi-partial b-metric spaces [8]. Jleli and Samet [12] introduced the definition of the generalized metric spaces on which some spaces mentioned above have been unified based, that is, all of the standard metric spaces, the dislocated metric spaces, and the modular metric spaces D m , which m are with Fatou property, are generalized metric space.…”