Fixed point theorems for modular contraction mappings on modulared spaces

Abstract

In this paper, we present some conditions that guarantee the existence of the fixed point for a certain type of modular contraction mapping on a modulared space. Mathematics Subject Classification: 46A40, 46B40, 47H10

Meir Keeler's Fixed-Point Theorem in Complex-Valued Modular Metric Space

“…The first step involves studying the concept of complexvalued modular metric spaces, as defined by Ozkan in [16], including the definitions, topology, convergent sequences, and fixedpoints. Based on these concepts, the notion of Meir-Keeler ωcontraction mappings is constructed in complex-valued modular metric spaces as previously defined in metric spaces [13], modular spaces [14], and modular metric spaces [15]. Subsequently, the sufficient conditions that the Meir-Keeler ω-contraction mappings must satisfy to ensure the existence and uniqueness of their fixed-points are investigated.…”

“…One of the most interesting generalizations of contractions is Meir Keeler contraction in a complete metric space [13]. In 2013, Kiftiah [14] proposed the concept of fixed-points from several contraction mappings developed from metric spaces to modular spaces. One of these mappings is the Meir Keeler ρcontraction.…”

Cyclic $(\alpha ,\beta )$-Admissible Mappings in Modular Spaces and Applications to Integral Equations

“…Firstly, Nakano initiated the concept of modulared spaces [25]. Later, some authors proved new fixed point theorems of Banach type in modular spaces [1,13,16,20,21,32,2,3,5,8,9,10,12,14,19,23,28,29,33]. In this work, we present some fixed point results as a generalization of Banach's fixed point theorem using some convenient constants in the contraction assumption in modular spaces.…”

“…Firstly, Nakano initiated the concept of modular spaces [26]. Later, some authors proved new fixed point theorems of Banach type in modular spaces [12,18,19,22,23,24,29,33]. Then, also the concept of the fixed point theory was studied in modular metric, modular function and modular vector spaces.…”