Common fixed point results of a pair of generalized $(\psi,\varphi )$-contraction mappings in modular spaces

Abstract

In this paper, we establish the existence of a common fixed point of almost generalized contractions on modular spaces. As an application, we present some fixed and common fixed point results for such mappings on modular spaces endowed with a graph. The existence of fixed and common points of mappings satisfying generalized contractive conditions of integral type is also obtained in such spaces. Some examples are presented to support the results obtained herein. Our results generalize and extend various comparable results in the existing literature. MSC: 47H10; 54H25; 54E50

Fixed points of relaxed (Ψ,φ)-weakly N-contraction mappings in modular spaces

“…If, in Theorem 3.5, we consider N = 1, then we obtain Theorem 3.1 ofÖztürk et.al [26]. We remark that the proof of Theorem 3.1 ofÖztürk et.al [26] has a gap in concluding the Cauchy nature of the sequence considered.…”

“…Moreover, for every x 0 ∈ C, the sequence of iterates {Tx n } ρ-converges to the unique fixed point of T. Remark 3.20. If, in Corollary 3.17, we assume that N = 1, then we obtain Theorem 2.3 ofÖztürk et.al [26]. We note that the proof of Theorem 2.3 ofÖztürk et.al [26] has a gap in concluding the Cauchy nature of the sequence considered.…”

“…Furthermore, we provide examples to show that our results apply to the class of mappings more general than the class of mappings considered by other authors, for instance, Mongkolkeha and Kumam [23] and Oztürk et. al [26]. Finally, a numerical examples are provided to validate our results.…”

“…Recently,Öztürk et. al [26] introduced and proved the existence of a common fixed point of a pair of mappings in modular spaces satisfying the generalized (ψ, ϕ)-weakly contractive condition provided that one of the mapping is ρ-continuous. A pair of mappings S, T : X ρ → X ρ , is said to satisfy a generalized (ψ, ϕ)-weakly contractive condition if for any x, y ∈ X ρ , we have…”

Modified Suzuki-Simulation Type Contractive Mapping in Non-Archimedean Quasi Modular Metric Spaces and Application to Graph Theory

“…After that, many fixed point researchers investigated fixed point results improving the Jachymski fixed point theorems in [17,[21][22][23].…”