Abstract
Motivated by the ideas of F -weak contractions and F , R g -contractions, the notion of F w , R g -contractions is introduced and studied in the present paper. The idea is to establish some interesting results for the existence and uniqueness of a coincidence point for these contractions. Further, using an additional condition of weakly compatible mappings, a common fixed-point theorem and a fixed-point result are proved for F w , R g -contractions in metric spaces equipped with a transitive binary relation. The results are elaborated by illustrative examples. Some consequences of these results are also deduced in ordered metric spaces and metric spaces endowed with graph. Finally, as an application, the existence of the solution of certain Voltera type integral equations is investigated.
Highlights
Introduction and PreliminariesIn the development of the metric fixed-point theory, one of the main pillar is the Banach contraction principle [1], which states that every contraction on a complete metric space has a unique fixed point
Later on, fixed points for F-contractions were proved by Secelean [11] using an iterated function
Abbas et al [12] extended the work of Wardowski and established various results of fixed points using F-contraction mappings
Summary
In the development of the metric fixed-point theory, one of the main pillar is the Banach contraction principle [1], which states that every contraction on a complete metric space has a unique fixed point. The idea of ðF, RÞ-contractions was established by Sawangsup et al [17] They used this idea to demonstrate some fixed-point consequences using a binary relation. Let ðX, dÞ be a metric space and R be a binary relation on X and T, g : X ⟶ X. Let ðM, dÞ be a metric space endowed with a binary relation R. Such a R is named to be d-self closed if for each R-preserving sequence fςng ⊆ M so that fςng ⟶ x, there is fςnk g of fςng so that 1⁄2ςnk , x ∈ R∀k ∈ N0.
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