Relation-theoretic coincidence and common fixed point results under $(F,\mathcal{R})_{g}$-contractions with an application

Abstract

In this paper, we begin with some observations on F-contractions. Thereafter, we introduce the notion of (F, R) g-contractions and utilize the same to prove some coincidence and common fixed point results in the setting of metric spaces endowed with binary relations. An example is also given to exhibit the utility of our results. We also deduce some consequences in the setting of ordered metric spaces. As an application, we investigate the existence and uniqueness of a solution of integral equation of Volterra type.

On Relational Weak Fℜm,η-Contractive Mappings and Their Applications

“…Finally, we give an example different to the above example and others given in the literature [38] which satisfies all conditions of Theorem 15. Observe that given the function A(α, σ, ξ) = ξ(σ) 1+ξ(σ) in the third variable is nondecreasing and that 1 3 α ≤ 5 3 α − α 1+α + α 0 ξ(σ) 1+ξ(σ) mσ for all α in [0, 1] such that ξ(α) = 1 3 α is a lower solution of ( 16), then the following below inequality holds:…”

Coincidence Point Results on Relation Theoretic F

“…It is further investigated by Imdad et al [18]. In present paper, we study the results presented by Alfaqih et al [19] and we define ðF w , RÞ g -contractions. We also prove similar results for ðF w , RÞ g -contractions.…”

New Relation-Theoretic Fixed Point Theorems in Fuzzy Metric Spaces with an Application to Fractional Differential Equations

“…The authors in [8][9][10] provided several interested applications to boundary value problems and matrix equations which supported their fixed point results strongly. Thereafter, a lot of fixed point theorems have been provided in which various definitions of binary relations were equipped (e.g., [11][12][13][14][15] and several others). Now, let us recall some basic definitions, notions, and results which will be needed in the following.…”