Generalized Krasnoselskii fixed point theorem involving auxiliary functions in bimetric spaces and application to two-point boundary value problem

Generalized Contractive Mappings and Related Results in b-Metric Like Spaces with an Application

“…If the nonlinear mappings T, S : Ω Ñ Ω are weakly compatible such that TpΩq Ă SpΩq. Assume that ψ P Ψ, φ P Φ, β P r0, 1 2 q and q ě 2 such that the condition…”

“…It's obvious that ω b is a b-metric like on Ω, with coefficient s " 2 and pΩ, ω b q is a complete. Define nonlinear self-mappings T, S : Ω Ñ Ω by Tκ " 1 16 lnp1`κ 4 q, Sκ " 1 4 lnp1`κ 2 q for all κ, τ P Ω, and the functions ψptq " t, φptq " t 4 and constant q " 2. It is clear that TpΩq Ă SpΩq.…”

“…Problems in nonlinear analysis are solved by a popular tool called the Banach contraction principle. A lot of publications are devoted to the study and solutions of many practical and theoretical problems by using this principle [1][2][3][4][5][6]. One of the interesting generalizations of this basic principle was given by Bakhtin [7] (and also Czerwik [8]) by introducing the concept of b-metric spaces.…”

Generalized contraction mappings of rational type and applications to nonlinear integral equations

“…Generalizations of the Banach contraction principle have been extensively used to study common fixed points for contractive type pair of mappings, as well as in the existence of solutions of differential and integral equations, (see e.g., [3,4,6,7,10,11,12,15,17,18,19,20]). In this paper, first, we establish some common fixed point theorems for a class of contractions of rational type wherein contractive inequality is controlled by a positive function satisfying a stability condition at 0.…”

Fixed point theorems in bimetric space endowed with binary relation and applications

“…They showed a theorem subsumes many known results in the literature. For further study about contractive mappings in a metric space endowed with binary relation, we refer the reader to [3][4][5][6][7], [13], [17] and [19].…”