Coincidence and common fixed point theorems for four mappings satisfying (alpha(s),F)-contraction

Abstract

In this paper, we manifest some coincidence and common fixed point theorems for four self-mappings satisfying Círíc-type and Hardy–Rogers-type (αs,F)-contractions defined on an αs-complete b-metric space. We apply these results to infer several new and old corresponding results in ordered b-metric spaces and graphic b-metric spaces. Our work generalizes several recent results existing in the literature. We present examples to validate our results. We discuss an application of main result to show the existence of common solution of the system of Volterra type integral equations.

Generalized Fixed-Point Results for Almost (α,Fσ)-Contractions with Applications to Fredholm Integral Inclusions

“…We denote by ∆ , the set of all mappings F : R + → R satisfying (F 1 )-(F 3 ) and continuous from the right. For more details in the direction of F-contractions, we refer the readers to [5][6][7][8][9][10].…”

Extraction new results of common fixed point theorems for $({T}, {\alpha }_{{s}}, {F})$-contraction of six mappings in a tripled b-metric space with an application of integral equations

“…Also, Minak, Helvaci, and Altun presented a fixed point result for Ćirićtype generalized F-contraction [26]. In 2018, Nazam, Muhammad, and Postolache investigated some common fixed point results for four self-mappings satisfying such kind of contractions on the α s -complete b-metric space and applied their conclusion to infer several new and old results, based on the idea of Ćirić-type and Hardy-Rogers-type (α s , F)contractions [27].…”

“…In this study, motivated by [27] and among these achievements, we are working to stretch out the Ćirić-type and Hardy-Rogers-type (α s , F)-contractions based on six selfmappings defined on a b-metric space. Also, some common fixed point results for six selfmappings satisfying such kind of contractions are shown in the (T, α s , F)-complete tripled b-metric space.…”

“…Hence all the assumptions in Theorem 1.7 are satisfied and thus T has a fixed point which is x = 0. Definition 1.9 (see [27]…”

“…Theorem 1.10 (see [27]) Let M be a nonempty set and α s be as defined in Definition 1.9. Let f , g, S, T be α sb-continuous self-mappings defined on an α s -complete b-metric space…”