Fixed point results of a generalized reversed $ F $-contraction mapping and its application

Remarks on Recent Results for Generalized F-Contractions

“…The above theorem shows several things. First, it generalizes and corrects the recent results on a fixed point for a so-called F-contraction (see [7][8][9][10]. Secondly, various consequences can be obtained by assuming Condition (I) or Condition (II) if we choose the special values of parameters α, β, γ, δ, and η.…”

“…Taking the limit as n → ∞ in (7), we obtain τ + F( + ) ≤ F( + ) which is a contradiction with τ > 0. Consequently, we obtain = 0, i.e., lim n→∞ d(x n−1 , x n ) = 0.…”

“…Subsequently, several interesting modifications and extensions dealing with the original results of Wardowski have been carried out in various ways by many researchers. For the details on F-contractions, the reader may refer to [7][8][9][10] and references therein. Motivated by the previous work on F-contractions, throughout this paper, we introduce a generalized F-contraction, which embeds a Hardy-Rogers type function (see [3]).…”

On F-Contractions: A Survey

“…Generalized F-contractions for complete metric spaces also appear in [29,30]. Bashir et al [31], extend Wardowski's idea of F-contraction by introducing the reversed generalized F-contraction mapping. Further generalizations are F ωcontractions [32], F-g-contractions [33], F-contractive mappings of Hardy-Rogers-type [34,35].…”

Unique Solution of Integral Equations via Intuitionistic Extended Fuzzy b-Metric-Like Spaces

“…Gregory et al [8] proved various fixed point theorems in fuzzy metric spaces. Bashir et al [9] established several fixed point results of a generalized reversed F-contraction mapping and its application.…”