On Convex F-Contraction in b-Metric Spaces

Abstract

In this paper, we introduce a notion of convex F-contraction and establish some fixed point results for such contractions in b-metric spaces. Moreover, we give a supportive example to show that our convex F-contraction is quite different from the F-contraction used in the existing literature since our convex F-contraction does not necessarily contain the continuous mapping but the F-contraction contains such mapping. In addition, via some facts, we claim that our results indeed generalize and improve some previous results in the literature.

Existence Results for Wardoski-Type Convex Contractions and the Theory of Iterated Function Systems

“…Not long ago, in 2021, Huang et al [37] introduced the notion of a convex F contraction and established some fixed-point results for such contractions in the context of b-MS.…”

“…Motivated by the works in [35,37], in this paper, we refine the notion of the convex F contraction in the setting of b-MS by introducing the extended convex F contraction. Our results unify and generalise many existing results in the literature, including those in [5,14,35,37].…”

Remarks on Recent Results for Generalized F-Contractions

“…(2) F(0 + ) = lim x→0 + F(x) = −∞ (for more details, see [1,[13][14][15]). That is to say, each F ∈ F ↑ satisfies either (1) or (2) (see Proposition 1, Section 8 of [1]).…”

“…(s, y(s)) X ds ≤ cτ ≤ r, then T maps Y into Y. In order to finish the proof of(13), by induction on n we need to show that, for every t ∈ I τ , T n y 1 (t) − T n y 2 (t) X…”

Cyclic Mappings and Further Results in B-Metric-Like Spaces

“…In 2021, a new cyclic mapping was studied by Weng et al and they called it as φ-type cyclic mapping [18]; some fixed point results from 2018 to 2021 can also be found in [18]. On the other hand, Huang et al [19] in 2021 introduced the concept of F-contraction and established some fixed point theorems for such contractions in B-metric spaces. us, it can be seen that the generalization of research work of metric space and the extended research work of many kinds of mappings in different generalized metric spaces are simultaneous.…”