Fixed point theorems for generalized multivalued nonlinear F -contractions

Abstract

In this paper, we introduce certain new concepts of α-η-lower semi-continuous and α-η-upper semicontinuous mappings. By using these concepts, we prove some fixed point results for generalized multivalued nonlinear F-contractions in metric spaces and ordered metric spaces. As an application of our results we deduce Suzuki-Wardowski type fixed point results and fixed point results for orbitally lower semi-continuous mappings in complete metric spaces. Our results generalize and extend many recent fixed point theorems including the main results of Minak et al.

Contraction Mappings and Applications

“…0 such that for all x, y ∈ X , ðÞ , then T has a fixed point in X . For more in this direction, see, [28][29][30][31]. Here, we give the concept of multivalued α-F-weak-contractions and prove some fixed point results.…”

Existence and stability results for fixed points of multivalued $F$ contractions and application to Volterra type non homogeneous integral equation of second kind

“…To fulfill our purpose we use the recent technique, which was given by Wardowski [37]. For the sake of completeness, we will discuss the basic lines [23,24,25].…”

Common and Coincidence Fixed-Point Theorems for ℑ-Contractions with Existence Results for Nonlinear Fractional Differential Equations

“…Recently, some authors demonstrated the Wardowski original conclusions without the criteria ( 2 ) and ( 3 ) in various ways (see, [6,7]). For more in this direction, see [8][9][10][11][12][13][14][15]. Very recently, Derouiche and Ramoul [16] introduced the notions of extended -contractions of the Suzuki-Hardy-Rogers type, extended -contractions of the Hardy-Rogers type, and generalized -weak contractions of the Hardy-Rogers type as well as establishing some new fixed-point results for such kinds of mappings in the setting of complete b-metric spaces.…”