A generalization of Istrățescu’s fixed point theorem for convex contractions

Abstract

Abstract. In this paper we prove a generalization of Istrȃţescu's theorem for convex contractions. More precisely, we introduce the concept of iterated function system consisting of convex contractions and prove the existence and uniqueness of the attractor of such a system. In addition we study the properties of the canonical projection from the code space into the attractor of an iterated function system consisting of convex contractions.

F-Convex Contraction via Admissible Mapping and Related Fixed Point Theorems with an Application

“…Further, he showed with example (see Example 1.3, [4]) that T is in the class of convex contraction but it is not a contraction. Recently, some researchers studied on generalization of such class of mappings in the setting of various spaces (for example, Alghamdi et al [5], Ghorbanian et al [6], Latif et al [7], Miandaragh et al [8], Miculescu [9], etc.). Khan et al [10], introduced the notion of generalized convex contraction mapping of type-2 by extending the generalized convex contraction (respectively, generalized convex contraction of order-2) of Miandaragh et al [8] and the convex contraction mapping of type-2 of Istrǎţescu [4].…”

On generalized convex contractions of type-2 in b-metric and 2-metric spaces

“…Recently, some works have appeared on the generalization of such classes of mappings in the setting of metric, ordered metric, orthogonal metric and cone metric spaces: Alghamdi et al [1], Ghorbanian et al [15], Latif et al [22], Miandaragh et al [24], Miculescu and Mihail [26], Ramezani [27], and Sastry et al [30]. Definition 1.1 ([3, 10]).…”

Iterated Function Systems Consisting of Generalized Convex Contractions in the Framework of Complete Strong b-metric Spaces

“…-to work with more general contractive conditions on the constitutive functions of the iterated function systems (see, for example, [18], [34], [36], [37], [38], [39], [45], [48], [52], [53], [57] and [58]). …”