We define the multivalued Reich (G, ρ)-contraction mappings on a modular function space. Then we obtain sufficient conditions for the existence of fixed points for such mappings. As an application, we introduce a ρ-valued Bernstein operator on the set of functions f : [0, 1] → Lρ and then give the modular analogue to Kelisky-Rivlin theorem. c ©2016 All rights reserved.

In this paper a general fixed point theorem for converse commuting multivalued mappings, which generalize Theorems 2.1 and 2.2 from [3], is proved.

Some results on the existence of solution for certain fuzzy equations are revised and extended. In this paper, we establish the existence of a solution for the fuzzy equation Ex2 +Fx+G= x, where E, F, G, and x are positive fuzzy numbers satisfying certain conditions. To this purpose, we use fixed point theory, applying results such as the wellknown fixed point theorem of Tarski, presenting some...

We prove that for an action of a finite group G on a systolic complex X there exists a G–invariant subcomplex of X of diameter 5. For 7–systolic locally finite complexes we prove there is a fixed point for the action of any finite G. This implies that free products with amalgamation (and HNN extensions) of 7–systolic groups over finite subgroups are also 7–systolic.

New fixed point results are presented for admissible pairs and maps (admissible in the sense of Górniewicz) defined on subsets of a Fréchet space E. The proof relies on the notion of a pseudo open set, degree theory, and on viewing E as the projective limit of a sequence of Banach spaces.

We apply the Luxemburg–Jung fixed point theorem in generalized metric spaces to study the Hyers–Ulam stability for two functional equations in a single variable.

*Correspondence: [email protected] 1Department of Mathematics, King Abdulaziz University, P.O. Box 80203, Jeddah, 21589, Saudi Arabia Full list of author information is available at the end of the article Abstract We first introduce the concept of b-metric-like space which generalizes the notions of partial metric space, metric-like space and b-metric space. Then we establish the existence and...

We use the fixed point alternative theorem to prove the stability of the set-valued function equation c(x)F (h(x)) = F (x). This result enable us to prove the stability of some set-valued functional equations.

We investigate the class of groups admitting an action on a set with an invariant mean. It turns out that many free products admit interesting actions of that kind. A complete characterization of such free products is given in terms of a fixed point property.

The aim of this note is to indicate an example that demonstrates the incorrectness of Iimura’s discrete fixed point theorem [J. Mathematical Economics 39 (2003) 725] and to present a corrected statement using the concept of integrally convex sets.