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.

*Correspondence: [email protected] 1Departamento de Análise Matemática, Facultade de Matemáticas, Universidade de Santiago de Compostela, Santiago de Compostela, 15782, Spain Full list of author information is available at the end of the article Abstract We prove a new fixed point theorem of Schauder type, which applies to discontinuous operators in noncompact domains. In order to do so, we...

*Correspondence: [email protected] Department of Mathematics and Statistics, Central South University, 932 Lushan South Road, Changsha, 410083, China †Equal contributors Abstract In this paper, we study a class of generalized fractional order three-point boundary value problems that involve fractional derivative defined in terms of weight and scale functions. Using several fixed point t...

It is shown that the master equation of the affine-Virasoro construction on the unitary affine algebra naturally emerges in the fusion algebra of the nonunitary level k WZNW model. Operators corresponding to solutions of the master equation are suitable for performing one-parametrical renormalizable perturbation around the given conformal nonunitary WZNW model. In the large |k| limit, the infra...

Several new fixed point results for compact permissible self maps in extension type spaces are presented in this paper.