Terminal continua and quasi-monotone mappings

Mappings of Terminal Continua

Various kinds of nonseparating subcontinua were studied by a number of authors, see, for example, the expository paper [2], where a large amount of information on this subject is given. In the topological literature, or in continuum theory (to be more precise), the term “terminal,” when applied either to subcontinua of a given continuum or to points, and the same name “terminal” was assigned to...

On Monotone Ćirić Quasi–contraction Mappings

We prove the existence of fixed points of monotone quasi-contraction mappings in metric and modular metric spaces. This is the extension of Ran and Reurings fixed point theorem for monotone contraction mappings in partially ordered metric spaces to the case of quasicontraction mappings introduced by Ćirić. The proofs are based on Lemmas ?? and ??, which contain two crucial inequalities essentia...

Non-metric continua and multi-valued mappings

A continuum is an arboroid if it is hereditarily unicoherent and arcwise connected. A metric arboroid is a dendroid. A generalized dendrite is a locally connected arboroid. Among other things, we shall prove that a locally connected continuum X is a generalized dendrite if and only if X has the fixed point property for continuous, closed set-valued mappings.

Quasi-convex Functions and Quasi-monotone Operators

The notions of a quasi-monotone operator and of a cyclically quasi-monotone operator are introduced, and relations between such operators and quasi-convex functions are established.

Generalized Variational Inequalities Involving Relaxed Monotone Mappings and Nonexpansive Mappings