Countably condensing multimaps and fixed points

Fixed Points for w-Contractive Multimaps

Fixed Points for Contractive Type Multimaps

Without using the concept of the Hausdorff metric, we prove some results on the existence of fixed points and strict fixed points for multivalued maps satisfying some generalized Latif-Albar type conditions. Consequently, several known fixed point results either generalized or improved including the corresponding recent results of Feng and Liu [J. Math. Anal. Appl. 317 (2006) 103-112], Latif an...

Fixed Points of Multimaps Which Are Not Necessarily Nonexpansive

Let C be a nonempty closed bounded convex subset of a Banach space X whose characteristic of noncompact convexity is less than 1 and T a continuous 1-χ-contractive SL map (which is not necessarily nonexpansive) from C to KC(X) satisfying an inwardness condition, where KC(X) is the family of all nonempty compact convex subsets of X . It is proved that T has a fixed point. Some fixed points resul...

FIXED POINTS OF n-VALUED MULTIMAPS OF THE CIRCLE

A multifunction φ : X ( Y is n-valued if φ(x) is an unordered subset of n points of Y for each x ∈ X. The (continuous) n-valued multimaps φ : S ( S are classified up to homotopy by an integer-valued degree. In the Nielsen fixed point theory of such multimaps, due to Schirmer, the Nielsen number N(φ) of an n-valued φ : S ( S of degree d equals |n − d| and φ is homotopic to an n-valued power map ...

Fixed Points and Coincidence Points for Multimaps with Not Necessarily Bounded Images

Many authors have been using the Hausdorffmetric to obtain fixed point and coincidence point theorems for multimaps on a metric space. In most cases, the metric nature of the Hausdorff metric is not used and the existence part of theorems can be proved without using the concept of Hausdorff metric under much less stringent conditions on maps. The aim of this paper is to illustrate this and to o...