Cone-valued lower semicontinuous maps are used to generalize Cristi-Kirik’s fixed point theorem to Cone metric spaces. The cone under consideration is assumed to be strongly minihedral and normal. First we prove such a type of fixed point theorem in compact cone metric spaces and then generalize to complete cone metric spaces. Some more general results are also obtained in quasicone metric spaces.

By introducing a new concept called ‘‘set-valued asymptotic contraction’’ in metric spaces, the existence and uniqueness of endpoints for a set-valued asymptotic contraction which has the approximate endpoint property have been established. © 2010 Elsevier Ltd. All rights reserved.

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.

Fixed points are also called as invariant points. Invariant point theorems very essential tools in solving problems arising different branches of mathematical analysis. In the present paper, we establish three unique common using two self-mappings, four self-mappings and six bicomplex valued metric space. first theorem, generate a theorem for by weaker conditions such weakly compatible, general...

In this paper, we shall generalize the definition of (φ− k) −B contraction to multi-valued mappings which was presented before in single valued case by Mihet. Then we shall prove two fixed point theorems for multi-valued (φ− k) − B contraction mappings in probabilistic metric space.