we characterize compact composition operators on real banach spaces of complex-valued bounded lipschitz functions on metric spaces, not necessarily compact, with lipschitz involutions and determine their spectra.

We apply Preuss' concept of $mbbe$-connectedness to the categories of lattice-valued uniform convergence spaces and of lattice-valued uniform spaces. A space is uniformly $mbbe$-connected if the only uniformly continuous mappings from the space to a space in the class $mbbe$ are the constant mappings. We develop the basic theory for $mbbe$-connected sets, including the product theorem. Furtherm...

This paper is devoted to the solvability of generalized mixed variational inequalities in reflexive Banach spaces. We prove the existence of solutions of the generalized mixed variational inequalities for f quasimonotone set-valued mappings without any assumption on bounded values. Furthermore, we give some conditions that guarantee the existence of solutions of the generalized mixed variationa...

the notion of a bead metric space is defined as a nice generalization of the uniformly convex normed space such as $cat(0)$ space, where the curvature is bounded from above by zero. in fact, the bead spaces themselves can be considered in particular as natural extensions of convex sets in uniformly convex spaces and normed bead spaces are identical with uniformly convex spaces. in this paper, w...

In 2008, Al-Thaga and Shahzad [Generalized I-nonexpansive self-maps and invariant approximations, Acta Math. Sinica 24(5) (2008), 867{876]introduced the notion of occasionally weakly compatible mappings (shortly owcmaps) which is more general than all the commutativity concepts. In the presentpaper, we prove common xed point theorems for families of owc maps in Mengerspaces. As applications to ...