Two fixed point theorems for uniformly lipschitzian mappings in metric spaces, due respectively to E. Lif̌sic and to T.-C. Lim and H.-K. Xu, are compared within the framework of the so-called CAT(0) spaces. It is shown that both results apply in this setting, and that Lif̌sic’s theorem gives a sharper result. Also, a new property is introduced that yields a fixed point theorem for uniformly lipsc...

Abstract In a real Hilbert space, let the VIP, GSVI, HVI, and CFPP denote variational inequality problem, general system of inequalities, hierarchical inequality, common fixed-point problem countable family uniformly Lipschitzian pseudocontractive mappings an asymptotically nonexpansive mapping, respectively. We design two Mann implicit composite subgradient extragradient algorithms with line-s...

In this paper we examine the basic structure of metric trees and prove fixed point theorems for uniformly Lipschitzian mappings in metric trees.

Let H be a real Hilbert space, and let C be a nonempty closed convex subset of H. Let α > 0, and let A be an α-inverse strongly-monotone mapping of C into H. Let T be a generalized hybrid mapping of C into H. Let B andW be maximal monotone operators on H such that the domains of B andW are included in C. Let 0 < k < 1, and let g be a k-contraction of H into itself. Let V be a γ -strongly monoto...