In 1985 V. P. Okhezin proved that the cartesian product of a Bspace X and a compact metric AR space has the fixed point property. In this paper it is shown that the cone over X and the suspension of X have the fixed point property.

It is shown that if X is a Banach space and C is a union of finitely many nonempty, pairwise disjoint, closed, and connected subsets {Ci : 1≤ i≤ n} of X , and each Ci has the fixed-point property (FPP) for asymptotically regular nonexpansive mappings, then any asymptotically regular nonexpansive self-mapping of C has a fixed point. We also generalize the Goebel-Schöneberg theorem to some Banach...

In recent time, fixed point theory has been developed rapidly in partially ordered metric space. Bhaskar and Lakshmikantham (2006) introduced the concept of mixed monotone property. Lakshmikanthem and Ciric (2009) generalized the concept of mixed monotone mapping and proved a common coupled fixed point theorem. In this paper, we find a new type of contractive condition on Gmetric spaces also th...

We examine the close analogy which exists between Helly graphs and hyperconvex metric spaces, and propose the hyperconvex semi-metric space as an unifying concept. Unlike the metric spaces, these semi-metric spaces have a rich theory in the discrete case. Apart from some new results on Helly graphs, the main results concern: fixed point property of contractible semi-metric spaces (for nonexpans...

In this paper, we define the modular space Z σ (s, p) by using the Zweier operator and a modular. Then, we consider it equipped with the Luxemburg norm and also examine the uniform Opial property and property β. Finally, we show that this space has the fixed point property.

A topological space is said to have the fixed point property if every continuous self-map of it has at least one fixed point. In this text, we investigate the additional restraints imposed by the requirement that a fixed point can be chosen continuously when the self-map is varied continuously. While we are able to present a class of universal fixed point spaces, where this is always possible, ...

The collection CL(T ) of nonempty convex sublattices of a lattice T ordered by bi-domination is a lattice. We say that T has the fixed point property for convex sublattices (CLFPP for short) if every order preserving map f ∶ T → CL(T ) has a fixed point, that is x ∈ f(x) for some x ∈ T . We examine which lattices may have CLFPP. We introduce the selection property for convex sublattices (CLSP);...