Some Relations Between Nonexpansive and Order Preserving Mappings

Generating Sets of Order Preserving Mappings

Sierpiński proved in 1935 that any countable set of mappings on an infinite set X is contained in a subsemigroup of the semigroup of all maps on X, where this subsemigroup is generated by just two mappings. Since then, it has been of interest whether the result also holds when certain restrictions are placed on the properties of the maps. In this paper we investigate the minimum number of order...

On Firmly Nonexpansive Mappings

It is shown that any A-firmly, 0 < A < 1 , nonexpansive mapping T: C —> C has a fixed point in C whenever C is a finite union of nonempty, bounded, closed convex subsets of a uniformly convex Banach space. Let C be a nonempty subset of a Banach space X, and let X £ (0, 1). Then a mapping T: C —> X is said to be X-firmly nonexpansive if (1) \\Tx Ty\\ < ||(1 X)(x y)+X(Tx Ty)\\ for all x, y £ C. I...

Some Sufficient Conditions for Fixed Points of Multivalued Nonexpansive Mappings

We show some sufficient conditions on a Banach space X concerning the generalized James constant, the generalized Jordan-von Neumann constant, the generalized Zbagănu constant, the coefficient ε̃0 X , the weakly convergent sequence coefficientWCS X , and the coefficient of weak orthogonality, which imply the existence of fixed points for multivalued nonexpansive mappings. These fixed point theor...

Note on Some Results for Asymptotically Pseudocontractive Mappings and Asymptotically Nonexpansive Mappings

Common Fixed Points for Nonexpansive and Nonexpansive Type Fuzzy Mappings

In this paper we define g-nonexpansive and g-nonexpansive type fuzzy mappings and prove common fixed point theorems for sequences of fuzzy mappings satisfying certain conditions on a Banach space. Thus we obtain fixed point theorems for nonexpansive type multi-valued mappings.