Fixed Point Theorems for Nonexpansive Mappings Satisfying Certain Boundary Conditions

Fixed Point Theorems for Nonexpansive Mappings Satisfying Certain Boundary Conditions1

Let K be a bounded closed convex subset of a Banach space X with int K 40, and suppose K has the fixed point property with respect to nonexpansive self-mappings (i.e., mappings U: K^K such that \\U(x) U(y)\\ < ||* y||, x,y € K). Let T: K -X be nonexpansive and satisfy inf{||* T(x)\\: x e boundary K, T'x) /Kl > 0. It is shown that if in addition, either (i) T satisfies the Leray-Schauder boundar...

Fixed Point Theorems for Mappings Satisfying Inwardness Conditions

Let A" be a normed linear space and let K be a convex subset of X. The inward set, I¡((x), of x relative to K is defined as follows: I^(x) = {x + c(u x):c > 1, u e K). A mapping T:K —► X is said to be inward if Tx S I/ç(x) for each x e K, and weakly inward if Tx belongs to the closure of If¿(x) for each x e K. In this paper a characterization of weakly inward mappings is given in terms of a con...

Fixed point theorems for $alpha$-contractive mappings

In this paper we prove existence the common fixed point with different conditions for $alpha-psi$-contractive mappings. And generalize weakly Zamfirescu map in to modified weakly Zamfirescu map.

Fixed Point Theorems for Single Valued Mappings Satisfying the Ordered non-Expansive Conditions on Ultrametric and Non-Archimedean Normed Spaces

In this paper, some fixed point theorems for nonexpansive mappings in partially ordered spherically complete ultrametric spaces are proved. In addition, we investigate the existence of fixed points for nonexpansive mappings in partially ordered non-Archimedean normed spaces. Finally, we give some examples to discuss the assumptions and support our results.

Some Fixed Point Theorems for Weakly Compatible Multivalued Mappings Satisfying Some General Contractive Conditions of Integral Type