Fixed point theorems for multivalued nonexpansive mappings satisfying inwardness conditions

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 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...

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

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...

some fixed point theorems for weakly compatible multivalued mappings satisfying some general contractive conditions of integral type