Displaying similar documents to “The characteristic of noncompact convexity and random fixed point theorem for set-valued operators”

Random fixed point theorems for a certain class of mappings in Banach spaces

Jong Soo Jung, Yeol Je Cho, Shin Min Kang, Byung-Soo Lee, Balwant Singh Thakur (2000)

Czechoslovak Mathematical Journal

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Let ( Ω , Σ ) be a measurable space and C a nonempty bounded closed convex separable subset of p -uniformly convex Banach space E for some p > 1 . We prove random fixed point theorems for a class of mappings T Ω × C → C satisfying: for each x , y ∈ C , ω ∈ Ω and integer n ≥ 1 , ∥ T n ( ω , x ) - T n ( ω , y ) ∥ ≤ a ( ω ) · ∥ x - y ∥ + b ( ω ) { ∥ x - T n ( ω , x ) ∥ + ∥ y - T n ( ω , y ) ∥ } + c ( ω ) { ∥ x - T n ( ω , y ) ∥ + ∥ y - T n ( ω , x ) ∥ } , where a , b , c Ω → [ 0 , ∞ ) are functions satisfying certain conditions and T n ( ω , x ) is the value at x of the n -th iterate of the mapping T ( ω , · ) . Further we establish for these mappings some random fixed point theorems in a Hilbert space, in L p spaces, in Hardy spaces H p and in Sobolev...

On a problem of Gulevich on nonexpansive maps in uniformly convex Banach spaces

Sehie Park (1996)

Commentationes Mathematicae Universitatis Carolinae

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Let X be a uniformly convex Banach space, D ⊂ X , f : D → X a nonexpansive map, and K a closed bounded subset such that co ¯ K ⊂ D . If (1) f | K is weakly inward and K is star-shaped or (2) f | K satisfies the Leray-Schauder boundary condition, then f has a fixed point in co ¯ K . This is closely related to a problem of Gulevich [Gu]. Some of our main results are generalizations of theorems due to Kirk and Ray [KR] and others.