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Fixed point theorems for nonexpansive operators with dissipative perturbations in cones

Shih-sen Chang;  Yu-Qing Chen;  Yeol Je Cho;  Byung-Soo Lee — 1998

Commentationes Mathematicae Universitatis Carolinae

Let P be a cone in a Hilbert space H , A : P → 2 P be an accretive mapping (equivalently, - A be a dissipative mapping) and T : P → P be a nonexpansive mapping. In this paper, some fixed point theorems for mappings of the type - A + T are established. As an application, we utilize the results presented in this paper to study the existence problem of solutions for some kind of nonlinear integral equations in L 2 ( Ω ) .

Coincidence point theorems in certain topological spaces

Jong Soo Jung;  Yeol Je Cho;  Shin Min Kang;  Yong Kab Choi;  Byung Soo Lee — 1999

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

In this paper, we establish some new versions of coincidence point theorems for single-valued and multi-valued mappings in F-type topological space. As applications, we utilize our main theorems to prove coincidence point theorems and fixed point theorems for single-valued and multi-valued mappings in fuzzy metric spaces and probabilistic metric spaces.

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

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 spaces H k , p ...

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