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Iterative algorithms for variational inclusions, mixed equilibrium and fixed point problems with application to optimization problems

Yonghong Yao;  Yeol Cho;  Yeong-Cheng Liou — 2011

Open Mathematics

In this paper, we introduce an iterative algorithm for finding a common element of the set of solutions of a mixed equilibrium problem, the set of fixed points of a nonexpansive mapping, and the the set of solutions of a variational inclusion in a real Hilbert space. Furthermore, we prove that the proposed iterative algorithm converges strongly to a common element of the above three sets, which is a solution of a certain optimization problem related to a strongly positive bounded linear operator....

Existence of a common solution for a system of nonlinear integral equations via fixed point methods inb-metric spaces

Oratai Yamaod;  Wutiphol Sintunavarat;  Yeol Je Cho — 2016

Open Mathematics

In this paper we introduce a property and use this property to prove some common fixed point theorems in b-metric space. We also give some fixed point results on b-metric spaces endowed with an arbitrary binary relation which can be regarded as consequences of our main results. As applications, we applying our result to prove the existence of a common solution for the following system of integral equations: x (t) =  ∫ a b K 1  (t,r,x(r)) dr, x (t) =  ∫ a b K 2  (t,r,x(r)) dr,       x ( t ) = ∫ a b K 1 ( t , r , x ( r ) ) d r , x ( t ) = ∫ a b K 2 ( t , r , x ( r ) ) d r , where a, b...

Coincidence and fixed point theorems for nonlinear hybrid generalized contractions

H. K. Pathak;  Shin Min Kang;  Yeol Je Cho — 1998

Czechoslovak Mathematical Journal

In this paper we first prove some coincidence and fixed point theorems for nonlinear hybrid generalized contractions on metric spaces. Secondly, using the concept of an asymptotically regular sequence, we give some fixed point theorems for Kannan type multi-valued mappings on metric spaces. Our main results improve and extend several known results proved by other authors.

Random fixed points for a certain class of asymptotically regular mappings

Balwant Singh Thakur;  Jong Soo Jung;  Daya Ram Sahu;  Yeol Je Cho — 1998

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

Let (Ω, σ) be a measurable space and K a nonempty bounded closed convex separable subset of a p-uniformly convex Banach space E for p > 1. We prove a random fixed point theorem for a class of mappings T:Ω×K ∪ K satisfying the condition: For each x, y ∈ K, ω ∈ Ω and integer n ≥ 1, ⃦Tⁿ(ω,x) - Tⁿ(ω,y) ⃦ ≤ aₙ(ω)· ⃦x - y ⃦ + bₙ(ω) ⃦x -Tⁿ(ω,x) ⃦ + ⃦y - Tⁿ(ω,y) ⃦ + cₙ(ω) ⃦x - Tⁿ(ω,y) ⃦ + ⃦y - Tⁿ(ω,x) ⃦, where aₙ, bₙ, cₙ: Ω → [0, ∞) are functions satisfying certain conditions and Tⁿ(ω,x) is the value...

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 ) .

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