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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 ) .

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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