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Steady state and scaling limit for a traffic congestion model

Ilie GrigorescuMin Kang — 2010

ESAIM: Probability and Statistics

In a general model (AIMD) of transmission control protocol (TCP) used in internet traffic congestion management, the time dependent data flow vector () > 0 undergoes a biased random walk on two distinct scales. The amount of data of each component () goes up to ()+ with probability 1- () on a unit scale or down to (), 0 < < 1 with probability () on a logarithmic scale, where ...

Coincidence and fixed point theorems for nonlinear hybrid generalized contractions

H. K. PathakShin Min KangYeol 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.

Weak and strong convergence theorems of common fixed points for a pair of nonexpansive and asymptotically nonexpansive mappings

Zeqing LiuRavi P. AgarwalChi FengShin Min Kang — 2005

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

The purpose of this paper is to establish some weak and strong convergence theorems of modified three-step iteration methods with errors with respect to a pair of nonexpansive and asymptotically nonexpansive mappings in uniformly convex Banach spaces. The results presented in this paper generalize, improve and unify a few results due to Chang [1], Liu and Kang [5], Osilike and Aniagbosor [7], Rhoades [8] and Schu [9], [10] and others. An example is included to demonstrate that our results are sharp....

Strong convergence theorems of k -strict pseudo-contractions in Hilbert spaces

Xiao Long QinShin Min KangMei Juan Shang — 2009

Czechoslovak Mathematical Journal

Let K be a nonempty closed convex subset of a real Hilbert space H such that K ± K K , T K H a k -strict pseudo-contraction for some 0 k < 1 such that F ( T ) = { x K x = T x } . Consider the following iterative algorithm given by x 1 K , x n + 1 = α n γ f ( x n ) + β n x n + ( ( 1 - β n ) I - α n A ) P K S x n , n 1 , where S K H is defined by S x = k x + ( 1 - k ) T x , P K is the metric projection of H onto K , A is a strongly positive linear bounded self-adjoint operator, f is a contraction. It is proved that the sequence { x n } generated by the above iterative algorithm converges strongly to a fixed point of T , which solves a variational inequality related...

Strong convergence of an iterative method for variational inequality problems and fixed point problems

Xiao Long QinShin Min KangYong Fu SuMei Juan Shang — 2009

Archivum Mathematicum

In this paper, we introduce a general iterative scheme to investigate the problem of finding a common element of the fixed point set of a strict pseudocontraction and the solution set of a variational inequality problem for a relaxed cocoercive mapping by viscosity approximate methods. Strong convergence theorems are established in a real Hilbert space.

Coincidence point theorems in certain topological spaces

Jong Soo JungYeol Je ChoShin Min KangYong Kab ChoiByung 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 JungYeol Je ChoShin Min KangByung-Soo LeeBalwant 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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