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Start Over Creator Kang, Shin Min

1. Coincidence and fixed point theorems for nonlinear hybrid generalized contractions

Creator:
Pathak, H. K., Kang, Shin Min, and Cho, Yeol Je
Format:
bez média and svazek
Type:
model:article and TEXT
Subject:
weakly commuting, compatible and weakly compatible mappings, asymptotically regular sequence, coincidence point and fixed point, and Kannan mapping
Language:
English
Description:
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.
Rights:
http://creativecommons.org/publicdomain/mark/1.0/ and policy:public

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

Creator:
Jung, Jong Soo, Cho, Yeol Je, Kang, Shin Min, Lee, Byung Soo, and Thakur, Balwant Singh
Format:
bez média and svazek
Type:
model:article and TEXT
Subject:
$p$-uniformly convex Banach space, normal structure, asymptotic center, random fixed points, and generalized random uniformly Lipschitzian mapping
Language:
English
Description:
Let $(\Omega,\Sigma)$ 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 $T\: \Omega \times C \rightarrow C$ satisfying: for each $x, y \in C$, $\omega \in \Omega $ and integer $n \ge 1$, \[\Vert T^n(\omega , x) - T^n(\omega , y) \Vert \le a(\omega )\cdot \Vert x - y \Vert + b(\omega )\lbrace \Vert x - T^n(\omega ,x) \Vert + \Vert y - T^n(\omega ,y) \Vert \rbrace + c(\omega )\lbrace \Vert x - T^n(\omega ,y) \Vert + \Vert y - T^n(\omega ,x) \Vert \rbrace , \] where $a,b,c\: \Omega \rightarrow [0, \infty )$ are functions satisfying certain conditions and $T^n(\omega ,x)$ is the value at $x$ of the $n$-th iterate of the mapping $T(\omega ,\cdot )$. 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} $ for $1 < p < \infty $ and $k \ge 0$. As a consequence of our main result, we also extend the results of Xu [43] and randomize the corresponding deterministic ones of Casini and Maluta [5], Goebel and Kirk [13], Tan and Xu [37], and Xu [39, 41].
Rights:
http://creativecommons.org/publicdomain/mark/1.0/ and policy:public

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

Creator:
Qin, Xiaolong, Kang, Shin Min, and Shang, Meijuan
Format:
bez média and svazek
Type:
model:article and TEXT
Subject:
Hilbert space, nonexpansive mapping, strict pseudo-contraction, iterative algorithm, and fixed point
Language:
English
Description:
Let $K$ be a nonempty closed convex subset of a real Hilbert space $H$ such that $K\pm K\subset K$, $T\: K\rightarrow H$ a $k$-strict pseudo-contraction for some $0\leq k<1$ such that $F(T)=\{x\in K\: x=Tx\}\neq \emptyset $. Consider the following iterative algorithm given by $$ \forall x_1\in K,\quad x_{n+1}=\alpha _n\gamma f(x_n)+\beta _nx_n+((1-\beta _n)I-\alpha _n A)P_KSx_n,\quad n\geq 1, $$ where $S\: K\rightarrow H$ is defined by $Sx=kx+(1-k)Tx$, $P_K$ 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 to the linear operator $A$. Our results improve and extend the results announced by many others.
Rights:
http://creativecommons.org/publicdomain/mark/1.0/ and policy:public