Search

Start Over Creator Jung, Jong Soo

1. Dual convergences of iteration processes for nonexpansive mappings in Banach spaces

Creator:
Jung, Jong Soo and Sahu, Dara Yam
Format:
bez média and svazek
Type:
model:article and TEXT
Subject:
Banach limit, dual convergence theorem, duality mapping, Ishikawa iteration process, and nonexpansive mapping
Language:
English
Description:
In this paper we establish a dual weak convergence theorem for the Ishikawa iteration process for nonexpansive mappings in a reflexive and strictly convex Banach space with a uniformly Gâteaux differentiable norm, and then apply this result to study the problem of the weak convergence of the iteration process.
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