Recent Issues

 Volume 50 Volume 49 Volume 48 Volume 47 Volume 46

Past Issues

The Journal

 Vietnam Journal of Mathematics 40:4(2012) 515-525 Viscosity Approximation Method for Lipschitzian Pseudocontraction Semigroups in Banach Spaces Duong Viet Thong Faculty of  Economics Mathematics, National Economics University, 207 Giai Phong, Hai Ba Trung, Hanoi, Vietnam October 27, 2010 April 22, 2012 Abstract. Let E be a real Banach space which admits a weakly sequentially continuous duality mapping from E to E*, and K be a nonempty closed convex subset of E. Let {T(t):t\geq 0} be a Lipschitzian pseudocontractive semigroup on K such that $F:=\underset{t\geq 0}{\cap}\Fix(T(t))\ne \emptyset,$ and $f:K\to K$ be a fixed contractive mapping. When {αn}, {tn} satisfy some appropriate conditions, the iterative process given by xn=αnf(xn)+(1-αn)T(tn)xn              for n \in N, converges strongly to p\in F, which is the unique solution in F to the following variational inequality: <(f-I)p,j(x-p)> ≤ 0   \forall x\in F. Our results presented in this paper extend and improve recent results of R. Chen and H. He [1], Y. Song and R. Chen [8], Xu [13]. 2000 Mathematics Subject Classification. 47H09, 47H10, 47H20. Keywords. Lipschitzian pseudocontraction semigroup, demiclosed principle, common fixed point, Opial's condition, implicit iteration process.

 Established by Vietnam Academy of Science and Technology & Vietnam Mathematical Society Published by Springer since January 2013