ZHENHUA HE - Department of Mathematics, Honghe university, Mengzi, Yunnan, 661100, China.. CAN CHEN - Department of Mathematics, Honghe university, Mengzi, Yunnan, 661100, China.. FENG GU - Department of Mathematics, Hangzhou normal university, Zhejiang, 310036, China..
Let \(E\) be a real reflexive Banach space which has uniformly Gâteaux differentiable norm. Let \(K\) be aclosed convex subset of \(E\) which is also a sunny nonexpansive retract of \(E\), and \(T : K \rightarrow E\) be nonexpansive mapping satisfying the weakly inward condition and \(F(T) = \{x \in K, Tx = x\} \neq\emptyset\), and \(f : K \rightarrow K\) be a contractive mapping. Suppose that \(x_0 \in K,\quad \{x_n\}\) is defined by \[ \begin{cases} x_{n+1} = \alpha_nf(x_n) + (1 - \alpha_n)((1 - \delta)x_n + \delta y_n)\\ y_n = P(\beta_nx_n + (1 - \beta_n)Tx_n),\quad n \geq 0, \end{cases} \] where \(\delta \in (0; 1), \alpha_n, \beta_n \in [0; 1], P\) is sunny nonexpansive retractive from \(E\) into \(K\). Under appropriate conditions, it is shown that \(\{x_n\}\) converges strongly to a fixed point \(T\) and the fixed point solutes some variational inequalities. The results in this paper extend and improve the corresponding results of [2] and some others.
ZHENHUA HE, CAN CHEN, FENG GU, VISCOSITY APPROXIMATION METHOD FOR NONEXPANSIVE NONSELF-MAPPING AND VARIATIONAL INEQUALITY, Journal of Nonlinear Sciences and Applications, 1 (2008), no. 3, 169-178
HE ZHENHUA, CHEN CAN, GU FENG, VISCOSITY APPROXIMATION METHOD FOR NONEXPANSIVE NONSELF-MAPPING AND VARIATIONAL INEQUALITY. J. Nonlinear Sci. Appl. (2008); 1(3):169-178
HE, ZHENHUA, CHEN , CAN, GU, FENG. "VISCOSITY APPROXIMATION METHOD FOR NONEXPANSIVE NONSELF-MAPPING AND VARIATIONAL INEQUALITY." Journal of Nonlinear Sciences and Applications, 1, no. 3 (2008): 169-178
