%0 Journal Article
%T Strong Convergence of modified Halpern's iterations for $k$-strictly pseudocontractive mapping
%A Suhong Li
%A Lihua Li
%A Lingmin Zhang and xiujuan He
%J Journal of Inequalities and Applications
%D 2013
%I 
%R 10.1186/1029-242X-2013-98
%X In this paper, we discuss three modified Halpern's iterations as follows: $$ x_{n+1}=\alpha_nu+(1-\alpha_n)((1-\delta)x_n+\delta Tx_n) \eqno{(I)}$$ $$ x_{n+1}=\alpha_n((1-\delta)u+\delta x_n)+(1-\alpha_n)Tx_n, \eqno{(II)}$$ $$ x_{n+1}=\alpha_nu+\beta_nx_n+\gamma_nTx_n, n\geq 0, \eqno{(III)}$$ and obtained the strong convergence results of the iterations (I)-(III) for $k$-strictly pseudocontractive mapping , where $\{\alpha_n\}$ satisfies the conditions:\\ (C1)$\lim_{n\rightarrow\infty}\alpha_n=0$ and (C2)$\sum_{n=1}^\infty\alpha_n=+\infty$, respectively. The results presented in this work improve on the corresponding ones announced by many others.
%U http://www.journalofinequalitiesandapplications.com/content/2013/1/98/abstract