An explicit iterative algorithm for \(k\)-strictly pseudo-contractive mappings in Banach spaces


Authors

Qinwei Fan - School of Science, Xi'an Polytechnic University, Xi'an, Shaanxi 710048, China. Xiaoyin Wang - Department of Mathematics, Tianjin Polytechnic University, Tianjin 300387, China.


Abstract

Let \(E\) be a real uniformly smooth Banach space. Let \(K\) be a nonempty bounded closed and convex subset of \(E\). Let \(T : K \rightarrow K\) be a strictly pseudo-contractive map and \(f\) be a contraction on \(K\). Assume \(F(T) := \{x \in K : Tx = x\} \neq\emptyset\). Consider the following iterative algorithm in \(K\) given by \[x_{n+1} = \alpha_nf(x_n) + \beta_nx_n +\gamma_nS_nx_n,\] where \(S_n : K \rightarrow K\) is a mapping defined by \(S_nx := (1 -\delta_n)x + \delta_nTx\). It is proved that the sequence \(\{x_n\}\) generated by the above iterative algorithm converges strongly to a fixed point of \(T\). Our results mainly extend and improve the results of [C. O. Chidume, G. De Souza, Nonlinear Anal., 69 (2008), 2286-2292] and [J. Balooee, Y. J. Cho, M. Roohi, Numer. Funct. Anal. Optim., 37 (2016), 284-303].


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ISRP Style

Qinwei Fan, Xiaoyin Wang, An explicit iterative algorithm for \(k\)-strictly pseudo-contractive mappings in Banach spaces, Journal of Nonlinear Sciences and Applications, 9 (2016), no. 7, 5021--5028

AMA Style

Fan Qinwei, Wang Xiaoyin, An explicit iterative algorithm for \(k\)-strictly pseudo-contractive mappings in Banach spaces. J. Nonlinear Sci. Appl. (2016); 9(7):5021--5028

Chicago/Turabian Style

Fan, Qinwei, Wang, Xiaoyin. "An explicit iterative algorithm for \(k\)-strictly pseudo-contractive mappings in Banach spaces." Journal of Nonlinear Sciences and Applications, 9, no. 7 (2016): 5021--5028


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