Convergence analysis of a novel iteration algorithm for solving split feasibility problems
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Authors
Qinwei Fan
- School of Science, Xi’an Polytechnic University, Xi’an, Shaanxi 710048, China.
Abstract
In this paper, our aim is to construct a convergence theorem in Banach spaces via the following Ishikawa recursive algorithm
\[
\begin{cases}
x_{n+1}=(1-\alpha_n)x_n+\alpha_nT_ny_n,\\
y_n=(1-\beta_n)x_n+\beta_nT_nx_n,
\end{cases}
\]
where \(\{\alpha_n\}\), \(\{\beta_n\}\) are sequences in \([0, 1]\) and \(\{T_n\}\) is a sequence of nonexpansive mappings. Moreover, we also apply these results
to solve a split feasibility problem.
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ISRP Style
Qinwei Fan, Convergence analysis of a novel iteration algorithm for solving split feasibility problems, Journal of Nonlinear Sciences and Applications, 10 (2017), no. 2, 647--655
AMA Style
Fan Qinwei, Convergence analysis of a novel iteration algorithm for solving split feasibility problems. J. Nonlinear Sci. Appl. (2017); 10(2):647--655
Chicago/Turabian Style
Fan, Qinwei. "Convergence analysis of a novel iteration algorithm for solving split feasibility problems." Journal of Nonlinear Sciences and Applications, 10, no. 2 (2017): 647--655
Keywords
- Split feasibility problem
- fixed point
- nonexpansive mapping
- weak convergence.
MSC
References
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