Semi-implicit iterative schemes with perturbed operators for infinite accretive mappings and infinite nonexpansive mappings and their applications to parabolic systems
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Authors
Li Wei
- School of Mathematics and Statistics, Hebei University of Economics and Business, Shijiazhuang 050061, Hebei, China.
Ravi P. Agarwal
- Department of Mathematics, Texas A & M University-Kingsville, Kingsville, TX78363, USA.
- Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah, 21589, Saudi Arabia.
Yaqin Zheng
- College of Science, Agricultural University of Hebei, Baoding 071001, Hebei, China.
Abstract
In a real uniformly convex and uniformly smooth Banach space, we first prove a new path convergence theorem and
then present some new semi-implicit iterative schemes with errors which are proved to be convergent strongly to the common
element of the set of zero points of infinite m-accretive mappings and the set of fixed points of infinite nonexpansive mappings.
The superposition of perturbed operators are considered in the construction of the iterative schemes and new proof techniques
are employed compared to some of the recent work. Some examples are listed and computational experiments are conducted,
which guarantee the effectiveness of the proposed iterative schemes. Moreover, a kind of parabolic systems is exemplified, which
sets up the relationship among iterative schemes, nonlinear systems and variational inequalities.
Share and Cite
ISRP Style
Li Wei, Ravi P. Agarwal, Yaqin Zheng, Semi-implicit iterative schemes with perturbed operators for infinite accretive mappings and infinite nonexpansive mappings and their applications to parabolic systems, Journal of Nonlinear Sciences and Applications, 10 (2017), no. 3, 902--921
AMA Style
Wei Li, Agarwal Ravi P., Zheng Yaqin, Semi-implicit iterative schemes with perturbed operators for infinite accretive mappings and infinite nonexpansive mappings and their applications to parabolic systems. J. Nonlinear Sci. Appl. (2017); 10(3):902--921
Chicago/Turabian Style
Wei, Li, Agarwal, Ravi P., Zheng, Yaqin. "Semi-implicit iterative schemes with perturbed operators for infinite accretive mappings and infinite nonexpansive mappings and their applications to parabolic systems." Journal of Nonlinear Sciences and Applications, 10, no. 3 (2017): 902--921
Keywords
- M-accretive mapping
- \(\tau_i\)-strongly accretive mapping
- contractive mapping
- \(\lambda_i\)-strictly pseudocontractive mapping
- semi-implicit iterative scheme
- parabolic systems.
MSC
References
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