Accelerated hybrid iterative algorithm for common fixed points of a finite families of countable Bregman quasi-Lipschitz mappings and solutions of generalized equilibrium problem with application
Volume 11, Issue 1, pp 108--130
http://dx.doi.org/10.22436/jnsa.011.01.09
Publication Date: December 31, 2017
Submission Date: July 11, 2017
Revision Date: September 06, 2017
Accteptance Date: September 09, 2017
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2002
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Authors
Jingling Zhang
- Department of Mathematics, Tianjin University, Tianjin 300350, P. R. China.
Ravi P. Agarwal
- Department of Mathematics, Texas A&M University-Kingsville, Texas 78363, U. S. A..
Nan Jiang
- Department of Mathematics, Tianjin University, Tianjin 300350, P. R. China.
- School of Mechanical Engineering, Tianjin University, Tianjin 300350, P. R. China.
Abstract
The purpose of this paper is to introduce and consider a new
accelerated hybrid shrinking projection method for finding a
common element of the set \(EP \cap F\) in reflexive Banach spaces,
where \(EP\) is the set of all solutions of a generalized equilibrium problem,
and \(F\) is the common fixed point set of finite uniformly closed families of
countable Bregman quasi-Lipschitz mappings.
It is proved that the sequence generated by the accelerated
hybrid shrinking projection iteration, converges strongly to the
point in \(EP \cap F,\) under some conditions. This result is also
applied to find the fixed point of Bregman asymptotically
quasi-nonexpansive mappings.
It is worth mentioning that, there are multiple projection
points from the multiple points in the projection algorithm.
Therefore the new projection method in this paper can accelerate the convergence
speed of iterative sequence. The new results improve and extend
the previously known ones in the literature.
Share and Cite
ISRP Style
Jingling Zhang, Ravi P. Agarwal, Nan Jiang, Accelerated hybrid iterative algorithm for common fixed points of a finite families of countable Bregman quasi-Lipschitz mappings and solutions of generalized equilibrium problem with application, Journal of Nonlinear Sciences and Applications, 11 (2018), no. 1, 108--130
AMA Style
Zhang Jingling, Agarwal Ravi P., Jiang Nan, Accelerated hybrid iterative algorithm for common fixed points of a finite families of countable Bregman quasi-Lipschitz mappings and solutions of generalized equilibrium problem with application. J. Nonlinear Sci. Appl. (2018); 11(1):108--130
Chicago/Turabian Style
Zhang, Jingling, Agarwal, Ravi P., Jiang, Nan. "Accelerated hybrid iterative algorithm for common fixed points of a finite families of countable Bregman quasi-Lipschitz mappings and solutions of generalized equilibrium problem with application." Journal of Nonlinear Sciences and Applications, 11, no. 1 (2018): 108--130
Keywords
- Bregman distance
- Bregman quasi-Lipschitz mapping
- accelerated hybrid algorithm
- Bregman asymptotically quasi-nonexpansive mappings
- equilibrium problem
MSC
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