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Hybrid iterative algorithm for finite families of countable Bregman quasi-Lipschitz mappings with applications in Banach spaces
- Source :
- Journal of Inequalities and Applications. 2015(1)
- Publisher :
- Springer Nature
-
Abstract
- The purpose of this paper is to introduce and consider a new hybrid shrinking projection method for finding a common element of the set EP of solutions of a generalized equilibrium problem, the common fixed point set F of finite uniformly closed families of countable Bregman quasi-Lipschitz mappings in reflexive Banach spaces. It is proved that under appropriate conditions, the sequence generated by the hybrid shrinking projection method converges strongly to some point in $\mathit{EP} \cap F$ . Relative examples are given. Strong convergence theorems are proved. The application for Bregman asymptotically quasi-nonexpansive mappings is also given. The main innovative points in this paper are as follows: (1) the notion of the uniformly closed family of countable Bregman quasi-Lipschitz mappings is presented and the useful conclusions are given; (2) the relative examples of the uniformly closed family of countable Bregman quasi-Lipschitz mappings are given in classical Banach spaces $l^{2}$ and $L^{2}$ ; (3) the application for Bregman asymptotically quasi-nonexpansive mappings is also given; (4) because the main theorems do not need the boundedness of the domain of mappings, so a corresponding technique for the proof is given. This new results improve and extend the previously known ones in the literature.
Details
- Language :
- English
- ISSN :
- 1029242X
- Volume :
- 2015
- Issue :
- 1
- Database :
- OpenAIRE
- Journal :
- Journal of Inequalities and Applications
- Accession number :
- edsair.doi.dedup.....893d2dce54246c94c154554d57d1df98
- Full Text :
- https://doi.org/10.1186/s13660-015-0731-3