Convergence theorems for mixed type asymptotically nonexpansive mappings in the intermediate sense
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Authors
Gurucharan S. Saluja
- Department of Mathematics, Govt. N. P. G. College of Science, Raipur-492010 (C. G.), India.
Mihai Postolache
- China Medical University, No.91, Hsueh-Shih Road, Taichung, Taiwan.
- Department of Mathematics & Informatics, University "Politehnica" of Bucharest, Splaiul Independentei 313, Bucharest 060042, Romania.
Adrian Ghiura
- Department of Mathematics & Informatics, University , Splaiul Independentei 313, Bucharest 060042, Romania.
Abstract
We provide a new two-step iteration scheme of mixed type for two asymptotically nonexpansive self
mappings in the intermediate sense and two asymptotically nonexpansive non-self mappings in the intermediate sense and establish some strong and weak convergence theorems for mentioned scheme and mappings
in uniformly convex Banach spaces. Our results extend and generalize the corresponding results of Chidume
et al. [C. E. Chidume, E. U. Ofoedu, H. Zegeye, J. Math. Anal. Appl., 280 (2003), 364-374] and [C. E.
Chidume, N. Shahzad, H. Zegeye, Numer. Funct. Anal. Optim., 25 (2004), 239-257], Guo et al. [W. Guo,
W. Guo, Appl. Math. Lett., 24 (2011), 2181-2185] and [W. Guo, Y. J. Cho, W. Guo, Fixed Point Theory
Appl., 2012 (2012), 15 pages], Saluja [G. S. Saluja, J. Indian Math. Soc. (N.S.), 81 (2014), 369-385], Schu
[J. Schu, Bull. Austral. Math. Soc., 43 (1991), 153-159], Tan and Xu [K. K. Tan, H. K. Xu, J. Math. Anal.
Appl., 178 (1993), 301-308], Wang [L. Wang, J. Math. Anal. Appl., 323 (2006), 550-557], Wei and Guo
[S. I. Wei, W. Guo, Commun. Math. Res., 31 (2015), 149-160] and [S. Wei, W. Guo, J. Math. Study, 48
(2015), 256-264].
Share and Cite
ISRP Style
Gurucharan S. Saluja, Mihai Postolache, Adrian Ghiura, Convergence theorems for mixed type asymptotically nonexpansive mappings in the intermediate sense, Journal of Nonlinear Sciences and Applications, 9 (2016), no. 7, 5119--5135
AMA Style
Saluja Gurucharan S., Postolache Mihai, Ghiura Adrian, Convergence theorems for mixed type asymptotically nonexpansive mappings in the intermediate sense. J. Nonlinear Sci. Appl. (2016); 9(7):5119--5135
Chicago/Turabian Style
Saluja, Gurucharan S., Postolache, Mihai, Ghiura, Adrian. "Convergence theorems for mixed type asymptotically nonexpansive mappings in the intermediate sense." Journal of Nonlinear Sciences and Applications, 9, no. 7 (2016): 5119--5135
Keywords
- Asymptotically nonexpansive self and non-self mapping in intermediate sense
- new two-step iteration scheme of mixed type
- common fixed point
- uniformly convex Banach space
- strong convergence
- weak convergence.
MSC
References
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