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A NEW ITERATION SCHEME FOR A HYBRID PAIR OF NONEXPANSIVE MAPPINGS
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  • Journal title : Honam Mathematical Journal
  • Volume 38, Issue 1,  2016, pp.127-139
  • Publisher : The Honam Mathematical Society
  • DOI : 10.5831/HMJ.2016.38.1.127
 Title & Authors
A NEW ITERATION SCHEME FOR A HYBRID PAIR OF NONEXPANSIVE MAPPINGS
Uddin, Izhar; Imdad, Mohammad;
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 Abstract
In this paper, we construct an iteration scheme involving a hybrid pair of nonexpansive mappings and utilize the same to prove some convergence theorems. In process, we remove a restricted condition (called end-point condition) in Sokhuma and Kaewkhao`s results [Sokhuma and Kaewkhao, Fixed Point Theory Appl. 2010, Art. ID 618767, 9 pp.].
 Keywords
Banach spaces;Fixed point;Nonexpansive mapping;
 Language
English
 Cited by
 References
1.
E. Picard, Memoire sur la theorie des equations aux derivees partielles et la methode des approximations successives, J. Math. Pures et Appl.,6, (1890), 145-210.

2.
W.R. Mann,Mean value methods in iterations, Proc. Amer. Math. Soc., 4 (1953), 506-510. crossref(new window)

3.
S. Ishikawa,Fixed points by a new iteration method, Proc. Amer. Math. Soc., 44 (1974), 147-150. crossref(new window)

4.
B. E. Rhoades,Comments on two fixed point iteration methods, J. Math. Anal. Appl. 56 (1976), 741-750. crossref(new window)

5.
S. B. Nadler Jr.,Multivalued contraction mappings, Pacific J Math. 30, (1969), 475-488. crossref(new window)

6.
J. T. Markin,Continuous dependence of fixed point sets, Proc. Amer. Math. Soc., 38,(1973), 545-547. crossref(new window)

7.
L. Gorniewicz, Topological fixed point theory of multivalued mappings, Kluwer Academic Pub., Dordrecht, Netherlands, (1999).

8.
T. C. Lim,A fixed point theorem for multivalued nonexpansive mappings in a uniformly convex Banach spaces, Bull. Amer. Math. Soc. 80, (1974), 1123-1126. crossref(new window)

9.
K.P.R. Sastry and G.V.R. Babu, Convergence of Ishikawa iterates for a multi-valued mapping with a fixed point, Czechoslovak Math. J. 55, (2005), 817-826. crossref(new window)

10.
B. Panyanak, Mann and Ishikawa iterative processes for multivalued mappings in Banach spaces, Comput. Math. Appl. 54, (2007), 872-877. crossref(new window)

11.
Y. Song and H. Wang, Convergence of iterative algorithms for multivalued mappings in Banach spaces, Nonlinear Anal. 70, (2009), 1547-1556. crossref(new window)

12.
N. Shahzad and H. Zegeye, On Mann and Ishikawa iteration schemes for multi-valued maps in Banach spaces, Nonlinear Anal. 71, (2009), 838-844. crossref(new window)

13.
V. Berinde, Iterative Approximation of Fixed Points, Lecture Notes in Mathematics, 1912, Springer, Berlin, 2007.

14.
K. Sokhuma and A. Kaewkhao, Ishikawa iterative process for a pair of single-valued and multivalued nonexpansive mappings in Banach spaces, Fixed Point Theory Appl. Art. ID 618767 (2010).

15.
N. Akkasriworn, K. Sokhuma and K. Chuikamwong, Ishikawa iterative process for a pair of Suzuki generalized nonexpansive single valued and multivalued mappings in Banach spaces, Int. Journal of Math. Analysis, 6 (19), (2012), 923-932.

16.
Izhar Uddin, M. Imdad and Javid Ali, Convergence theorems for a hybrid pair of generalized nonexpansive mappings in Banach spaces, Bull. Malays. Math. Sci. Soc., 38, (2015), 695705 crossref(new window)

17.
K. Sokhuma, Convergence Theorems for a Pair of Asymptotically and Multi-Valued Nonexpansive Mapping in Banach Spaces Int. Journal of Math. Analysis, 7(19), (2013),927-936.

18.
K. Sokhuma, ${\Delta}$-Convergence theorems for a pair of single-valued and multivalued nonexpansive mappings in CAT(0) spaces, Journal of Mathematical Analysis, 4(2), (2013), 23-31.

19.
J. Schu,Weak and strong convergence to fixed points of asymptotically nonexpansive mappings, Bull. Austral. Math. Soc., 43, (1991), 153-159. crossref(new window)

20.
Y. Song and y. J. Cho,Some notes on Ishikawa iteration for multivalued mappings, Bull Korean Math Soc., 48(3), (2011), 575-584. crossref(new window)

21.
S.H. Khan and H. Fukhar-ud-din,Weak and strong convergence of a scheme with errors for two nonexpansive mappings, Nonlinear Anal., 8, (2005), 1295-1301.

22.
H. Fukhar-ud-din and S.H. Khan, Convergence of iterates with errors of asymptotically quasi- nonexpansive mappings and applications, J. Math. Anal. Appl. 328, (2007), 821-829. crossref(new window)

23.
H. F. Senter and W. G. Dotson, Approximatig fixed points of nonexpansive mappings, Proc. Am. Math. Soc. 44(2), (1974), 375-380. crossref(new window)