Weak convergence theorems for two asymptotically quasi-nonexpansive non-self mappings in uniformly convex Banach spaces
-
1538
Downloads
-
2362
Views
Authors
G. S. Saluja
- Department of Mathematics and I.T., Govt. N.P.G. College of Science, Raipur (C.G.), India.
Abstract
The purpose of this paper is to establish some weak convergence theorems of modified two-step iteration
process with errors for two asymptotically quasi-nonexpansive non-self mappings in the setting of real
uniformly convex Banach spaces if E satisfies Opial's condition or the dual \(E^*\) of \(E\) has the Kedec-Klee
property. Our results extend and improve some known corresponding results from the existing literature.
Share and Cite
ISRP Style
G. S. Saluja, Weak convergence theorems for two asymptotically quasi-nonexpansive non-self mappings in uniformly convex Banach spaces, Journal of Nonlinear Sciences and Applications, 7 (2014), no. 2, 138--149
AMA Style
Saluja G. S., Weak convergence theorems for two asymptotically quasi-nonexpansive non-self mappings in uniformly convex Banach spaces. J. Nonlinear Sci. Appl. (2014); 7(2):138--149
Chicago/Turabian Style
Saluja, G. S.. "Weak convergence theorems for two asymptotically quasi-nonexpansive non-self mappings in uniformly convex Banach spaces." Journal of Nonlinear Sciences and Applications, 7, no. 2 (2014): 138--149
Keywords
- Asymptotically quasi-nonexpansive non-self mappings
- common fixed point
- the modified two-step iteration process with errors for non-self maps
- uniformly convex Banach space
- weak convergence.
MSC
References
-
[1]
S. C. Bose , Weak convergence to a fixed point of an asymptotically nonexpansive mappings, Proc. Amer. Math. Soc., 68 (1978), 305-308.
-
[2]
S. S. Chang, Y. J. Cho, H. Zhou, Demi-closed principle and weak convergence problems for asymptotically nonexpansive mappings, J. Korean Math. Soc., 38:6 (2001), 1245-1260.
-
[3]
C. E. Chidume, On the approximation of fixed points of nonexpansive mappings, Houston J. Math., 7 (1981), 345-355.
-
[4]
C. E. Chidume , Nonexpansive mappings, generalizations and iterative algorithms, In: Agarwal R.P., O'Reagan D.eds. Nonlinear Analysis and Application. To V. Lakshmikantam on his 80th Birthday (Research Monograph), Dordrecht: Kluwer Academic Publishers, (), 383-430.
-
[5]
C. E. Chidume, E. U. Ofoedu, H. Zegeye , Strong and weak convergence theorems for asymptotically nonexpansive mappings, J. Math. Anal. Appl., 280 (2003), 364-374.
-
[6]
C. E. Chidume, N. Shahzad, H. Zegeye, Convergence theorems for mappings which are asymptotically nonexpansive in the intermediate sense, Numer. Funct. Anal. Optimiz., 25:3-4 (2004), 239-257.
-
[7]
C. E. Chidume, N. Shahzad, H. Zegeye, Strong convergence theorems for nonexpansive mappings in arbitrary Banach spaces, Nonlinear Anal. , (Submitted),
-
[8]
K. Goebel, W. A. Kirk, A fixed point theorem for asymptotically nonexpansive mappings, Proc. Amer. Math. Soc., 35 (1972), 171-174.
-
[9]
S. Ishikawa, Fixed points by a new iteration method, Proc. Amer. Math. Soc., 44 (1974), 147-150.
-
[10]
S. Ishikawa, Fixed points and iteration of a nonexpansive mapping in a Banach space, Proc. Amer. Math. Soc., 59 (1976), 65-71.
-
[11]
W. Kaczor , Weak convergence of almost orbits of asymptotically nonexpansive commutative semigroups, J. Mathematical Analysis and Applications, 272:2 (2002), 565-574.
-
[12]
S. H. Khan, W. Takahashi, Approximating common fixed points of two asymptotically nonexpansive mappings, Sci. Math. Jpn., 53 (2001), 143-148.
-
[13]
W. R. Mann , Mean value methods in iteration , Proc. Amer. Math. Soc. , 4 (1953), 506-510.
-
[14]
Z. Opial, Weak convergence of the sequence of successive approximatins for nonexpansive mappings , Bull. Amer. Math. Soc., 73 (1967), 591-597.
-
[15]
M. O. Osilike, S. C. Aniagbosor, Weak and strong convergence theorems for fixed points of asymptotically nonexpansive mappings, Math. Comput. Modelling, 32 (2000), 1181-1191.
-
[16]
G. B. Passty , Construction of fixed points for asymptotically nonexpansive mappings, Proc. Amer. Math. Soc., 84 (1982), 212-216.
-
[17]
S. Reich, Weak convergence theorems for nonexpansive mappings in Banach spaces, J. Math. Anal. Appl., 67 (1979), 274-276.
-
[18]
B. E. Rhoades , Fixed point iteration for certain nonlinear mappings, J. Math. Anal. Appl., 183 (1994), 118-120.
-
[19]
G. S. Saluja, Convergence of fixed point of asymptotically quasi-nonexpansive type mappings in convex metric spaces, J. Nonlinear Sci. Appl., 1:3 (2008), 132-144.
-
[20]
J. Schu, Iterative construction of fixed points of asymptotically nonexpansive mappings , J. Math. Anal. Appl., 158 (1991), 407-413.
-
[21]
J. Schu, Weak and strong convergence theorems to fixed points of asymptotically nonexpansive mappings, Bull. Austral. Math. Soc., 43 (1991), 153-159.
-
[22]
K. K. Tan, H. K. Xu, A nonlinear ergodic theorem for asymptotically nonexpansive mappings, Bull. Austral. Math. Soc., 45 (1992), 25-36.
-
[23]
K. K. Tan, H. K. Xu, The nonlinear ergodic theorem for asymptotically nonexpansive mapping in Banach spaces, Proc. Amer. Math. Soc., 114 (1992), 399-404.
-
[24]
K. . Tan, H. K. Xu , Approximating fixed points of nonexpansive mappings by the Ishikawa iteration process, J. Math. Anal. Appl., 178 (1993), 301-308.
-
[25]
K. K. Tan, H. K. Xu, Fixed point iteration processes for asymptotically nonexpansive mappings , Proc. Amer. Math. Soc., 122 (1994), 733-739.
-
[26]
T. Thianwan, Convergence criteria of modified Noor iterations with errors for three asymptotically nonexpansive non-self mappings , J. Nonlinear Sci. Appl., 6:3 (2013), 181-197.
-
[27]
H. K. Xu, Existence and convergence for fixed points of mappings of asymptotically nonexpansive type, Nonlinear Analysis, 16 (1991), 1139-1146.
-
[28]
Y. Xu , Ishikawa and Mann iterative processes with errors for nonlinear strongly accretive operator equations, J. Math. Anal. Appl., 224 (1998), 91-101.