CONVERGENCE THEOREMS FOR THE ZEROS OF A FINITE FAMILY OF GENERALIZED ACCRETIVE OPERATORS
-
1772
Downloads
-
3176
Views
Authors
N. GURUDWAN
- School of Studies in Mathematics, Pt. Ravishankar Shukla University Raipur - 492010 (C.G.), India.
B. K. SHARMA
- School of Studies in Mathematics, Pt. Ravishankar Shukla University Raipur - 492010 (C.G.), India.
Abstract
A strong convergence theorem for the common zero for a finite family of Generalized
Lipschitz operators in a uniformly smooth Banach space is proved when atleast one
of the operator is Generalized \(\Phi\)- accretive, using a new iteration formula. Similar result
for Generalized Lipschitz and Generalized \(\Phi\)- pseudocontractive map is also proved. Our
result extends the convergence results of Chidume [4] to a finite family improving many
other results.
Share and Cite
ISRP Style
N. GURUDWAN, B. K. SHARMA, CONVERGENCE THEOREMS FOR THE ZEROS OF A FINITE FAMILY OF GENERALIZED ACCRETIVE OPERATORS, Journal of Nonlinear Sciences and Applications, 2 (2009), no. 4, 260-269
AMA Style
GURUDWAN N., SHARMA B. K., CONVERGENCE THEOREMS FOR THE ZEROS OF A FINITE FAMILY OF GENERALIZED ACCRETIVE OPERATORS. J. Nonlinear Sci. Appl. (2009); 2(4):260-269
Chicago/Turabian Style
GURUDWAN, N., SHARMA, B. K.. "CONVERGENCE THEOREMS FOR THE ZEROS OF A FINITE FAMILY OF GENERALIZED ACCRETIVE OPERATORS." Journal of Nonlinear Sciences and Applications, 2, no. 4 (2009): 260-269
Keywords
- Generalized \(\Phi\)-accretive
- generalized Lipschitz
- uniformly smooth Banach space
- mann iteration.
MSC
References
-
[1]
F. E. Browder, Nonlinear mappings of nonexpansive and accretive type in Banach space, Bull. Amer. Math. Soc., 73 (1967), 875–882
-
[2]
F. E. Browder, W. V. Petryshyn, Construction of fixed points of nonlinear mappings in Hilbert space, J. Math. Anal. Appl.,, 20 (1967), 197–228
-
[3]
S. S. Chang, K. K. Tan, H. W. J. Lee, C. K. Chan, On the convergnce of implicit iteration process wih error for a finite family of asymptotically nonexpansive mappings, J. Math. Anal. Appl., 313 (2006), 273–283
-
[4]
C. E. Chidume, C. O. Chidume, Convergence theorems for zeros of generalized Lipschitz generalized \(\Phi\)-quasi accretive operators, Proc. Amer. Math. Soc., 134 (2006), 243–251
-
[5]
H. Hirano, Z. Huang, Convergence theorems for multi-valued \(\phi\)-hemicontractive operators and - strongly accretive operators, Comp. Math. Appl., 46 (2003), 1461–1471
-
[6]
J. S. Jung, Iterative approaches to common fixed points of nonexpansive mappings in Banach spaces, J. Math. Anal. Appl., 302 (2005), 509–520
-
[7]
R. De Marr, Common fixed points for commuting contraction mappings, Pacific J. Math., 53 (1974), 487–493
-
[8]
A. Markov, Quelques theorems sur les ensembles abeliens, , Dokl. Akad. Nauk. SSSR (N.S.)., 10 (1936), 311–314
-
[9]
W. V. Petryshyn, A characterization of strict convexity of Banach spaces and other uses of duality mappings, J. Func. Anal., 6 (1970), 282–291
-
[10]
Z. Sun, Strong convergence of an implicit ieration process for a finite family of asymptotically quasinonexpansive mappings, J. Math. Anal. Appl., 286 (2003), 351–358
-
[11]
Y. Xu, Ishikawa and Mann iterative processses with erors for nonlinear strongly accretive operator equations, J. Math. Anal. Appl., 224 (1998), 91–101
-
[12]
L. C. Zhao, S. S. Chang , Strong convergence theorems for equilibrium problems and fixed point problems, J. Nonlinear Sci. Appl., 2 (2009), 78–91
-
[13]
H. Zhou, L. Wei, Y. J. Cho , Strong convrgence theorems on an iteraive method for family of finite nonexpansive mappings in reflexive Banach spaces, Appl. Math. Comput., 173 (2006), 196–212