Geodesic
CONVERGENCE THEOREMS OF A SCHEME WITH ERRORS FOR I-ASYMPTOTICALLY QUASI-NONEXPANSIVE MAPPINGS :
TEMIR, SEYIT 1
1 Department of Mathematics, Art and Science Faculty, Harran University, 63200, Sanliurfa, Turkey
Journal of nonlinear sciences and its applications, Tome 3 (2010) no. 3, p. 222-233 Cet article a éte moissonné depuis la source International Scientific Research Publications

Voir la notice de l'article

In this paper, we prove weak and strong convergence of the Ishikawa iterative scheme with errors to common fixed point I-asymptotically quasi- nonexpansive mappings in a Banach space. The results obtained in this paper improve and generalize the corresponding results in the existing literature.

DOI : 10.22436/jnsa.003.03.08
Classification : 47H09, 47H10
Keywords: I-asymptotically quasi-nonexpansive mapping, Ishikawa iterative schemes, convergence theorems.

TEMIR, SEYIT  1

1 Department of Mathematics, Art and Science Faculty, Harran University, 63200, Sanliurfa, Turkey 
@article{10_22436_jnsa_003_03_08,
     author = {TEMIR, SEYIT},
     title = {  CONVERGENCE {THEOREMS} {OF} {A} {SCHEME} {WITH} {ERRORS} {FOR} {I-ASYMPTOTICALLY} {QUASI-NONEXPANSIVE} {MAPPINGS}},
     journal = {Journal of nonlinear sciences and its applications},
     pages = {222-233},
     year = {2010},
     volume = {3},
     number = {3},
     doi = {10.22436/jnsa.003.03.08},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.22436/jnsa.003.03.08/}
}
TY  - JOUR
AU  - TEMIR, SEYIT
TI  - CONVERGENCE THEOREMS OF A SCHEME WITH ERRORS FOR I-ASYMPTOTICALLY QUASI-NONEXPANSIVE MAPPINGS
JO  - Journal of nonlinear sciences and its applications
PY  - 2010
SP  - 222
EP  - 233
VL  - 3
IS  - 3
UR  - http://geodesic.mathdoc.fr/articles/10.22436/jnsa.003.03.08/
DO  - 10.22436/jnsa.003.03.08
LA  - en
ID  - 10_22436_jnsa_003_03_08
ER  - 
%0 Journal Article
%A TEMIR, SEYIT
%T CONVERGENCE THEOREMS OF A SCHEME WITH ERRORS FOR I-ASYMPTOTICALLY QUASI-NONEXPANSIVE MAPPINGS
%J Journal of nonlinear sciences and its applications
%D 2010
%P 222-233
%V 3
%N 3
%U http://geodesic.mathdoc.fr/articles/10.22436/jnsa.003.03.08/
%R 10.22436/jnsa.003.03.08
%G en
%F 10_22436_jnsa_003_03_08
TEMIR, SEYIT. CONVERGENCE THEOREMS OF A SCHEME WITH ERRORS FOR I-ASYMPTOTICALLY QUASI-NONEXPANSIVE MAPPINGS. Journal of nonlinear sciences and its applications, Tome 3 (2010) no. 3, p. 222-233. doi: 10.22436/jnsa.003.03.08

[1] Ghosh, M. K.; L. Debnath Convergence of Ishikawa iterates of quasi-nonexpansive mappings , J. Math. Anal. Appl. , Volume 207 (1997), pp. 96-103

[2] Goebel, K.; Kirk, W. A. A fixed point theorem for asymptotically nonexpansive mappings, Proc. Amer. Math. Soc., Volume 35 (1972), pp. 171-174

[3] Ishikawa, S. Fixed points by a new iteration method, Proc. Amer. Math. Soc., Volume 44 (1974), pp. 147-150

[4] Lan, H. Y. Common fixed point iterative processes with errors for generalized asymptotically quasi-nonexpansive mappings, Computers and Math. with Applications, Volume 52 (2006), pp. 1403-1412

[5] Liu, Q. H. Iterative sequences for asymptotically quasi-nonexpansive mappings with Error Member, J. Math. Anal. Appl., Volume 259 (2001), pp. 18-24

[6] Opial, Z. Weak convergence of successive approximations for nonexpansive mappings, Bull. Amer. Math. Soc., Volume 73 (1967), pp. 591-597

[7] Petryshyn, W. V.; Williamson, T. E. Strong and weak convergence of the sequence of successive approximations for quasi-nonexpansive mappings, J. Math. Anal. Appl., Volume 43 (1973), pp. 459-497

[8] Rhoades, B. E.; Temir, S. Convergence theorems for I-nonexpansive mapping, IJMMS, Article ID 63435, Volume 2006 (2006), pp. 1-4

[9] Schu, J. Weak and strong convergence to fixed points of asymptotically nonexpansive mappings, Bulletin of the Australian Mathematical Society, Volume 43 (1991), pp. 153-159

[10] Shahzad, N.; Udomene, A. Apprximating common fixed points of two asymptotically quasi-nonexpansive mappings in Banach spaces, Fixed Point Theory and Applications, Article ID18909, Volume 2006 (2006), pp. 1-10

[11] Tan, K. K.; Xu, H. K. Approximating fixed points of nonexpansive mappings by the Ishikawa iterative process, J. Math. Anal. Appl., Volume 178 (1993), pp. 301-308

[12] Temir, S.; Gul, O. Convergence theorem for I-asymptotically quasi-nonexpansive mapping in Hilbert space, J. Math. Anal. Appl., Volume 329 (2007), pp. 759-765

[13] Yao, S. S.; Wang, L. Strong convergence theorems for I-quasi-nonexpansive mappings, Far east J. Math.Sci.(FJMS), Volume 27 (1) (2007), pp. 111-119

Cité par Sources :