Geodesic
CONVERGENCE OF FIXED POINT OF ASYMPTOTICALLY QUASI-NONEXPANSIVE TYPE MAPPINGS IN CONVEX METRIC SPACE
SALUJA, GURUCHARAN SINGH 1
1 Department of Mathematics & Information Technology, Govt. Nagarjun P.G. College of Science, Raipur (C.G.), India.
Journal of nonlinear sciences and its applications, Tome 1 (2008) no. 3, p. 132-144.

Voir la notice de l'article provenant de la source International Scientific Research Publications

In this paper, we give some necessary and sufficient conditions for three-step iterative sequence with errors for asymptotically quasi-nonexpansive type mapping converging to a fixed point in convex metric spaces. The results presented in this paper extend the corresponding results of Kim et al. [9, 10] and many others. Also the corresponding results in [1, 2, 3, 6, 12, 13, 14, 16, 18, 20] are spcial cases of our results.
DOI : 10.22436/jnsa.001.03.02
Classification : 47H05, 47H09, 49M05
Keywords: Asymptotically nonexpansive mapping, asymptotically nonexpansive type mapping, asymptotically quasi-nonexpansive type mapping, convex metric space, fixed point, three-step iterative process with errors.

SALUJA, GURUCHARAN SINGH  1

1 Department of Mathematics & Information Technology, Govt. Nagarjun P.G. College of Science, Raipur (C.G.), India. 
@article{JNSA_2008_1_3_a1,
     author = {SALUJA, GURUCHARAN SINGH },
     title = {CONVERGENCE {OF} {FIXED} {POINT} {OF} {ASYMPTOTICALLY} {QUASI-NONEXPANSIVE} {TYPE} {MAPPINGS} {IN} {CONVEX} {METRIC} {SPACE}},
     journal = {Journal of nonlinear sciences and its applications},
     pages = {132-144},
     publisher = {mathdoc},
     volume = {1},
     number = {3},
     year = {2008},
     doi = {10.22436/jnsa.001.03.02},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.22436/jnsa.001.03.02/}
}
TY  - JOUR
AU  - SALUJA, GURUCHARAN SINGH 
TI  - CONVERGENCE OF FIXED POINT OF ASYMPTOTICALLY QUASI-NONEXPANSIVE TYPE MAPPINGS IN CONVEX METRIC SPACE
JO  - Journal of nonlinear sciences and its applications
PY  - 2008
SP  - 132
EP  - 144
VL  - 1
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.22436/jnsa.001.03.02/
DO  - 10.22436/jnsa.001.03.02
LA  - en
ID  - JNSA_2008_1_3_a1
ER  - 
%0 Journal Article
%A SALUJA, GURUCHARAN SINGH 
%T CONVERGENCE OF FIXED POINT OF ASYMPTOTICALLY QUASI-NONEXPANSIVE TYPE MAPPINGS IN CONVEX METRIC SPACE
%J Journal of nonlinear sciences and its applications
%D 2008
%P 132-144
%V 1
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.22436/jnsa.001.03.02/
%R 10.22436/jnsa.001.03.02
%G en
%F JNSA_2008_1_3_a1
SALUJA, GURUCHARAN SINGH . CONVERGENCE OF FIXED POINT OF ASYMPTOTICALLY QUASI-NONEXPANSIVE TYPE MAPPINGS IN CONVEX METRIC SPACE. Journal of nonlinear sciences and its applications, Tome 1 (2008) no. 3, p. 132-144. doi : 10.22436/jnsa.001.03.02. http://geodesic.mathdoc.fr/articles/10.22436/jnsa.001.03.02/

[1] S. S. Chang Some results for asymptotically pseudo-contractive mapping and asymptotically nonexpansive mappings, Proc. Amer. Math. Soc., Volume 129(3) (2001), pp. 845-853 | DOI

[2] S. S. Chang Iterative approximation problem of fixed points for asymptotically nonexpansive mappings in Banach spaces, Acta Math. Appl. , Volume 24(2) (2001), pp. 236-241

[3] S. S. Chang On the approximating problem of fixed points for asymptotically nonexpansive mappings, Indian J. Pure and Appl., Volume 32(9) (2001), pp. 1-11

[4] Chang, S. S.; Kim, J. K.; Jin, D. S. Iterative sequences with errors for asymptotically quasi- nonexpansive type mappings in convex metric spaces , Archives of Inequality and Applications , Volume 2 (2004), pp. 365-374 | Zbl

[5] Cho, Y. J.; Zhou, H.; G. Guo Weak and strong convergence theorems for three step iterations with errors for asymptotically nonexpansive mappings, Computers and Math. with Appl. , Volume 47 (2004), pp. 707-717 | DOI

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

[7] Glowinski, R.; P. Le Tallec Augmented Lagrangian Operator-Splitting Metods in Non-linear Mechanics, SIAM, Philadelphia , 1989

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

[9] Kim, J. K.; Kim, K. H.; K. S. Kim Convergence theorems of modiied three-step iterative sequences with mixed errors for asymptotically quasi-nonexpansive mappings in Banach spaces, PanAmerican Math. Jour., Volume 14(1) (2004), pp. 45-54

[10] Kim, J. K.; Kim, K. H.; K. S. Kim Three-step iterative sequences with errors for asymptotically quasi-nonexpansive mappings in convex metric spaces , Nonlinear Anal. Convex Anal. RIMS Vol., Volume 1365 (2004), pp. 156-165

[11] W. A. Kirk Fixed point theorems for non-lipschitzian mappings of asymptotically nonexpansive type, Israel J. Math., Volume 17 (1974), pp. 339-346 | DOI

[12] Q. H. Liu Iterative sequences for asymptotically quasi-nonexpansive mappings, J. Math. Anal. Appl. , Volume 259 (2001), pp. 1-7

[13] Liu, Q. H. Iterative sequences for asymptotically quasi-nonexpansive mappings with error member, J. Math. Anal. Appl., Volume 259 (2001), pp. 18-24 | DOI | Zbl

[14] Liu, Q. H. Iterative sequences for asymptotically quasi-nonexpansive mappings with error member of uniformly convex Banach spaces, J. Math. Anal. Appl. , Volume 266 (2002), pp. 468-471 | Zbl | DOI

[15] M. A. Noor New approximation schemes for general variational inequalities, J. Math. Anal. Appl. , Volume 251 (2000), pp. 217-229 | DOI

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

[17] Takahashi, W. A convexity in metric space and nonexpansive mappings I, Kodai Math. Sem. Rep. , Volume 22 (1970), pp. 142-149 | DOI

[18] Xu, B. L.; M. A. Noor Fixed point iterations for asymptotically nonexpansive mappings in Banach spaces, J. Math. Anal. Appl., Volume 267 (2002), pp. 444-453 | DOI

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

[20] Tan, K. K.; H. K. Xu Fixed point iteration processes for asymptotically nonexpansive mappings, Proc. Amer. Math. Soc., Volume 122 (1994), pp. 733-739 | DOI

Cité par Sources :