Geodesic
A~double-sequence random iteration process for random fixed points of contractive type random operators
Lobachevskii journal of mathematics, Tome 14 (2004), pp. 33-38.

Voir la notice de l'article provenant de la source Math-Net.Ru

In this paper, we introduce the concept of a Mann-type double-sequence random iteration scheme and show that if it is strongly convergent then it converges to a random fixed point of continuous contractive type random operators. The iteration is a random version of double-sequence iteration introduced by Moore (Comput. Math. Appl. 43(2002), 1585–1589).
Keywords: Double-sequence iteration, Mann iteration, Strong convergence, Random Fixed point, Contractive mapping. 
@article{LJM_2004_14_a3,
     author = {G. Mustafa},
     title = {A~double-sequence random iteration process for random fixed points of contractive type random operators},
     journal = {Lobachevskii journal of mathematics},
     pages = {33--38},
     publisher = {mathdoc},
     volume = {14},
     year = {2004},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/LJM_2004_14_a3/}
}
TY  - JOUR
AU  - G. Mustafa
TI  - A~double-sequence random iteration process for random fixed points of contractive type random operators
JO  - Lobachevskii journal of mathematics
PY  - 2004
SP  - 33
EP  - 38
VL  - 14
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/LJM_2004_14_a3/
LA  - en
ID  - LJM_2004_14_a3
ER  - 
%0 Journal Article
%A G. Mustafa
%T A~double-sequence random iteration process for random fixed points of contractive type random operators
%J Lobachevskii journal of mathematics
%D 2004
%P 33-38
%V 14
%I mathdoc
%U http://geodesic.mathdoc.fr/item/LJM_2004_14_a3/
%G en
%F LJM_2004_14_a3
G. Mustafa. A~double-sequence random iteration process for random fixed points of contractive type random operators. Lobachevskii journal of mathematics, Tome 14 (2004), pp. 33-38. http://geodesic.mathdoc.fr/item/LJM_2004_14_a3/

[1] R. E. Bruck, “The iteration solution of the equation $y\in x+Tx$ for a monotone operator $T$ in Hilbert spaces”, Bull. Amer. Math. Soc., 79 (1973), 1259–1262 | DOI | MR

[2] Beg and Shahzad N, “Random fixed point theorems for nonexpansive and contractive type random opeartors on Banach spaces”, J. Appl. Math. Stoc. Anal., 7 (1994), 569–580 | DOI | MR | Zbl

[3] C. E. Chidume and C. Moore, “Fixed point iteration for pseudocontractive maps”, Proc. Amer. Math. Soc., 127 (1999), 1163–1170 | DOI | MR | Zbl

[4] B. S. Choudhury, “Convergence of a random iteration scheme to a random fixed point”, J. Appl. Math. Stoc. Anal., 8 (1995), 139–142 | DOI | MR | Zbl

[5] J. A. Park, “Mann-iteration process for the fixed point of strictly pseudocontractive mappings in some Banach spaces”, J. Korean Soc., 31 (1994), 333–337 | MR | Zbl

[6] S. Ishikawa, “Fixed points by a new iteration method”, Proc. Amer. Math. Soc., 44 (1974), 147–150 | DOI | MR | Zbl

[7] Bharucha-Reid A T, “Fixed point theorems in probabilistic analysis”, Bull. Amer. Math. Soc., 82 (1976), 641–645 | DOI | MR

[8] C. Moore, “A double-sequence iteration process for fixed points of continuous pseudoconstructions”, Comput. Math. Appl., 43 (2002), 1585–1589 | DOI | MR | Zbl

[9] W. R. Mann, “Mean value methods in iteration”, Proc. Amer. Math. Soc., 4 (1953), 506–510 | DOI | MR | Zbl

[10] Adrian Constantin, “A random fixed point theorem for multifunctions”, Stoch. Anal. Appl., 12 (1994), 65–73 | DOI | MR | Zbl

[11] G. Mustafa, “Some random coincidence and random fixed point theorems for non-self hybrid contractions”, Lobachevskii J. Math., 18 (2005), 139–149 | MR | Zbl

[12] C. J. Himmelberg, “Measurable relations”, Fund. Math., 87 (1975), 53–72 | MR | Zbl

[13] B. E. Rhoades, “Fixed point iterations for certain nonlinear mappings”, J. Math. Anal. Appl., 183 (1994), 118–120 | DOI | MR | Zbl