A result on segmenting Jungck–Mann iterates
Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica, Tome 47 (2008) no. 1, pp. 115-119 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

Voir la notice de l'article

In this paper, following the concepts in [5, 7], we shall establish a convergence result in a uniformly convex Banach space using the Jungck–Mann iteration process introduced by Singh et al [13] and a certain general contractive condition. The authors of [13] established various stability results for a pair of nonself-mappings for both Jungck and Jungck–Mann iteration processes. Our result is a generalization and extension of that of [7] and its corollaries. It is also an improvement on the result of [7].
In this paper, following the concepts in [5, 7], we shall establish a convergence result in a uniformly convex Banach space using the Jungck–Mann iteration process introduced by Singh et al [13] and a certain general contractive condition. The authors of [13] established various stability results for a pair of nonself-mappings for both Jungck and Jungck–Mann iteration processes. Our result is a generalization and extension of that of [7] and its corollaries. It is also an improvement on the result of [7].
Classification : 47H06, 47H10, 47J25
Keywords: Jungck–Mann iteration process; uniformly convex Banach space
@article{AUPO_2008_47_1_a9,
     author = {Olatinwo, Memudu Olaposi},
     title = {A result on segmenting {Jungck{\textendash}Mann} iterates},
     journal = {Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica},
     pages = {115--119},
     year = {2008},
     volume = {47},
     number = {1},
     mrnumber = {2482721},
     zbl = {1181.47069},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/AUPO_2008_47_1_a9/}
}
TY  - JOUR
AU  - Olatinwo, Memudu Olaposi
TI  - A result on segmenting Jungck–Mann iterates
JO  - Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica
PY  - 2008
SP  - 115
EP  - 119
VL  - 47
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/AUPO_2008_47_1_a9/
LA  - en
ID  - AUPO_2008_47_1_a9
ER  - 
%0 Journal Article
%A Olatinwo, Memudu Olaposi
%T A result on segmenting Jungck–Mann iterates
%J Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica
%D 2008
%P 115-119
%V 47
%N 1
%U http://geodesic.mathdoc.fr/item/AUPO_2008_47_1_a9/
%G en
%F AUPO_2008_47_1_a9
Olatinwo, Memudu Olaposi. A result on segmenting Jungck–Mann iterates. Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica, Tome 47 (2008) no. 1, pp. 115-119. http://geodesic.mathdoc.fr/item/AUPO_2008_47_1_a9/

[1] Browder F. E.: Nonexpansive nonlinear operators in a Banach space. Proc. Acad. Sci. 54 (1965), 1041–1044. | MR | Zbl

[2] Browder F. E., Petryshyn W. V.: The solution by iteration of nonlinear functional equations in Banach spaces. Bull. Amer. Math. Soc. 72 (1966), 571–575. | MR | Zbl

[3] Browder F. E., Petryshyn W. V.: Construction of fixed points of nonlinear mappings in a Hilbert space. J. Math. Anal. Appl. 20 (1967), 197–228. | MR

[4] Chidume C. E.: Geometric properties of Banach spaces and nonlinear iterations. The Abdus Salam International Centre for Theoretical Physics, Trieste, Italy, October 2000. | Zbl

[5] Outlaw C., Groetsch C. W.: Averaging iteration in a Banach space. Bull. Amer. Math. Soc. 75 (1969), 430–432. | MR | Zbl

[6] Dotson W. G., Jr.: On the Mann iterative process. Trans. Amer. Math. Soc. 149 (1970), 65–73. | MR | Zbl

[7] Groetsch C. W.: A Note on Segmenting Mann Iterates. J. Math. Anal. Appl. 40 (1972), 369–372. | MR | Zbl

[8] Jungck G.: Commuting mappings and fixed points. Amer. Math. Monthly 83, 4 (1976), 261–263. | MR | Zbl

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

[10] Opial Z.: Weak convergence of the successive approximations for nonexpansive mappings in Banach spaces. Bull. Amer. Math. Soc. 73 (1967), 591–597. | MR

[11] Petryshyn W. V.: Construction of fixed points of demicompact mappings in Hilbert space. J. Math. Anal. Appl. 14 (1966), 276–284. | MR | Zbl

[12] Schaefer H.: Über die Methode Sukzessiver Approximationen. Jahresber. Deutsch. Math. Verein. 59 (1957), 131–140. | MR | Zbl

[13] Singh S. L., Bhatnagar C., Mishra S. N.: Stability of Jungck-type iterative procedures. Internat. J. Math. & Math. Sci. 19 (2005), 3035–3043. | MR | Zbl