Title:
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A result on segmenting Jungck–Mann iterates (English) |
Author:
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Olatinwo, Memudu Olaposi |
Language:
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English |
Journal:
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Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica |
ISSN:
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0231-9721 |
Volume:
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47 |
Issue:
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1 |
Year:
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2008 |
Pages:
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115-119 |
Summary lang:
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English |
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Category:
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math |
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Summary:
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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]. (English) |
Keyword:
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Jungck–Mann iteration process |
Keyword:
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uniformly convex Banach space |
MSC:
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47H06 |
MSC:
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47H10 |
MSC:
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47J25 |
idZBL:
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Zbl 1181.47069 |
idMR:
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MR2482721 |
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Date available:
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2009-08-27T11:28:20Z |
Last updated:
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2012-05-04 |
Stable URL:
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http://hdl.handle.net/10338.dmlcz/133407 |
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Reference:
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[1] Browder F. E.: Nonexpansive nonlinear operators in a Banach space.Proc. Acad. Sci. 54 (1965), 1041–1044. Zbl 0128.35801, MR 0187120 |
Reference:
|
[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. Zbl 0138.08202, MR 0190745 |
Reference:
|
[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 0217658 |
Reference:
|
[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 1167.47002 |
Reference:
|
[5] Outlaw C., Groetsch C. W.: Averaging iteration in a Banach space.Bull. Amer. Math. Soc. 75 (1969), 430–432. Zbl 0199.44903, MR 0239478 |
Reference:
|
[6] Dotson W. G., Jr.: On the Mann iterative process.Trans. Amer. Math. Soc. 149 (1970), 65–73. Zbl 0203.14801, MR 0257828 |
Reference:
|
[7] Groetsch C. W.: A Note on Segmenting Mann Iterates.J. Math. Anal. Appl. 40 (1972), 369–372. Zbl 0244.47042, MR 0341204 |
Reference:
|
[8] Jungck G.: Commuting mappings and fixed points.Amer. Math. Monthly 83, 4 (1976), 261–263. Zbl 0321.54025, MR 0400196 |
Reference:
|
[9] Mann W. R.: Mean value methods in iteration.Proc. Amer. Math. Soc. 4 (1953), 506–510. Zbl 0050.11603, MR 0054846 |
Reference:
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[10] Opial Z.: Weak convergence of the successive approximations for nonexpansive mappings in Banach spaces.Bull. Amer. Math. Soc. 73 (1967), 591–597. MR 0211301 |
Reference:
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[11] Petryshyn W. V.: Construction of fixed points of demicompact mappings in Hilbert space.J. Math. Anal. Appl. 14 (1966), 276–284. Zbl 0138.39802, MR 0194942 |
Reference:
|
[12] Schaefer H.: Über die Methode Sukzessiver Approximationen.Jahresber. Deutsch. Math. Verein. 59 (1957), 131–140. Zbl 0077.11002, MR 0084116 |
Reference:
|
[13] Singh S. L., Bhatnagar C., Mishra S. N.: Stability of Jungck-type iterative procedures.Internat. J. Math. & Math. Sci. 19 (2005), 3035–3043. Zbl 1117.26005, MR 2206082 |
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