A result on segmenting Jungck–Mann iterates

Memudu Olaposi Olatinwo

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica (2008)

  • Volume: 47, Issue: 1, page 115-119
  • ISSN: 0231-9721

Abstract

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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].

How to cite

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Olatinwo, Memudu Olaposi. "A result on segmenting Jungck–Mann iterates." Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica 47.1 (2008): 115-119. <http://eudml.org/doc/32475>.

@article{Olatinwo2008,
abstract = {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].},
author = {Olatinwo, Memudu Olaposi},
journal = {Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica},
keywords = {Jungck–Mann iteration process; uniformly convex Banach space; uniformly convex Banach space; common fixed point; Jungck-Mann iteration process},
language = {eng},
number = {1},
pages = {115-119},
publisher = {Palacký University Olomouc},
title = {A result on segmenting Jungck–Mann iterates},
url = {http://eudml.org/doc/32475},
volume = {47},
year = {2008},
}

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
PB - Palacký University Olomouc
VL - 47
IS - 1
SP - 115
EP - 119
AB - 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].
LA - eng
KW - Jungck–Mann iteration process; uniformly convex Banach space; uniformly convex Banach space; common fixed point; Jungck-Mann iteration process
UR - http://eudml.org/doc/32475
ER -

References

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  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. (1967) MR0217658
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  7. Groetsch C. W., A Note on Segmenting Mann Iterates, J. Math. Anal. Appl. 40 (1972), 369–372. (1972) Zbl0244.47042MR0341204
  8. Jungck G., Commuting mappings and fixed points, Amer. Math. Monthly 83, 4 (1976), 261–263. (1976) Zbl0321.54025MR0400196
  9. Mann W. R., Mean value methods in iteration, Proc. Amer. Math. Soc. 4 (1953), 506–510. (1953) Zbl0050.11603MR0054846
  10. Opial Z., Weak convergence of the successive approximations for nonexpansive mappings in Banach spaces, Bull. Amer. Math. Soc. 73 (1967), 591–597. (1967) MR0211301
  11. Petryshyn W. V., Construction of fixed points of demicompact mappings in Hilbert space, J. Math. Anal. Appl. 14 (1966), 276–284. (1966) Zbl0138.39802MR0194942
  12. Schaefer H., Über die Methode Sukzessiver Approximationen, Jahresber. Deutsch. Math. Verein. 59 (1957), 131–140. (1957) Zbl0077.11002MR0084116
  13. Singh S. L., Bhatnagar C., Mishra S. N., Stability of Jungck-type iterative procedures, Internat. J. Math. & Math. Sci. 19 (2005), 3035–3043. Zbl1117.26005MR2206082

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