On the Stability of Jungck–Mann, Jungck–Krasnoselskij and Jungck Iteration Processes in Arbitrary Banach Spaces

Alfred Olufemi Bosede

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica (2011)

  • Volume: 50, Issue: 1, page 17-22
  • ISSN: 0231-9721

Abstract

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In this paper, we establish some stability results for the Jungck–Mann, Jungck–Krasnoselskij and Jungck iteration processes in arbitrary Banach spaces. These results are proved for a pair of nonselfmappings using the Jungck–Mann, Jungck–Krasnoselskij and Jungck iterations. Our results are generalizations and extensions to a multitude of stability results in literature including those of Imoru and Olatinwo [8], Jungck [10], Berinde [1] and many others.

How to cite

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Bosede, Alfred Olufemi. "On the Stability of Jungck–Mann, Jungck–Krasnoselskij and Jungck Iteration Processes in Arbitrary Banach Spaces." Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica 50.1 (2011): 17-22. <http://eudml.org/doc/197067>.

@article{Bosede2011,
abstract = {In this paper, we establish some stability results for the Jungck–Mann, Jungck–Krasnoselskij and Jungck iteration processes in arbitrary Banach spaces. These results are proved for a pair of nonselfmappings using the Jungck–Mann, Jungck–Krasnoselskij and Jungck iterations. Our results are generalizations and extensions to a multitude of stability results in literature including those of Imoru and Olatinwo [8], Jungck [10], Berinde [1] and many others.},
author = {Bosede, Alfred Olufemi},
journal = {Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica},
keywords = {stability; nonselfmappings; Jungck–Mann; Jungck–Krasnoselskij and Jungck iteration processes; coincidence point; iteration process; Banach space; stability; nonselfmappings; Jungck-Mann iteration; Jungck-Krasnoselskij iteration; Jungck iteration process},
language = {eng},
number = {1},
pages = {17-22},
publisher = {Palacký University Olomouc},
title = {On the Stability of Jungck–Mann, Jungck–Krasnoselskij and Jungck Iteration Processes in Arbitrary Banach Spaces},
url = {http://eudml.org/doc/197067},
volume = {50},
year = {2011},
}

TY - JOUR
AU - Bosede, Alfred Olufemi
TI - On the Stability of Jungck–Mann, Jungck–Krasnoselskij and Jungck Iteration Processes in Arbitrary Banach Spaces
JO - Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica
PY - 2011
PB - Palacký University Olomouc
VL - 50
IS - 1
SP - 17
EP - 22
AB - In this paper, we establish some stability results for the Jungck–Mann, Jungck–Krasnoselskij and Jungck iteration processes in arbitrary Banach spaces. These results are proved for a pair of nonselfmappings using the Jungck–Mann, Jungck–Krasnoselskij and Jungck iterations. Our results are generalizations and extensions to a multitude of stability results in literature including those of Imoru and Olatinwo [8], Jungck [10], Berinde [1] and many others.
LA - eng
KW - stability; nonselfmappings; Jungck–Mann; Jungck–Krasnoselskij and Jungck iteration processes; coincidence point; iteration process; Banach space; stability; nonselfmappings; Jungck-Mann iteration; Jungck-Krasnoselskij iteration; Jungck iteration process
UR - http://eudml.org/doc/197067
ER -

References

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  1. Berinde, V., On stability of some fixed point procedures, Bul. Śtiint. Univ. Baia Mare, Ser. B, Mathematică–Informatică 17, 1 (2002), 7–14. (2002) MR2014277
  2. Berinde, V., Iterative Approximation of Fixed Points, Editura Efemeride, Baia Mare, 2002. (2002) Zbl1036.47037MR1995230
  3. Bosede, A. O., Noor iterations associated with Zamfirescu mappings in uniformly convex Banach spaces, Fasciculi Mathematici 42 (2009), 29–38. (2009) Zbl1178.47042MR2573523
  4. Bosede, A. O., Some common fixed point theorems in normed linear spaces, Acta Univ. Palacki. Olomuc., Fac. rer. nat., Math. 49, 1 (2010), 19–26. (2010) MR2797519
  5. Bosede, A. O., Strong convergence results for the Jungck-Ishikawa and Jungck-Mann iteration processes, Bulletin of Mathematical Analysis and Applications 2, 3 (2010), 65–73. (2010) MR2718198
  6. Bosede, A. O., Rhoades, B. E., Stability of Picard and Mann iterations for a general class of functions, Journal of Advanced Mathematical Studies 3, 2 (2010), 1–3. (2010) MR2722440
  7. Harder, A. M., Hicks, T. L., Stability results for fixed point iteration procedures, Math. Japonica 33 (1988), 693–706. (1988) Zbl0655.47045MR0972379
  8. Imoru, C. O., Olatinwo, M. O., Some stability theorems for some iteration processes, Acta Univ. Palacki. Olomuc., Fac. rer. nat., Math. 45 (2006), 81–88. (2006) Zbl1138.47046MR2321300
  9. Ishikawa, S., 10.1090/S0002-9939-1974-0336469-5, Proc. Amer. Math. Soc. 44 (1974), 147–150. (1974) Zbl0286.47036MR0336469DOI10.1090/S0002-9939-1974-0336469-5
  10. Jungck, G., 10.2307/2318216, Amer. Math. Monthly 83 (1976), 261–263. (1976) Zbl0321.54025MR0400196DOI10.2307/2318216
  11. Krasnoselskij, M. A., Two remarks on the method of successive approximations, Uspehi Mat. Nauk. 10, 1 (1955), 123–127 (in Russian). (1955) MR0068119
  12. Mann, W. R., 10.1090/S0002-9939-1953-0054846-3, Proc. Amer. Math. Soc. 4 (1953), 506–510. (1953) MR0054846DOI10.1090/S0002-9939-1953-0054846-3
  13. Olatinwo, M. O., Some stability and strong convergence results for the Jungck–Ishikawa iteration process, Creat. Math. Inform. 17 (2008), 33–42. (2008) Zbl1199.47282MR2409230
  14. Rhoades, B. E., Fixed point theorems and stability results for fixed point iteration procedures, Indian J. Pure Appl. Math. 21, 1 (1990), 1–9. (1990) Zbl0692.54027MR1048010
  15. Singh, S. L., Bhatmagar, C., Mishra, S. N., 10.1155/IJMMS.2005.3035, International J. Math. & Math. Sc. 19 (2005), 3035–3043. (2005) MR2206082DOI10.1155/IJMMS.2005.3035

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