Previous |  Up |  Next

Article

Keywords:
stability; nonselfmappings; Jungck–Mann, Jungck–Krasnoselskij and Jungck iteration processes
Summary:
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.
References:
[1] Berinde, V.: On stability of some fixed point procedures. Bul. Śtiint. Univ. Baia Mare, Ser. B, Mathematică–Informatică 17, 1 (2002), 7–14. MR 2014277
[2] Berinde, V.: Iterative Approximation of Fixed Points. Editura Efemeride, Baia Mare, 2002. MR 1995230 | Zbl 1036.47037
[3] Bosede, A. O.: Noor iterations associated with Zamfirescu mappings in uniformly convex Banach spaces. Fasciculi Mathematici 42 (2009), 29–38. MR 2573523 | Zbl 1178.47042
[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. MR 2797519
[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. MR 2718198
[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. MR 2722440
[7] Harder, A. M., Hicks, T. L.: Stability results for fixed point iteration procedures. Math. Japonica 33 (1988), 693–706. MR 0972379 | Zbl 0655.47045
[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. MR 2321300 | Zbl 1138.47046
[9] Ishikawa, S.: Fixed points by a new iteration method. Proc. Amer. Math. Soc. 44 (1974), 147–150. DOI 10.1090/S0002-9939-1974-0336469-5 | MR 0336469 | Zbl 0286.47036
[10] Jungck, G.: Commuting mappings and fixed points. Amer. Math. Monthly 83 (1976), 261–263. DOI 10.2307/2318216 | MR 0400196 | Zbl 0321.54025
[11] Krasnoselskij, M. A.: Two remarks on the method of successive approximations. Uspehi Mat. Nauk. 10, 1 (1955), 123–127 (in Russian). MR 0068119
[12] Mann, W. R.: Mean value methods in iterations. Proc. Amer. Math. Soc. 4 (1953), 506–510. DOI 10.1090/S0002-9939-1953-0054846-3 | MR 0054846
[13] Olatinwo, M. O.: Some stability and strong convergence results for the Jungck–Ishikawa iteration process. Creat. Math. Inform. 17 (2008), 33–42. MR 2409230 | Zbl 1199.47282
[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. MR 1048010 | Zbl 0692.54027
[15] Singh, S. L., Bhatmagar, C., Mishra, S. N.: Stability of Jungck-type iterative procedures. International J. Math. & Math. Sc. 19 (2005), 3035–3043. DOI 10.1155/IJMMS.2005.3035 | MR 2206082
Partner of
EuDML logo