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Abstrakty
We show that the convergences of Jungck, Jungck- Mann, Jungck-Ishikawa, Jungck-Noor and Jungck-multistep itera¬tion processes are equivalent for a class of generalized contractive- like operators defined on a Banach space. Our results are general¬izations and extensions of the work of Soltuz [20, 21], Zhiqun [23] and some other numerous ones in literature.
Czasopismo
Rocznik
Tom
Strony
47--61
Opis fizyczny
Bibliogr. 24 poz.
Twórcy
autor
- Department of Mathematics University of Lagos Akoka, Yaba, Lagos, jolaleru@unilag.edu.ng
autor
- Department of Mathematics University of Lagos Akoka, Yaba, Lagos, hudsonmolas@yahoo.com
Bibliografia
- [1] Berinde V., On the convergence of the Ishikawa iteration in the class of quasi-contractive operators, Acta Math. Univ. Comenianae, LXXIII (1)(2004), 119-126.
- [2] Berinde V., A convergence theorem for Mann iteration in the class of Zam- firescu operators, Seria Matematica Informatica XLV, 1(2007), 33-41.
- [3] Chatterjea S.K., Fixed point theorems, C.R. Acad. Bulgare Sci., 25(1972), 727-730.
- [4] Edwards Jr. C.H., Advanced calculus of several variables, Academic Press, New York and London, 1973.
- [5] Ishikawa S., Fixed points by a new iteration method, Proc. Amer. Math. Soc., 44(1974), 147-150.
- [6] Jungck G., Commuting mappings and fixed points, Amer. Math. Monthly, 83(4)(1976), 261-263.
- [7] Jungck G., Compatible mappings and common fixed points, Int. J. Math. Math. Sci., 9(4)(1986), 771-779.
- [8] Jungck G., Common fixed points for commuting and compatible maps on compacta, Proc. Amer. Math. Soc., 103(1988), 977-983.
- [9] Kannan R., Some results on fixed points, Bull. Calcutta Math. Soc., 10 (1968), 71-76.
- [10] Mann W.R., Mean value methods in iterations, Proc. Amer. Math. Soc, 44 (1953), 506-510.
- [11] Noor M.A., New approximation schemes for general variational inequalities, Journal of Mathematical Analysis and Applications, 251(1)9(2004), 217-229.
- [12] Olaleru J.O., On the convergence of the Mann iteration in locally convex spaces, Carpathian Journal of Mathematics, 22(1-2)(2006), 115-120.
- [13] Olaleru J.O., On the equivalence of Picard, Mann and Ishikawa iterations for a class of quasi-contractive operators, J. Nig. Assoc. Math. Phys., 11(2007), 51-56.
- [14] Olaleru J.O., Akewe H., On multistep iterative scheme for approximating the common fixed point of contractive-like operators, Int. J. Math. and Math. Sci., Vol. 2010, Article ID 530964, 11 pages.
- [15] Olatinwo M.O., Imoru C.O., Some convergence results of the Jungck- Mann and Jungck-Ishikawa iterations processes in the class of generalized Zamfirescu operators, Acta Math. Comenianae, Vol. LXXVII, 2(2008), 299¬304.
- [16] Olatinwo M.O., Some stability and strong convergence results for the Jungck-Ishikawa iteration process, Creative Math. and Inf., 17(2008), 33-42.
- [17] Olatinwo M.O., A generalization of some convergence results using a Jungck -Noor three-step iteration process in arbitrary Banach space, Fasc. Math., 40(2008), 37-43.
- [18] Rafiq A., On the convergence of the three-step iteration process in the class of quasi-contractive operators, Acta Math. Acad. Paedagog, Nyiregy-haziensis, 22(2006), 305-309.
- [19] Rhoades B.E., A comparison of various definition of contractive mappings, Trans. Amer. Math., 266(1977), 257-290.
- [20] Singh S.L., Bhatnagar C., Mishra S.N., Stability of Jungck-type itera¬tion procedures, Int. J. Math. Math. Sci., 19(2005), 3035-3043.
- [21] Soltuz S.M., The equivalence of Picard, Mann and Ishikawa iterations deal¬ing with quasi-contractive operators, Math. Commun., 10(2005), 81-88.
- [22] Soltuz S.M., The equivalence between Krasnoselskij, Mann, Ishikawa, Noor and multistep iterations, Math. Commun., 12(2007), 53-61.
- [23] Zamfirescu T., Fixed point theorems in metric spaces, Arch. Math. (Basel), 23(1972), 292-298.
- [24] Zhiqun X., Remarks of equivalence among Picard, Mann and Ishikawa iter¬ations in normed spaces, Fixed Point Theory and Appl., (2007), 1-5.
Typ dokumentu
Bibliografia
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bwmeta1.element.baztech-503ae7d0-4729-49b1-b10a-5d78dc5f37bf