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Abstrakty
The purpose of this study is to introduce a Jungck-Kirk-Noor type random iterative scheme and prove stability and strong convergence of this to establish a general theorem to approximate the unique common random coincidence point for two or more nonself random commuting mappings under general contractive condition in various spaces. Also we give the stability and convergence for random Jungck-Kirk-Ishikawa and random Jungck-Kirk-Mann as a corollaries. The results obtained in this paper improve the corresponding results announced recently.
Czasopismo
Rocznik
Tom
Strony
167--182
Opis fizyczny
Bibliogr. 29 poz.
Twórcy
autor
- Department of Mathematics, Faculty of Science, Assuit University, Assuit 71516, Egypt
autor
- Department of Mathematics, Faculty of Science, Sohag University, Sohag 82524, Egypt
Bibliografia
- [1] Alotaibi A., Kumar V., Hussain N., Convergence comparison and stability of Jungck- Krik-type algorithms for common fixed point problems, Fixed Point Theory Appl., 173(2013), 1-30.
- [2] Berinde V., On the convergence of the Ishikawa iteration in the class of quasi-contractive operators, Acta Math. Univ. Comenianae, 73(2004), 119-126.
- [3] Bharucha-Reid A.T., Fixed point theorems in probabilistic analysis, Bull. Amer. Math. Soc., 82(1976), 641-657.
- [4] Bosede, Olufemi A., On the stability of Jungck-Mann, Jungck-Krasnoselskij and Jungck iteration process in arbitrary Banach spaces, Acta Univ. Palacki. Olomuc. Fac. Rer. Nat. Mathematica, 50(2011), 17-22.
- [5] Choudhury B.S., Convergence of a random iteration scheme to a random fixed point, J. Appl. Math. Stochastic Anal., 8(1995), 139-142.
- [6] Choudhury B.S., A random fixed point iteration for three random operators on uniformly convex Banach spaces, Anal. Theory Appl., 19(2003), 99-107.
- [7] Chugh R., Kumar V., Narwal S., Some strong convergence results of random iterative algorithms with errors in Banach spaces, Commun. Korean Math. Soc., 31(1)(2016), 147-161.
- [8] Hanš O., Reduzierende zufăllige transformationen, Czechoslov. Math. J., 7 (1957), 154-158.
- [9] Himmelberg C.J., Measurable relations, Fund. Math., 87(1975), 53-71.
- [10] Hussain N., Chugh R., Kumar V., Rafiq A., On the rate of convergence of Kirk type iterative schemes, J. Appl. Math., Article ID 526503(2012), 1-22.
- [11] Hussain N., Kumar V., Chugh R., Malik P., Jungck-type implicit iterative algorithms with numerical examples, Filomat, 31(2017), 2303-2320.
- [12] Ioana, Stability of Jungck-type iterative procedure for some contractive type mappings via implicit relations, Miskolc Math. Notes, 13(2012), 555-567.
- [13] Itoh S., Random fixed-point theorems with an application to random differential equations in Banach spaces, J. Math. Anal. Appl., 67(1979), 261-273.
- [14] Jungck G., Commuting mappings and fixed points, Amer. Math. Manthly, 83(1976), 261-263.
- [15] Khan A.R., Kumar V., Hussain N., Analytical and numerical treatment of Jungck type iterative schemes, Appl. Math. Comput., 231(2014), 521-535.
- [16] Khan A.R., Kumar V., Narwal S., Chugh R., Random iterative algorithms and almost sure stability in Banach Spaces, Filomat, 31(2017).
- [17] Kumar V., Chugh R., Strong convergence of hybrid fixed point iterative algorithms of Kirk-Noor type with errors in an arbitrary Banach space, Int. J. Pure Appl. Math., 80(2012), 161-171.
- [18] Lin T.C., Random approximation and random fixed point theorems for non self mappings, Proc. Amer. Math. Soc., 103(1988), 1129-1135.
- [19] Olatinwo M.O., A Generalization of some convergence results using the Jungck-Noor three step iteration process in arbitrary Banach space, Fasciculi Math., 40(2008), 37-43.
- [20] Olatinwo M.O., Some stability and strong convergence results for the Jungck-Ishikawa iteration process, Creative Math. Informatics, 17(2008), 33-42.
- [21] Olatinwo M.O., Some stability results for two hybrid fixed point iterative algorithms in normed linear space, Mathematique Vesnik, 61(2009), 247-256.
- [22] Olatinwo M.O., Convergence results for Jungck-type iterative process in convex metric spaces,, Acta Univ. Palacki Olomue, Fac. Rer. Nat. Math., 51(2012), 79-87.
- [23] Olatinwo M.O., Stability results for Jungck-kirk-Mann and Jungck-kirk hybrid iterative algorithms, Anal. Theory Appl., 29(2013), 12-20.
- [24] Olatinwo M.O., Imoru C.O., Some convergence result for the JungckMann and Jungck-Ishikawa iteration process in the class of generalized Zam- firescu operators, Acta Math. Univ. Comenianae, 77(2008), 299-304.
- [25] Osilike M.O., Udomene A., Short proofs of stability results for fixed point iteration procedures for a class of contractive-type mappings, Indian J. Pure Appl. Math., 30(12)(1999), 1229-1234.
- [26] Ostrowski A.M., The round-off stability of iterations, Z. Angew. Math. Mech., 47(1967), 77-81.
- [27] Rashwan R.A., Rafiq A., Hakim A., On the convergence of three-steps iteration process with errors in the class of quasi-contractive, Paki. Acad. Sci., 46(2009), 41-46.
- [28] Rashwan R.A., Hammad H.A., Okeke G.A., Convergence and almost sure (S, T)-stability for random iterative schemes, Int. J. Advances in Math., 2016(2016), 1-16.
- [29] Špaček A., ˇ Zufăllige Gleichungen, Czechoslovak, Math. J., 5(1955), 462-466.
Uwagi
Opracowanie ze środków MNiSW w ramach umowy 812/P-DUN/2016 na działalność upowszechniającą naukę (zadania 2017).
Typ dokumentu
Bibliografia
Identyfikator YADDA
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