Previous |  Up |  Next

Article

Title: Stability of Noor Iteration for a General Class of Functions in Banach Spaces (English)
Author: Bosede, Alfred Olufemi
Language: English
Journal: Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica
ISSN: 0231-9721
Volume: 51
Issue: 2
Year: 2012
Pages: 19-25
Summary lang: English
.
Category: math
.
Summary: In this paper, we prove the stability of Noor iteration considered in Banach spaces by employing the notion of a general class of functions introduced by Bosede and Rhoades [6]. We also establish similar result on Ishikawa iteration as a special case. Our results improve and unify some of the known stability results in literature. (English)
Keyword: stability
Keyword: Noor and Ishikawa iterations
MSC: 47H10
MSC: 47J25
MSC: 54H25
idZBL: Zbl 06204927
idMR: MR3058870
.
Date available: 2012-11-26T10:14:26Z
Last updated: 2014-03-12
Stable URL: http://hdl.handle.net/10338.dmlcz/143064
.
Reference: [1] Agarwal, R. P., Meehan, M., O’Regan, D.: Fixed Point Theory and Applications. Cambridge University Press, Cambridge, 2001. Zbl 0960.54027, MR 1825411
Reference: [2] Berinde, V.: Iterative Approximation of Fixed Points. Editura Efemeride, Baia Mare, 2002. Zbl 1036.47037, MR 1995230
Reference: [3] Bosede, A. O.: Noor iterations associated with Zamfirescu mappings in uniformly convex Banach spaces. Fasciculi Mathematici 42 (2009), 29–38. Zbl 1178.47042, MR 2573523
Reference: [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
Reference: [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
Reference: [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), 23–25. MR 2722440
Reference: [7] Bosede, A. O., Akinbo, G.: Some stability theorems associated with $A$-distance and $E$-distance in uniform spaces. Acta Universitatis Apulensis 26 (2011), 121–128. Zbl 1274.54117, MR 2850603
Reference: [8] Ciric, L. B.: Fixed point theorems in Banach spaces. Publ. Inst. Math. (Beograd) 47, 61 (1990), 85–87. Zbl 0722.47046, MR 1103533
Reference: [9] Ciric, L. B.: Fixed Point Theory. Contraction Mapping Principle. FME Press, Beograd, 2003.
Reference: [10] Harder, A. M., Hicks, T. L.: Stability results for fixed point iteration procedures. Math. Japonica 33 (1988), 693–706. Zbl 0655.47045, MR 0972379
Reference: [11] Imoru, C. O., Akinbo, G., Bosede, A. O.: On the fixed points for weak compatible type and parametrically $\varphi (\epsilon , \delta ; a)$-contraction mappings. Math. Sci. Res. Journal 10, 10 (2006), 259–267. MR 2277967
Reference: [12] Imoru, C. O., Olatinwo, M. O.: On the stability of Picard and Mann iteration processes. Carpathian J. Math. 19, 2 (2003), 155–160. Zbl 1086.47512, MR 2069844
Reference: [13] Imoru, C. O., Olatinwo, M. O., Akinbo, G., Bosede, A. O.: On a version of the Banach’s fixed point theorem. General Mathematics 16, 1 (2008), 25–32. Zbl 1235.54038, MR 2438519
Reference: [14] Ishikawa, S.: Fixed points by a new iteration method. Proc. Amer. Math. Soc. 44 (1974), 147–150. Zbl 0286.47036, MR 0336469, 10.1090/S0002-9939-1974-0336469-5
Reference: [15] Mann, W. R.: Mean value methods in iterations. Proc. Amer. Math. Soc. 4 (1953), 506–510. MR 0054846, 10.1090/S0002-9939-1953-0054846-3
Reference: [16] Noor, M. A.: General variational inequalities. Appl. Math. Letters 1 (1988), 119–121. Zbl 0655.49005, MR 0953368, 10.1016/0893-9659(88)90054-7
Reference: [17] Noor, M. A.: New approximations schemes for general variational inequalities. J. Math. Anal. Appl. 251 (2000), 217–299. MR 1790406, 10.1006/jmaa.2000.7042
Reference: [18] Noor, M. A.: Some new developments in general variational inequalities. Appl. Math. Computation 152 (2004), 199–277. MR 2050063
Reference: [19] Noor, M. A., Noor, K. I., Rassias, T. M.: Some aspects of variational inequalities. J. Comput. Appl. Math. 47 (1993), 493–512. Zbl 0788.65074, MR 1251844
Reference: [20] Osilike, M. O.: Stability results for fixed point iteration procedures. J. Nigerian Math. Soc. 14/15 (1995/1996), 17–29. MR 1775011
Reference: [21] Rhoades, B. E.: Fixed point iteration using infinite matrices. Trans. Amer. Math. Soc. 196 (1974), 161–176. Zbl 0267.47032, MR 0348565, 10.1090/S0002-9947-1974-0348565-1
Reference: [22] Rhoades, B. E.: Comments on two fixed point iteration methods. J. Math. Anal. Appl. 56, 2 (1976), 741–750. Zbl 0353.47029, MR 0430880, 10.1016/0022-247X(76)90038-X
Reference: [23] Rhoades, B. E.: Fixed point theorems and stability results for fixed point iteration procedures. Indian J. Pure Appl. Math. 21, 1 (1990), 1–9. Zbl 0692.54027, MR 1048010
Reference: [24] Rus, I. A., Petrusel, A., Petrusel, G.: Fixed Point Theory, 1950–2000, Romanian Contributions. House of the Book of Science, Cluj-Napoca, 2002. Zbl 1005.54037, MR 1947195
Reference: [25] Zamfirescu, T.: Fix point theorems in metric spaces. Arch. Math. 23 (1972), 292–298. Zbl 0239.54030, MR 0310859, 10.1007/BF01304884
Reference: [26] Zeidler, E.: Nonlinear Functional Analysis and its Applications: Fixed Point Theorems. Springer, New York, 1986. MR 0816732
.

Files

Files Size Format View
ActaOlom_51-2012-2_2.pdf 196.9Kb application/pdf View/Open
Back to standard record
Partner of
EuDML logo