Daha Hızlı Yeni Bir İterasyon Metodu İçin Yakınsaklık Analizi

Yıl 2016, Cilt: 15 Sayı: 30, 35 - 53, 31.12.2016

Vatan Karakaya Yunus Atalan Kadri Doğan Nour El Houda Bouzara

Öz

Bu
makelde yeni bir iterasyon yöntemini tanımladık ve bu iterasyon yönteminin
hemen hemen büzülme dönüşümlerinin sabit noktasına yaklaşımı için
kullanılabilir olduğunu gösterdik. Ayrıca, yeni iterasyon yönteminin hem Mann
iterasyon yöntemi hem de Picard-Mann hibrid iterasyon yöntemine denk olduğunu
ve hemen hemen büzülme dönüşümleri sınıfı için Picard-Mann hibrid iterasyon
yönteminden daha hızlı yakınsadığını kanıtladık. Bunlara ek olarak, bu sonucu
destekleyen bir tablo ve grafik de verdik. Son olarak, yeni iterasyon yöntemini
kullanarak hemen hemen büzülme dönüşümleri için bir veri bağlılığı sonucunu
kanıtladık.

Anahtar Kelimeler

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Convergence Analysis For a New Faster Iteration Method

Öz

In
this paper, we introduce a new iteration method and show that this iteration
method can be used to approximate fixed point of almost contraction mappings.
Furthermore, we prove that the new iteration method is equivalent to both Mann
iteration method and Picard-Mann hybrid iteration method and also converges
faster than Picard-Mann hybrid iteration method for the class of almost
contraction mappings. In addition to these we give a table and graphics for
support this result. Finally, we prove a data dependence result for almost
contraction mappings by using the new iteration method

Anahtar Kelimeler

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Kaynakça

• Agarwal, R., O Regan, D., Sahu, D., (2007), Iterative construction of fixed points of nearly asymptotically nonexpansive mappings. Journal of Nonlinear and Convex Analysis 8:61- 79.
• Berinde, V., (2007), Iterative Approximation of Fixed Points, Springer, Berlin,.
• Chugh, R., Kumar,V., Kumar, S., (2012), Strong Convergence of a New Three Step Iterative Scheme in Banach Spaces, American Journal of Computational Mathematics, Vol. 2 No. 4, pp. 345-357.
• Gürsoy, F., Karakaya, V., Rhoades, B. E., (2013), Data dependence results of new multi-step and S-iterative schemes for contractive-like operators, Fixed Point Theory and Applications Vol. 2013, (2013), doi:10.1186/1687-1812-2013-76.
• Ishikawa, S., (1974), Fixed Point By a New Iteration Method, Proceedings of the American Mathematical Society, Vol. 44, No.1, pp. 147-150.
• Karahan, I., Özdemir, M., (2013), A general iterative method for approximation of fixed points and their applications, Advances in Fixed Point Theory, Vol. 3, No.3, pp. 510-526.
• Karakaya, V., Doğan, K., Gürsoy, F., Ertürk, M., (2013), Fixed Point of a New Three-Step Iteration Algorithm under Contractive-Like Operators over Normed Spaces, Abstract and Applied Analysis, vol. 2013, Article ID 560258, 9 pages.
• Khan, S. H., 2013, A Picard-Mann hybrid iterative process. Fixed Point Theory Appl. Article ID 69 (2013), doi:10.1186/1687-1812-2013-69.
• Mann, W.R., (1953), Mean Value Methods in Iteration, Proceedings of the American Mathematical Society, Vol. 4, No. 3, pp. 506-510. Osilike, M. O., (1995), Stability results for the Ishikawa fixed point iteration procedure. Indian J. Pure Appl. Math., 26 pp. 937--945.
• Pheungrattana, W.,.Suantai, R., (2011), On the Rate of convergence of Mann, Ishikawa, Nour and SP iterations for continuous on an Arbitrary interval, Journal of computtional and Applied Mathematics, Vol. 235, No. 9pp. 3006-3914.
• Picard, E. (1890), Memoire sur la theorie des equations aux derivees partielles et la methode des approximations successives". J. Math. Pures Appl. Vol. 6, No. 4, pp. 145-210.
• Şoltuz, S.M., Grosan, T., (2008), Data dependence for Ishikawa iteration when dealing with contractive like operators", Fixed Point Theory and Applications, Vol. 2008, 7 pages.
• Weng, X., (1991), Fixed point iteration for local strictly pseudocontractive mapping, Proc. Amer. Math. Soc., Vol. 113, pp. 727.