Yeni Bir İterasyon Yöntemi İçin Yakınsaklık Hızı

Bu çalışmada yeni bir iterasyon yöntemi tanımlanmıştır. Bu iterasyon yönteminin Banach uzaylarında uygun koşullar altında yakınsaklığı incelenmiştir ve başka bir iterasyon yöntemiyle yakınsama anlamında denk olduğu gösterilmiştir. Son olarak yeni iterasyon yönteminin literatürdeki mevcut bir iterasyon yöntemine göre daha iyi bir yakınsama hızına sahip olduğu ispatlanarak bu sonucu destekleyen bir örnek verilmiştir.
Anahtar Kelimeler:

Sabit nokta, Banach uzayı, denklik

Rate of Convergence for A New Iteration Method

In this study, a new iteration method has been defined. The convergence of this iteration method in Banach spaces under appropriate conditions has been examined and it has been shown that this iteration is equivalent in terms of convergence with another iteration method. Finally, it has been proved that the new iteration method has a better convergence rate than the existing iteration method in literature and an example supporting this result has been given.

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  • 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 (1): 61-79.
  • Atalan Y, 2018. Yeni Bir İterasyon Yöntemi İçin Hemen-Hemen Büzülme Dönüşümleri Altında Bazı Sabit Nokta Teoremleri. Marmara Fen Bilimleri Dergisi, 30 (3): 276-285.
  • Banach S, 1922. Sur les opérations dans les ensembles abstraits et leur application aux équations intégrales, Fundamenta Mathematicae 1 (3): 133-181.
  • Başarır M, 1988. On rates of convergence of sequences. Journal of the Orissa Mathematical Society, 7 (2): 89-98.
  • Başarır M, Şahin A, 2016. Two General Iteration Schemes for Multi-Valued Maps in Hyperbolic Spaces, Communications of the Korean Mathematical Society, 31 (4): 713-727.
  • Başarır M, Şahin A, 2017. Some Results of The New Iterative Scheme in Hyperbolic Space, Communications of the Korean Mathematical Society, 32 (4): 1009-1024.
  • Berinde V, 2003. On The Approximation of Fixed Points of Weak Contractive Mappings. Carpathian Journal of Mathematics, 19 (1): 7-22.
  • Berinde V, 2007. Iterative Approximation of Fixed Points, Springer, Berlin, 2007
  • Chugh R, Kumar V, Kumar S, 2012. Strong Convergence of a New Three Step Iterative Scheme in Banach Spaces. American Journal of Computational Mathematics, 2 (4): 345-357.
  • Dogan K, Karakaya V, 2014. On the Convergence and Stability Results for a New General Iterative Process. The Scientific World Journal, 2014: 1-8.
  • Gürsoy F, Karakaya V, Rhoades BE, 2013. Data dependence results of new multistep and S-iterative schemes for contractive-like operators. Fixed Point Theory and Applications, 2013: 1-12.
  • Ishikawa S, 1974. Fixed Point By a New Iteration Method. Proceedings of the American Mathematical Society, 44: 147-150.
  • Karakaya V, Atalan Y, Dogan K, Bouzara NEH, 2017. Some Fixed Point Results for a New Three Steps Iteration Process in Banach Spaces. Fixed Point Theory, 18 (2): 625-640.
  • Knopp K, 1931. Theory and Application of Infinite Series. Berlin.
  • Mann W R, 1953. Mean Value Methods in Iteration. Proceedings of the American Mathematical Society, 4 (3): 506-510.
  • Maldar S, 2019. Geleceğin Dünyasında Bilimsel ve Mesleki Çalışmalar: Matematik ve Fen Bilimleri. Ekin Basım Yayın Dağıtım No:1, s. 167-181, Bursa-Türkiye.
  • Miller HI, 1973. Rates of convergence and summability. Rad. Odjeljenje Prir. Mat. Nauka, 12 (1973), 85-92.
  • Noor MA, 2000. New Approximation Schemes for General Variational Inequalities. Journal of Mathematical Analysis and Applications, 251 (1): 217-229.
  • Picard E, 1890. Mémoire Sur la Théorie des Équations Aux Dérivées Partielles et la Méthodebdes Approximations Successives. Journal de mathématiques pures et appliquées, 6: 145-210.
  • Weng X, 1991. Fixed Point Iteration for Local Strictly Pseudo-Contractive Mapping. Proceedings of the American Mathematical Society, 113 (3): 727-731.