Keyfi Aralıkta Sürekli Fonksiyonlar İçin S-İterasyon Metodunun Yakınsaklığı

Bu makalede keyfi bir aralıkta tanımlanan sürekli fonksiyonların sabit noktalarını bulmak için S-iterasyonu

Anahtar Kelimeler:

Hesaplama maliyeti, sabit nokta, sürekli fonksiyon, yakınsaklık teoremleri, yakınsama oranı

Convergence of S-Iteration Method for Continuous Functions on An Arbitrary Interval

In this paper, we consider S-iteration to find fixed points of continuous mappings on an arbitraryinterval. We give some necessary and sufficient conditions for the convergence of this iteration. Also, we provedthat the rate of convergence of S-iteration is better than some other iterations for continuous and nondecreasingmappings. It is also noted that the method of proof of Lemma 3 using S-iteration is slightly different from that usingthe iteration schemes like Mann.

Keywords:

Computational cost, continuous function, convergence theorems, fixed point, rate of convergence,

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