Yeni Bir İterasyon Yöntemi İçin Yakınsaklık Hızı

Year 2020, Volume: 10 Issue: 2, 1263 - 1272, 01.06.2020

Samet Maldar

https://doi.org/10.21597/jist.663039

Cited By: 1

Abstract

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.

Keywords

Sabit nokta, Banach uzayı, denklik

Rate of Convergence for A New Iteration Method

Abstract

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.

Keywords

Fixed Point, Banach space, equivalence

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