Strong and Weak Convergence of Cesàro Mean for Some Iteration Methods

Year 2023, Volume: 10 Issue: 1, 236 - 253, 31.05.2023

Lale Cona , Çiğdem Kaygusuz

https://doi.org/10.35193/bseufbd.1190411

Abstract

In this article, firstly, summability techniques and iteration methods are investigated. In addition, studies on ergodic theory which are related to the Cesàro mean summability technique are examined for some iteration methods. Finally, a study on the strong convergence the Cesàro mean with the Halpren iteration for asymptotic non-expanding transformations is discussed.

Keywords

Cesàro Summability, Ergodic Theory, Iteration Methods, Strong Convergence, Fixed Point Approaches

Bazı İterasyon Yöntemleri için Cesàro Ortalamasının Kuvvetli ve Zayıf Yakınsaklığı

Abstract

Bu makalede, ilk olarak toplanabilme teknikleri ve iterasyon yöntemleri araştırılmıştır. Ayrıca, bazı iterasyon yöntemleri için Cesàro anlamında toplanabilme tekniğine bağlı olarak ergodik teori üzerine yapılan çalışmalar incelenmiştir. Son olarak asimptotik genişlemeyen dönüşümler için Halpren iterasyonu ile Cesàro ortalamasının güçlü yakınsaklığı üzerine yapılan bir çalışma irdelenmiştir.

Keywords

Cesàro Toplanabilme, Ergodik Teori, İterasyon Yöntemleri, Kuvvetli Yakınsaklık, Sabit Nokta Yaklaşımları

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