Daha Hızlı Mann Sabit Nokta Yinelemesi Üzerine Bir Çalışma

Year 2018, Volume: 18 Issue: 3, 852 - 860, 30.12.2018

Kadri Doğan

Abstract

Bu çalışmada, Mann yineleme yönteminden daha hızlı olan Mann tipinde bir yineleme

tanımlanmış ve bu yineleme yönteminin Banach uzaylarında hemen hemen büzülme dönüşümleri

için sabit noktaya yakınsadığı gösterilmiştir. Ayrıca düzenlenmiş Mann yineleme yönteminin

literatürdeki diğer sabit nokta yineleme yöntemlerine yakınsaklık denklikleri ispatlanmıştır. Son

olarak, Mann tipindeki yineleme yönteminin, klasik Mann yineleme yönteminden daha hızlı

olduğu gösterilmiştir.

Keywords

Mann sabit nokta yineleme yöntemi, Yakınsaklık hızı, Yakınsaklık denkliği, Kuvvetli yakınsaklık.

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