Daha Hızlı Yeni Bir İterasyon Metodu İçin Yakınsaklık Analizi

Year 2016, Volume: 15 Issue: 30, 35 - 53, 31.12.2016

Vatan Karakaya , Yunus Atalan Kadri Doğan , Nour El Houda Bouzara

Abstract

Bu
makelde yeni bir iterasyon yöntemini tanımladık ve bu iterasyon yönteminin
hemen hemen büzülme dönüşümlerinin sabit noktasına yaklaşımı için
kullanılabilir olduğunu gösterdik. Ayrıca, yeni iterasyon yönteminin hem Mann
iterasyon yöntemi hem de Picard-Mann hibrid iterasyon yöntemine denk olduğunu
ve hemen hemen büzülme dönüşümleri sınıfı için Picard-Mann hibrid iterasyon
yönteminden daha hızlı yakınsadığını kanıtladık. Bunlara ek olarak, bu sonucu
destekleyen bir tablo ve grafik de verdik. Son olarak, yeni iterasyon yöntemini
kullanarak hemen hemen büzülme dönüşümleri için bir veri bağlılığı sonucunu
kanıtladık.

Keywords

fp

Convergence Analysis For a New Faster Iteration Method

Abstract

In
this paper, we introduce a new iteration method and show that this iteration
method can be used to approximate fixed point of almost contraction mappings.
Furthermore, we prove that the new iteration method is equivalent to both Mann
iteration method and Picard-Mann hybrid iteration method and also converges
faster than Picard-Mann hybrid iteration method for the class of almost
contraction mappings. In addition to these we give a table and graphics for
support this result. Finally, we prove a data dependence result for almost
contraction mappings by using the new iteration method

Keywords

fp

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