An Examination of Data Dependence For Jungck-Type Iteration Method

Year 2020, Volume: 36 Issue: 3, 374 - 384, 31.12.2020

Samet Maldar

Abstract

Iteration methods are an important field of study in fixed point theory and have an extensive literature. Different types of iteration methods were defined in many spaces by researchers, and the results such as convergence, rate of convergence, stability and data dependence of these methods were examined. In this study, a new iteration method of Jungck Type was defined and the convergence of this method for a certain mapping class was investigated. Then, using this mapping class for this iteration method, the results of stability and data dependence were obtained. Additionally, the rate of convergence of the newly defined iteration method with Jungck CR iteration method was compared under suitable conditions and an example supporting this result was given.

Keywords

Iteration Method, Convergence, Data Dependence, Stability

Jungck-Tipi İterasyon Yöntemi İçin Veri Bağlılığının İncelenmesi

Abstract

İterasyon yöntemleri sabit nokta teorisinde önemli bir çalışma alanı olup geniş bir literatüre sahiptir. Araştırmacılar tarafından birçok uzayda farklı türden iterasyon yöntemleri tanımlanarak, bu yöntemlerin yakınsaklığı, yakınsaklık hızları, kararlılığı ve veri bağlılığı gibi sonuçlar irdelenmiştir. Bu çalışmada, Jungck tipi yeni bir iterasyon yöntemi tanımlanarak bu yöntemin belirli bir dönüşüm sınıfı için yakınsaklığı incelenmiştir. Daha sonra bu iterasyon yöntemi için söz konusu dönüşüm sınıfı kullanılarak kararlılık ve veri bağlılığı sonuçları elde edilmiştir. Ayrıca yeni tanımlanan iterasyon yönteminin uygun şartlar altında yakınsaklık hızı Jungck CR iterasyon yöntemiyle karşılaştırılarak bu sonucu destekleyen örnek verilmiştir.

Keywords

İterasyon Yöntemleri, Yakınsaklık, Veri Bağlılığı, kararlılık

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