Fixed point problems of the Picard-Mann hybrid iterative process for continuous functions on an arbitrary interval

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Atıf İçin Kopyala

KARAHAN İ., ÖZDEMİR M.

FIXED POINT THEORY AND APPLICATIONS, 2013 (SCI-Expanded)

• Yayın Türü: Makale / Tam Makale
• Basım Tarihi: 2013
• Doi Numarası: 10.1186/1687-1812-2013-244
• Dergi Adı: FIXED POINT THEORY AND APPLICATIONS
• Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
• Atatürk Üniversitesi Adresli: Evet

Özet

In this paper, we consider the iteration method called 'Picard-Mann hybrid iterative process' for finding a fixed point of continuous functions on an arbitrary interval. We give a necessary and sufficient condition for convergence of this iteration for continuous functions on an arbitrary interval. Also, we compare the rate of convergence of the Picard-Mann hybrid iteration with the other iterations and prove that it is better than the others under the same computational cost. Moreover, we present numerical examples.