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

Fixexd point theory and applications

Murat Ozdemir¹  Ibrahim Karahan² 

[1] Department of Mathematics, Faculty of Science, Ataturk University, Erzurum, Turkey;Department of Mathematics, Faculty of Science, Erzurum Technical University, Erzurum, Turkey

关键词: fixed point;    continuous function;    convergence theorems;    rate of convergence;    computational cost;   

DOI  :  10.1186/1687-1812-2013-244

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

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. MSC:26A18, 47H10, 54C05.

【 授权许可】

CC BY