Convergence and stability of modified multi-step Noor iterative procedure with errors for strictly hemicontractive-type mappings in Banach spaces

Fixed Point Theory and Applications Pub Date : 2021-03-08 DOI:10.1186/s13663-021-00692-6

Md. Asaduzzaman

引用次数: 0

Abstract

In this paper, we introduce and study a modified multi-step Noor iterative procedure with errors for two Lipschitz strictly hemicontractive-type mappings in arbitrary Banach spaces and constitute its convergence and stability. The obtained results in this paper generalize and extend the corresponding result of Hussain et al. (Fixed Point Theory Appl. 2012:160, 2012) and some analogous results of several authors in the literature. Finally, a numerical example is included to illustrate our analytical results and to display the efficiency of our proposed novel iterative procedure with errors.

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巴拿赫空间中严格半收缩型映射的修正多步努尔迭代程序的收敛性和稳定性（带误差

本文针对任意巴拿赫空间中的两个 Lipschitz 严格半收缩型映射，引入并研究了一个修正的多步 Noor 迭代过程（带误差），并构成了其收敛性和稳定性。本文得到的结果概括并扩展了 Hussain 等人（《定点理论应用》，2012:160，2012 年）的相应结果，以及文献中几位作者的一些类似结果。最后，本文还列举了一个数值示例来说明我们的分析结果，并展示了我们提出的新型误差迭代程序的效率。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Fixed Point Theory and Applications MATHEMATICS, APPLIED-MATHEMATICS

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期刊介绍： In a wide range of mathematical, computational, economical, modeling and engineering problems, the existence of a solution to a theoretical or real world problem is equivalent to the existence of a fixed point for a suitable map or operator. Fixed points are therefore of paramount importance in many areas of mathematics, sciences and engineering. The theory itself is a beautiful mixture of analysis (pure and applied), topology and geometry. Over the last 60 years or so, the theory of fixed points has been revealed as a very powerful and important tool in the study of nonlinear phenomena. In particular, fixed point techniques have been applied in such diverse fields as biology, chemistry, physics, engineering, game theory and economics. In numerous cases finding the exact solution is not possible; hence it is necessary to develop appropriate algorithms to approximate the requested result. This is strongly related to control and optimization problems arising in the different sciences and in engineering problems. Many situations in the study of nonlinear equations, calculus of variations, partial differential equations, optimal control and inverse problems can be formulated in terms of fixed point problems or optimization.