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Iterative algorithms of generalized nonexpansive mappings and monotone operators with application to convex minimization problem
Journal of Applied Mathematics and Computing ( IF 2.2 ) Pub Date : 2021-07-15 , DOI: 10.1007/s12190-021-01593-y
Samet Maldar 1
Affiliation  

In this paper, we present some convergence results for various iterative algorithms built from Hardy-Rogers type generalized nonexpansive mappings and monotone operators in Hilbert spaces. We obtain some comparison results for the rates of convergence of these algorithms to the solution of variational inequality problem including Hardy–Rogers type generalized nonexpansive mappings and monotone operators. A numerical example is given to validate these results. We apply the iterative algorithms handled herein to solve convex minimization problem and illustrate this result by providing a non-trivial numerical example. The presented results considerably improve the corresponding results in Ali et al. (Comput Appl Math 39:74, 2020. https://doi.org/10.1007/s40314-020-1101-4).



中文翻译:

广义非扩展映射和单调算子的迭代算法在凸最小化问题中的应用

在本文中,我们展示了由 Hardy-Rogers 类型的广义非扩张映射和希尔伯特空间中的单调算子构建的各种迭代算法的一些收敛结果。我们获得了这些算法对包括 Hardy-Rogers 型广义非扩张映射和单调算子在内的变分不等式问题的解决方案的收敛速度的一些比较结果。给出了一个数值例子来验证这些结果。我们应用这里处理的迭代算法来解决凸最小化问题,并通过提供一个重要的数值例子来说明这个结果。所呈现的结果大大改善了 Ali 等人的相应结果。(计算应用数学 39:74,2020 年。https://doi.org/10.1007/s40314-020-1101-4)。

更新日期:2021-07-15
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