The Experts below are selected from a list of 1275 Experts worldwide ranked by ideXlab platform
Qiaoli Dong - One of the best experts on this subject based on the ideXlab platform.
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on the optimal relaxation parameters of Krasnosel ski mann iteration
Optimization, 2021Co-Authors: Qiaoli Dong, Hanlin TianAbstract:This paper is devoted to the optimal selection of the relaxation parameter sequence for Krasnosel'ski–Mann iteration. Firstly, we establish the optimal relaxation parameter sequence of the Krasnose...
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multi step inertial Krasnosel skiǐ mann iteration with new inertial parameters arrays
Journal of Fixed Point Theory and Applications, 2021Co-Authors: Qiaoli Dong, Yeol Je Cho, Themistocles M RassiasAbstract:Recently, the authors (Dong et al. in J Global Optim 73(4):801–824, 2019) introduced the multi-step inertial Krasnosel’skiǐ–Mann iteration, where the inertial parameters involve the iterative sequence. Therefore, one has to compute the inertial parameters per iteration. The aim of this article is to present two kinds of inertial parameter arrays which do not depend on the iterative sequence. We first introduce a general Krasnosel’skiǐ–Mann iteration on the affine hull of orbits, based on which one inertial parameter array is presented. Second, we investigate the other inertial parameter array by introducing a modified Krasnosel’skii-Mann iteration. The convergence of the modified Krasnosel’skiǐ–Mann iteration is shown using an exhaustive convergence analysis and the running-average iteration-complexity bound is provided. Finally, we give two numerical examples to illustrate that the multi-step inertial Krasnosel’skiǐ–Mann iteration with inertial parameters proposed in this article behaves better than that with inertial parameters given in [10].
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convergence theorems and convergence rates for the general inertial Krasnosel skiǐ mann algorithm
2021Co-Authors: Qiaoli Dong, Yeol Je Cho, Themistocles M RassiasAbstract:The authors [13] introduced a general inertial Krasnosel’skiǐ–Mann algorithm: $$ \left\{ \begin{aligned}&y_n=x_n+\alpha _n(x_n-x_{n-1}),\\&z_n=x_n+\beta _n(x_n-x_{n-1}),\\&x_{n+1}=(1-\lambda _n)y_n+\lambda _nT(z_n) \end{aligned} \right. $$ for each \(n\ge 1\) and showed its convergence with the control conditions \(\alpha _n,\beta _n\in [0,1).\) In this paper, we present the convergence analysis of the general inertial Krasnosel’skiǐ–Mann algorithm with the control conditions \(\alpha _n\in [0,1]\), \(\beta _n\in (-\infty ,0]\) and \(\alpha _n\in [-1,0]\), \(\beta _n\in [0,+\infty )\), respectively. Also, we provide the convergence rate for the general inertial Krasnosel’skiǐ–Mann algorithm under mild conditions on the inertial parameters and some conditions on the relaxation parameters, respectively. Finally, we show that a numerical experiment provided compares the choice of inertial parameters.
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inertial Krasnosel skiǐ mann type hybrid algorithms for solving hierarchical fixed point problems
Journal of Fixed Point Theory and Applications, 2019Co-Authors: Qiaoli Dong, K R Kazmi, Rehan AliAbstract:In this paper, we suggest two inertial Krasnosel’skiǐ–Mann type hybrid algorithms to approximate a solution of a hierarchical fixed point problem for nonexpansive mappings in Hilbert space. We prove strong convergence theorems for these algorithms and the conditions of the convergence are very weak comparing other algorithms for the hierarchical fixed point problems. Further, we derive some consequences from the main results. Finally, we present two academic numerical examples for comparing these two algorithms with the algorithm in Dong et al. (J Fixed Point Theory A 19(4):3097–3118, 2017), which illustrate the advantage of the proposed algorithms. The methods and results presented in this paper generalize and unify previously known corresponding methods and results of this area.
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mikm multi step inertial Krasnosel skiǐ mann algorithm and its applications
Journal of Global Optimization, 2019Co-Authors: Qiaoli Dong, Jizu Huang, Yeol Je Cho, Themistocles M RassiasAbstract:In this paper, we first introduce a multi-step inertial Krasnosel’skiǐ–Mann algorithm (MiKM) for nonexpansive operators in real Hilbert spaces. We give the convergence of the MiKM by investigating the convergence of the Krasnosel’skiǐ–Mann algorithm with perturbations. We also establish global pointwise and ergodic iteration complexity bounds of the Krasnosel’skiǐ–Mann algorithm with perturbations. Based on the MiKM, we construct some multi-step inertial splitting methods, including the multi-step inertial Douglas–Rachford splitting method (MiDRS), the multi-step inertial forward–backward splitting method, multi-step inertial backward–forward splitting method and and the multi-step inertial Davis–Yin splitting method. Numerical experiments are provided to illustrate the advantage of the MiDRS over the one-step inertial DRS and the original DRS.
Mohamedaziz Taoudi - One of the best experts on this subject based on the ideXlab platform.
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new monch Krasnosel skii type fixed point theorems applied to solve neutral partial integrodifferential equations without compactness
Journal of Fixed Point Theory and Applications, 2020Co-Authors: Khalil Ezzinbi, Saifeddine Ghnimi, Mohamedaziz TaoudiAbstract:In this paper, we show the existence of mild solutions for a class of neutral partial integrodifferential equations with lack of compactness. The results are obtained using noncompact resolvent operators and a new fixed point theorem of Monch-Krasnosel’skii type. Our results are applied to a large variety of partial differential equations in which memory effects are considered. An example is provided at the end of the paper to illustrate the main results of this work.
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Krasnosel skii type fixed point theorems for convex power condensing mappings in locally convex spaces
Journal of Fixed Point Theory and Applications, 2017Co-Authors: Abdelmjid Khchine, Lahcen Maniar, Mohamedaziz TaoudiAbstract:In this paper, we prove some fixed point theorems for the sum $$T+S$$ of two nonlinear mappings acting on a locally convex space, where S is a contraction (nonexpansive or expansive) and T is S-convex-power condensing. Our fixed point results extend several earlier works. As an application, we investigate the solvability of a class of nonlinear Volterra integral equations in locally convex spaces.
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weakly noncompact fixed point results of the schauder and the Krasnosel skii type
Mediterranean Journal of Mathematics, 2014Co-Authors: Mohamedaziz Taoudi, Tian XiangAbstract:Invoking the technique of measures of weak noncompactness in Banach spaces, we establish some generalized fixed point results of the Schauder and Krasnoselskii type in the context that the involved operators are not weakly compact. It is shown that the obtained results encompass and extend a number of previously known generalizations of the quoted theorems. Finally, an application is presented to illustrate the results.
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Krasnosel skii type fixed point theorems with applications to volterra integral equations
Fixed Point Theory and Applications, 2013Co-Authors: Nawab Hussain, Mohamedaziz TaoudiAbstract:In this paper we present some fixed point results for the sum of two mappings where S is a strict contraction and T is not necessarily weakly compact and satisfies a new condition formulated in terms of an axiomatic measure of weak noncompactness. Our fixed point results extend and improve several earlier results in the literature. In particular, our results encompass the analogues of Krasnosel’skii’s and Sadovskii’s fixed point theorems for sequentially weakly continuous mappings and a number of their generalizations. Finally, an application to integral equations is given to illustrate the usability of the obtained results. MSC:37C25, 40D05, 31B10.
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Krasnosel skii type fixed point theorems under weak topology features
Nonlinear Analysis-theory Methods & Applications, 2010Co-Authors: Mohamedaziz TaoudiAbstract:Abstract In this paper we prove the following Krasnosel’skii type fixed point theorem: Let M be a nonempty bounded closed convex subset of a Banach space X . Suppose that A : M → X and B : X → X are two weakly sequentially continuous mappings satisfying: (i) A M is relatively weakly compact; (ii) B is a strict contraction; (iii) ( x = B x + A y , y ∈ M ) ⇒ x ∈ M . Then A + B has at least one fixed point in M . This result is then used to obtain some new fixed point theorems for the sum of a weakly compact and a nonexpansive mapping. The results presented in this paper encompass several earlier ones in the literature.
Themistocles M Rassias - One of the best experts on this subject based on the ideXlab platform.
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multi step inertial Krasnosel skiǐ mann iteration with new inertial parameters arrays
Journal of Fixed Point Theory and Applications, 2021Co-Authors: Qiaoli Dong, Yeol Je Cho, Themistocles M RassiasAbstract:Recently, the authors (Dong et al. in J Global Optim 73(4):801–824, 2019) introduced the multi-step inertial Krasnosel’skiǐ–Mann iteration, where the inertial parameters involve the iterative sequence. Therefore, one has to compute the inertial parameters per iteration. The aim of this article is to present two kinds of inertial parameter arrays which do not depend on the iterative sequence. We first introduce a general Krasnosel’skiǐ–Mann iteration on the affine hull of orbits, based on which one inertial parameter array is presented. Second, we investigate the other inertial parameter array by introducing a modified Krasnosel’skii-Mann iteration. The convergence of the modified Krasnosel’skiǐ–Mann iteration is shown using an exhaustive convergence analysis and the running-average iteration-complexity bound is provided. Finally, we give two numerical examples to illustrate that the multi-step inertial Krasnosel’skiǐ–Mann iteration with inertial parameters proposed in this article behaves better than that with inertial parameters given in [10].
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convergence theorems and convergence rates for the general inertial Krasnosel skiǐ mann algorithm
2021Co-Authors: Qiaoli Dong, Yeol Je Cho, Themistocles M RassiasAbstract:The authors [13] introduced a general inertial Krasnosel’skiǐ–Mann algorithm: $$ \left\{ \begin{aligned}&y_n=x_n+\alpha _n(x_n-x_{n-1}),\\&z_n=x_n+\beta _n(x_n-x_{n-1}),\\&x_{n+1}=(1-\lambda _n)y_n+\lambda _nT(z_n) \end{aligned} \right. $$ for each \(n\ge 1\) and showed its convergence with the control conditions \(\alpha _n,\beta _n\in [0,1).\) In this paper, we present the convergence analysis of the general inertial Krasnosel’skiǐ–Mann algorithm with the control conditions \(\alpha _n\in [0,1]\), \(\beta _n\in (-\infty ,0]\) and \(\alpha _n\in [-1,0]\), \(\beta _n\in [0,+\infty )\), respectively. Also, we provide the convergence rate for the general inertial Krasnosel’skiǐ–Mann algorithm under mild conditions on the inertial parameters and some conditions on the relaxation parameters, respectively. Finally, we show that a numerical experiment provided compares the choice of inertial parameters.
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mikm multi step inertial Krasnosel skiǐ mann algorithm and its applications
Journal of Global Optimization, 2019Co-Authors: Qiaoli Dong, Jizu Huang, Yeol Je Cho, Themistocles M RassiasAbstract:In this paper, we first introduce a multi-step inertial Krasnosel’skiǐ–Mann algorithm (MiKM) for nonexpansive operators in real Hilbert spaces. We give the convergence of the MiKM by investigating the convergence of the Krasnosel’skiǐ–Mann algorithm with perturbations. We also establish global pointwise and ergodic iteration complexity bounds of the Krasnosel’skiǐ–Mann algorithm with perturbations. Based on the MiKM, we construct some multi-step inertial splitting methods, including the multi-step inertial Douglas–Rachford splitting method (MiDRS), the multi-step inertial forward–backward splitting method, multi-step inertial backward–forward splitting method and and the multi-step inertial Davis–Yin splitting method. Numerical experiments are provided to illustrate the advantage of the MiDRS over the one-step inertial DRS and the original DRS.
Yeol Je Cho - One of the best experts on this subject based on the ideXlab platform.
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multi step inertial Krasnosel skiǐ mann iteration with new inertial parameters arrays
Journal of Fixed Point Theory and Applications, 2021Co-Authors: Qiaoli Dong, Yeol Je Cho, Themistocles M RassiasAbstract:Recently, the authors (Dong et al. in J Global Optim 73(4):801–824, 2019) introduced the multi-step inertial Krasnosel’skiǐ–Mann iteration, where the inertial parameters involve the iterative sequence. Therefore, one has to compute the inertial parameters per iteration. The aim of this article is to present two kinds of inertial parameter arrays which do not depend on the iterative sequence. We first introduce a general Krasnosel’skiǐ–Mann iteration on the affine hull of orbits, based on which one inertial parameter array is presented. Second, we investigate the other inertial parameter array by introducing a modified Krasnosel’skii-Mann iteration. The convergence of the modified Krasnosel’skiǐ–Mann iteration is shown using an exhaustive convergence analysis and the running-average iteration-complexity bound is provided. Finally, we give two numerical examples to illustrate that the multi-step inertial Krasnosel’skiǐ–Mann iteration with inertial parameters proposed in this article behaves better than that with inertial parameters given in [10].
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convergence theorems and convergence rates for the general inertial Krasnosel skiǐ mann algorithm
2021Co-Authors: Qiaoli Dong, Yeol Je Cho, Themistocles M RassiasAbstract:The authors [13] introduced a general inertial Krasnosel’skiǐ–Mann algorithm: $$ \left\{ \begin{aligned}&y_n=x_n+\alpha _n(x_n-x_{n-1}),\\&z_n=x_n+\beta _n(x_n-x_{n-1}),\\&x_{n+1}=(1-\lambda _n)y_n+\lambda _nT(z_n) \end{aligned} \right. $$ for each \(n\ge 1\) and showed its convergence with the control conditions \(\alpha _n,\beta _n\in [0,1).\) In this paper, we present the convergence analysis of the general inertial Krasnosel’skiǐ–Mann algorithm with the control conditions \(\alpha _n\in [0,1]\), \(\beta _n\in (-\infty ,0]\) and \(\alpha _n\in [-1,0]\), \(\beta _n\in [0,+\infty )\), respectively. Also, we provide the convergence rate for the general inertial Krasnosel’skiǐ–Mann algorithm under mild conditions on the inertial parameters and some conditions on the relaxation parameters, respectively. Finally, we show that a numerical experiment provided compares the choice of inertial parameters.
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mikm multi step inertial Krasnosel skiǐ mann algorithm and its applications
Journal of Global Optimization, 2019Co-Authors: Qiaoli Dong, Jizu Huang, Yeol Je Cho, Themistocles M RassiasAbstract:In this paper, we first introduce a multi-step inertial Krasnosel’skiǐ–Mann algorithm (MiKM) for nonexpansive operators in real Hilbert spaces. We give the convergence of the MiKM by investigating the convergence of the Krasnosel’skiǐ–Mann algorithm with perturbations. We also establish global pointwise and ergodic iteration complexity bounds of the Krasnosel’skiǐ–Mann algorithm with perturbations. Based on the MiKM, we construct some multi-step inertial splitting methods, including the multi-step inertial Douglas–Rachford splitting method (MiDRS), the multi-step inertial forward–backward splitting method, multi-step inertial backward–forward splitting method and and the multi-step inertial Davis–Yin splitting method. Numerical experiments are provided to illustrate the advantage of the MiDRS over the one-step inertial DRS and the original DRS.
Rosana Rodriguezlopez - One of the best experts on this subject based on the ideXlab platform.
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Krasnosel skii type compression expansion fixed point theorem for set contractions and star convex sets
Journal of Fixed Point Theory and Applications, 2020Co-Authors: Cristina Loisprados, Radu Precup, Rosana RodriguezlopezAbstract:In this paper, we give or improve compression-expansion results for set contractions in conical domains determined by balls or star convex sets. In the compression case, we use Potter’s idea of proof, while the expansion case is reduced to the compression one by means of a change of variable. Finally, to illustrate the theory, we give an application to the initial value problem for a system of implicit first order differential equations.
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a generalization of Krasnosel skii compression fixed point theorem by using star convex sets
Proceedings of The Royal Society A: Mathematical Physical and Engineering Sciences, 2020Co-Authors: Cristina Loisprados, Rosana RodriguezlopezAbstract:In the framework of fixed point theory, many generalizations of the classical results due to Krasnosel'skii are known. One of these extensions consists in relaxing the conditions imposed on the mapping, working with k-set contractions instead of continuous and compact maps. The aim of this work if to study in detail some fixed point results of this type, and obtain a certain generalization by using star convex sets.
