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JOURNAL OF NONLINEAR FUNCTIONAL ANALYSIS 2025年 2025卷

作者： Feng, Yuting Wang, Yaqin Shaoxing Univ Dept Math Shaoxing Peoples R China

In this paper, we introduce a self-adaptive inertial iterative algorithm for solving a split null point problem with maximal monotone operators and a common fixed point problem of a finite family of multivaluted demicontractive mappings and an infinite family of strict pseudo-contractive mappings between a Banach space and a Hilbert space. Next, we prove a strong convergence result for the proposed algorithm under some mild conditions on the control parameters without a priori estimate of the norm of the linear operator involved. Then, we give a numerical example to illustrate the effectiveness of the algorithm.

关键词： Demicontractive mapping inertial algorithm Priori estimate Split null point Strict pseudocontractive mapping

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inertial algorithm with self-adaptive step size for split common null point and common fixed point problems for multivalued mappings in Banach spaces

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OPTIMIZATION 2022年第10期71卷 3041-3075页

作者： Alakoya, T. O. Jolaoso, L. O. Taiwo, A. Mewomo, O. T. Univ KwaZulu Natal Sch Math Stat & Comp Sci Durban South Africa DST NRF Ctr Excellence Math & Stat Sci CoE MaSS Johannesburg South Africa

In this article we introduce an inertial iterative scheme with self-adaptive step size for finding a common solution of split common null point problem for a finite family of maximal monotone operators and fixed point problem for a finite family of multivalued demicontractive mappings between a Banach space and Hilbert space. Strong convergence result is obtained for the proposed algorithm. The self-adaptive step size ensures no requirement for a prior knowledge or estimate of the norm of the operator. The inertial term introduced in the algorithm is efficient, it helps to avoid imposing some strong conditions usually used for inertial-type algorithms by many authors. We give some applications of our results to game theory, split equilibrium and minimum-norm problems. Numerical experiment is also presented to demonstrate the efficiency of our proposed method as well as comparing with other existing method in the literature. Our results improve and generalize many well known results in this direction in the literature.

关键词： Split common null point inertial algorithm self-adaptive multivalued mappings demicontractive mappings strong convergence

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inertial algorithm for approximating a common fixed point for a countable family of relatively nonexpansive maps

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Fixed Point Theory and Applications 2018年第1期2018卷 1-9页

作者： Chidume, C.E. Ikechukwu, S.I. Adamu, A. African University of Science and Technology Abuja Nigeria

In this paper, we study an inertial algorithm for approximating a common fixed point for a countable family of relatively nonexpansive maps in a uniformly convex and uniformly smooth real Banach space. We prove a strong convergence theorem. This theorem is an improvement of the result of Matsushita and Takahashi (J. Approx. Theory 134:257–266, 2005) and the result of Dong et al. (Optim. Lett. 12:87–102, 2018). Finally, we give some applications of our theorem. © 2018, The Author(s).

关键词： Generalised projection inertial algorithm Relatively nonexpansive maps Strong convergence

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Convergence rates for an inertial algorithm of gradient type associated to a smooth non-convex minimization

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MATHEMATICAL PROGRAMMING 2021年第1-2期190卷 285-329页

作者： Laszlo, Szilard Csaba Tech Univ Cluj Napoca Dept Math Str Memorandumului 28 Cluj Napoca 400114 Romania

We investigate an inertial algorithm of gradient type in connection with the minimization of a non-convex differentiable function. The algorithm is formulated in the spirit of Nesterov's accelerated convex gradient method. We prove some abstract convergence results which applied to our numerical scheme allow us to show that the generated sequences converge to a critical point of the objective function, provided a regularization of the objective function satisfies the Kurdyka-Lojasiewicz property. Further, we obtain convergence rates for the generated sequences and the objective function values formulated in terms of the Lojasiewicz exponent of a regularization of the objective function. Finally, some numerical experiments are presented in order to compare our numerical scheme and some algorithms well known in the literature.

关键词： inertial algorithm Non-convex optimization Kurdyka-Lojasiewicz inequality Convergence rate Lojasiewicz exponent

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inertial hybrid algorithm for generalized mixed equilibrium problems, zero problems, and fixed points of some nonlinear mappings in the intermediate sense

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MATHEMATICAL METHODS IN THE APPLIED SCIENCES 2024年第11期47卷 8527-8550页

作者： Ahmad, Abdulwahab Kumam, Poom Harbau, Murtala Haruna Sitthithakerngkiet, Kanokwan King Mongkuts Univ Technol Thonburi KMUTT Fac Sci Ctr Excellence Theoret & Computat Sci TaCS CoE Bangkok Thailand King Mongkuts Univ Technol Thonburi KMUTT Fac Sci Dept Math Fixed Point Res Lab Bangkok Thailand Fed Coll Educ Sch Secondary Educ Dept Math Sci Katsina Nigeria Bayero Univ Fac Educ Dept Sci & Technol Educ Kano Nigeria King Mongkuts Univ Technol North Bangkok KMUTNB Fac Appl Sci Intelligent & Nonlinear Dynam Innovat Res Ctr Dept Math Bangkok Thailand King Mongkuts Univ Technol Thonburi KMUTT Fac Sci Ctr Excellence Theoret & Computat Sci TaCS CoE Room SCL 802Sci Lab Bldg126 Pracha Uthit Rd Thun Bangkok 10140 Thailand King Mongkuts Univ Technol Thonburi KMUTT Fac Sci Dept Math Fixed Point Res Lab Room SCL 802Sci Lab Bldg126 Pracha Uthit Rd Thun Bangkok 10140 Thailand

In this work, we establish the closedness and convexity of the set of fixed points of equally continuous and asymptotically demicontractive mapping in the intermediate sense. We proposed an inertial hybrid projection technique for determining an approximate common solution to three significant problems. The first is the system of generalized mixed equilibrium problems with relaxed eta-zeta$$ \eta -\zeta $$ monotone mappings, the second is the problem of fixed points of a countable family of equally continuous and asymptotically demicontractive mappings in the intermediate sense, and the third is of determining a point in a null space of a countable family of inverse strongly monotone mappings in Hilbert space. Based on these problems, we formulate a theorem and establish its strong convergence to their common solution. Additionally, we studied the applications of our algorithm to variational inequality problems and convex optimization problems. Finally, we numerically demonstrate the efficiency and robustness of our scheme. Several results available in the literature can be obtained as special cases of our result.

关键词： asymptotically demicontractive map in the intermediate sense equilibrium problems fixed point problems hybrid projection algorithms inertial algorithm relaxed monotone mapping zeros problems

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Hybrid inertial proximal algorithm for the split variational inclusion problem in Hilbert spaces with applications

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OPTIMIZATION 2017年第5期66卷 777-792页

作者： Chuang, Chih-Sheng Natl Chiayi Univ Dept Appl Math Chiayi Taiwan

In this paper, we present hybrid inertial proximal algorithms for the split variational inclusion problems in Hilbert spaces, and provide convergence theorems for the proposed algorithms. In fact, an inertial type algorithm was proposed as an acceleration process. As application, we study split minimization problem, split feasibility problem, relaxed split feasibility problem and linear inverse problem in real Hilbert spaces. Finally, numerical results are given for our main results.

关键词： Variational inclusion problem inertial algorithm resolvent mapping linear inverse problem split feasibility problem

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An inertial-type algorithm for approximation of solutions of Hammerstein integral inclusions in Hilbert spaces

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FIXED POINT THEORY AND algorithmS FOR SCIENCES AND ENGINEERING 2021年第1期2021卷 1-22页

作者： Bello, A. U. Omojola, M. T. Yahaya, J. African Univ Sci & Technol Abuja Nigeria Fed Univ Dutsinma Dutsinma Katsina State Nigeria Ahmadu Bello Univ Zaria Kaduna State Nigeria

Let H be a real Hilbert space. Let F:H -> 2H\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$F:H\rightarrow 2<^>{H}$\end{document} and K:H -> 2H\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$K:H\rightarrow 2<^>{H}$\end{document} be two maximal monotone and bounded operators. Suppose the Hammerstein inclusion 0 is an element of u+KFu\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$0\in u+KFu$\end{document} has a solution. We construct an inertial-type algorithm and show its strong convergence to a solution of the inclusion. As far as we know, this is the first inertial-type algorithm for Hammerstein inclusions in Hilbert spaces. We also give numerical examples to compare the new algorithm with some existing ones in the literature.

关键词： Maximal monotone maps Hammerstein integral inclusion inertial algorithm

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An inertial viscosity algorithm for solving monotone variational inclusion and common fixed point problems of strict pseudocontractions

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BOLETIN DE LA SOCIEDAD MATEMATICA MEXICANA 2023年第2期29卷 1-31页

作者： Alakoya, T. O. Ogunsola, O. J. Mewomo, O. T. Univ KwaZulu Natal Sch Math Stat & Comp Sci Durban South Africa Fed Univ Agr Abeokuta Nigeria

In this paper, we study the problem of finding the solution of monotone variational inclusion problem (MVIP) with constraint of common fixed point problem (CFPP) of strict pseudocontractions. We propose a new viscosity method, which combines the inertial technique with self-adaptive step size strategy for approximating the solution of the problem in the framework of Hilbert spaces. Unlike several of the existing results in the literature, our proposed method does not require the co-coerciveness and Lipschitz continuity assumptions of the associated single-valued operator. Also, our method does not involve any linesearch technique which could be time-consuming, rather we employ a self-adaptive step size technique that generates a nonmonotonic sequence of step sizes. Moreover, we prove strong convergence result for our algorithm under some mild conditions and apply our result to study other optimization problems. We present several numerical experiments to demonstrate the computational advantage of our proposed method over the existing methods in the literature. Our result complements several of the existing results in the current literature in this direction.

关键词： Variational inclusion problem inertial algorithm Self-adaptive step size Strict pseudocontractive mapping Strong convergence

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An inertial-viscosity algorithm for solving split generalized equilibrium problem and a system of demimetric mappings in Hilbert spaces

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RENDICONTI DEL CIRCOLO MATEMATICO DI PALERMO 2023年第3期72卷 1599-1628页

作者： Aphane, Maggie Jolaoso, Lateef Olakunle Aremu, Kazeem Olalekan Oyewole, Olawale Kazeem Sefako Makgatho Hlth Sci Univ POB 60 ZA-0204 Pretoria South Africa Fed Univ Agr Dept Math Abeokuta Ogun State Nigeria Usmanu Danfodiyo Univ Sokoto Dept Math Sokoto Sokoto State Nigeria Technion Israel Inst Technol Dept Math Haifa Israel

In this paper, we introduce a new inertial-viscosity approximation method for solving a split generalized equilibrium problem and common fixed point problem in real Hilbert spaces. The algorithm is designed such that its convergence does not require the norm of the bounded linear operator underlying the split equilibrium problem. Moreover, a strong convergence result is proved under mild conditions in real Hilbert spaces. Furthermore, we give some numerical examples to show the efficiency and accuracy of the proposed method and we also compare the performance of our algorithm with other related methods in the literature.

关键词： Split equilibrium problem inertial algorithm Demimetric mappings Monotone operator

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VISCOSITY APPROXIMATION OF A MODIFIED inertial SIMULTANEOUS algorithm FOR A FINITE FAMILY OF DEMICONTRACTIVE MAPPINGS

JOURNAL OF NONLINEAR FUNCTIONAL ANALYSIS

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JOURNAL OF NONLINEAR FUNCTIONAL ANALYSIS 2023年 2023卷

作者： Ying, Yike Huang, Lu Zhang, Yuanqin Wang, Yaqin Shaoxing Univ Dept Math Shaoxing 312000 Peoples R China

In this paper, we propose a new modified inertial simultaneous algorithm of common fixed point prob-lems for a finite family of demicontractive mappings and obtain some strong convergence results in real Hilbert spaces. Meanwhile, we also give a numerical example to demonstrate the efficiency of our proposed algorithm. Our results improve and extend some corresponding known results.

关键词： Keywords. Demicontractive mapping inertial algorithm Numerical example Split common fixed point problem Viscosity approximation.

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