Dynamical inertial extragradient techniques for solving equilibrium and fixed-point problems in real Hilbert spaces

Panyanak, Bancha; Khunpanuk, Chainarong; Pholasa, Nattawut; Pakkaranang, Nuttapol

doi:10.1186/s13660-023-02912-6

Cited by 4 publications

(2 citation statements)

References 38 publications

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“…For some other recent results on this topic, we refer to Abkar and Tavakkoli [121], Abkar and Shekarbaigi [122], Yao et al [123], Hanjing and Suantai [60], Ogbuisi and Isiogugu [124], Hanjing et al [125], Panyanak et al [126], and Vuong et al [127].…”

Section: Equilibrium Problemsmentioning

confidence: 99%

Single-Valued Demicontractive Mappings: Half a Century of Developments and Future Prospects

Berinde

2023

Symmetry

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Demicontractive operators form an important class of nonexpansive type mappings whose study led researchers to the creation of some beautiful results in the framework of metric fixed-point theory. This article aims to provide an overview of the most relevant results on the approximation of fixed points of single-valued demicontractive mappings in Hilbert spaces. Subsequently, we exhibit the role of additional properties of demicontractive operators, as well as the main features of the employed iterative algorithms to ensure weak convergence or strong convergence. We also include commentaries on the use of demicontractive mappings to solve some important nonlinear problems with the aim of providing a comprehensive starting point to readers who are attempting to apply demicontractive mappings to concrete applications. We conclude with some brief statements on our view on relevant and promising directions of research on demicontractive mappings in nonlinear settings (metric spaces) and some application challenges.

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Section: Equilibrium Problemsmentioning

confidence: 99%

Single-Valued Demicontractive Mappings: Half a Century of Developments and Future Prospects

Berinde

2023

Symmetry

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“…The algorithm is defined in such a way that the next iterate is obtained by making use of the previous two iterates. Recently, many fast convergence algorithms have been developed and studied by various researchers using the inertial extrapolation techniques; see, for example, previous studies [39][40][41].…”

Section: Introductionmentioning

confidence: 99%

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

Ahmad,

Kumam,

Harbau

et al. 2024

Math Methods in App Sciences

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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 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.

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Subgradient Extragradient Method for Finite Lipschitzian Demicontractions and Variational Inequality Problems in a Hilbert Space

Suwannaut

2024

Journal of Mathematics

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In this research, the modified subgradient extragradient method and K-mapping generated by a finite family of finite Lipschitzian demicontractions are introduced. Then, a strong convergence theorem for finding a common element of the common fixed point set of finite Lipschitzian demicontraction mappings and the common solution set of variational inequality problems is established. Furthermore, numerical examples are given to support the main theorem.

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Dynamical inertial extragradient techniques for solving equilibrium and fixed-point problems in real Hilbert spaces

Cited by 4 publications

References 38 publications

Single-Valued Demicontractive Mappings: Half a Century of Developments and Future Prospects

Single-Valued Demicontractive Mappings: Half a Century of Developments and Future Prospects

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

Subgradient Extragradient Method for Finite Lipschitzian Demicontractions and Variational Inequality Problems in a Hilbert Space

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