Nonlinear Functional Analysis and Applications

  • 제27권1호
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  • Pages.121-140
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  • 2022
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  • 1229-1595(pISSN)
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  • 2466-0973(eISSN)
경남대학교 수학교육과 (Kyungnam University, Department of Mathematics Eduaction)
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HALPERN TSENG'S EXTRAGRADIENT METHODS FOR SOLVING VARIATIONAL INEQUALITIES INVOLVING SEMISTRICTLY QUASIMONOTONE OPERATOR

  • Wairojjana, Nopparat (Applied Mathematics Program, Faculty of Science and Technology Valaya Alongkorn Rajabhat University under the Royal Patronage (VRU)) ;
  • Pakkaranang, Nuttapol (Mathematics and Computing Science Program, Faculty of Science and Technology Phetchabun Rajabhat University)
  • 투고 : 2021.05.27
  • 심사 : 2021.11.06
  • 발행 : 2022.03.15
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⟨ 이전 논문 다음 논문 ⟩

초록

In this paper, we study the strong convergence of new methods for solving classical variational inequalities problems involving semistrictly quasimonotone and Lipschitz-continuous operators in a real Hilbert space. Three proposed methods are based on Tseng's extragradient method and use a simple self-adaptive step size rule that is independent of the Lipschitz constant. The step size rule is built around two techniques: the monotone and the non-monotone step size rule. We establish strong convergence theorems for the proposed methods that do not require any additional projections or knowledge of an involved operator's Lipschitz constant. Finally, we present some numerical experiments that demonstrate the efficiency and advantages of the proposed methods.

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과제정보

Nuttapol Pakkaranang was partially financial supported by Phetchabun Rajabhat University.

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