Approximation of zeros of inverse strongly monotone operators in Banach spaces

Saejung, Satit; Yotkaew, Pongsakorn

doi:10.1016/j.na.2011.09.005

Cited by 213 publications

(41 citation statements)

References 19 publications

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“…(3.8) In the sequel from (3.5) and (3.8), we conclude that 31]). Let fs n g be a sequence of nonnegative real numbers, f˛ng be a sequence of real numbers in .0; 1/ with P 1 nD0˛n D 1 and ft n g be a sequence of real numbers.…”

Section: Halpern's Regularization Of the Em Methodsmentioning

confidence: 76%

Approximating solutions of equilibrium problems in Hadamard spaces

Khatibzadeh¹,

Mohebbi²

2019

MMN

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In this paper, we study-convergence and strong convergence of the sequence generated by the extragradient method for pseudo-monotone equilibrium problems in Hadamard spaces. We first show-convergence of the generated sequence to a solution of the equilibrium problem, then the strong convergence of Halpern regularization method is proved. Finally we give some examples where the main results can be applied.

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Section: Halpern's Regularization Of the Em Methodsmentioning

confidence: 76%

Approximating solutions of equilibrium problems in Hadamard spaces

Khatibzadeh¹,

Mohebbi²

2019

MMN

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“…Unfortunately, this constant is often unknown or difficult to approximate. Regarding this point, some stepsize rules in the related papers 43‐49 should be considered.…”

Section: Resultsmentioning

confidence: 99%

Tseng methods with inertial for solving inclusion problems and application to image deblurring and image recovery problems

Padcharoen

Kitkuan

Kumam

2020

Comp and Math Methods

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In this article, we offer two modifications of the modified forward‐backward splitting method based on inertial Tseng method and viscosity method for inclusion problems in real Hilbert spaces. Under standard assumptions, such as Lipschitz continuity and monotonicity (also maximal monotonicity), we establish weak and strong convergence of the proposed algorithms. We give the numerical experiments to show the efficiency and advantage of the proposed methods and we also used our proposed algorithm for solving the image deblurring and image recovery problems. Our result extends some related works in the literature and the primary experiments might also suggest their potential applicability.

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“…Lemma 2.4. [46] Let {a n } be the sequence of nonnegative real numbers, {α n } be sequence of real numbers in (0, 1) with ∞ n=1 α n = ∞ and {b n } be a sequence of real numbers. Assume that…”

Section: Preliminariesmentioning

confidence: 99%

Inertial method for split null point problems with pseudomonotone variational inequality problems

Okeke

Bello

Jolaoso

et al. 2022

NACO

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<p style='text-indent:20px;'>This paper analyzed the new extragradient type algorithm with inertial extrapolation step for solving self adaptive split null point problem and pseudomonotone variational inequality in real Hilbert space. Furthermore, in this study, a strong convergence result is obtained without assuming Lipschitz continuity of the associated mapping and the operator norm is self adaptive. Additionally, the proposed algorithm only uses one projections onto the feasible set in each iteration. More so, the strong convergence results are obtained under some relaxed conditions on the initial factor and the iterative parameters. Numerical results are presented to illustrate the performance of the proposed algorithm.The results obtained in this study improved and extended related studies in the literature.</p>

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Approximation of zeros of inverse strongly monotone operators in Banach spaces

Cited by 213 publications

References 19 publications

Approximating solutions of equilibrium problems in Hadamard spaces

Approximating solutions of equilibrium problems in Hadamard spaces

Tseng methods with inertial for solving inclusion problems and application to image deblurring and image recovery problems

Inertial method for split null point problems with pseudomonotone variational inequality problems

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