Results 21 to 30 of about 805 (130)
On variational nonlinear equations with monotone operators
Advances in Nonlinear Analysis, 2020 Using monotonicity methods and some variational argument we consider nonlinear problems which involve monotone potential mappings satisfying condition (S) and their strongly continuous perturbations.
Galewski Marek
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Mixed quasi invex equilibrium problems
International Journal of Mathematics and Mathematical Sciences, Volume 2004, Issue 57, Page 3057-3067, 2004., 2004 We introduce a new class of equilibrium problems, known as mixed quasi invex equilibrium (or equilibrium-like) problems. This class of invex equilibrium problems includes equilibrium problems, variational inequalities, and variational‐like inequalities as special cases.
Muhammad Aslam Noor
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International Journal of Mathematics and Mathematical Sciences, Volume 2004, Issue 70, Page 3849-3857, 2004., 2004 We introduce and study a class of general quasivariational‐like inequalities in Hilbert spaces, suggest two general algorithms, and establish the existence and uniqueness of solutions for these kinds of inequalities. Under certain conditions, we discuss convergence and stability of the three‐step iterative sequences generated by the algorithms.
Zeqing Liu +3 more
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Partially relaxed cocoercive variational inequalities and auxiliary problem principle
International Journal of Stochastic Analysis, Volume 2004, Issue 2, Page 143-148, 2004., 2004 Let T : K → H be a mapping from a nonempty closed convex subset K of a finite‐dimensional Hilbert space H into H. Let f : K → ℝ be proper, convex, and lower semicontinuous on K and let h : K → ℝ be continuously Frećhet‐differentiable on K with h′ (gradient of h), α‐strongly monotone, and β‐Lipschitz continuous on K.
Ram U. Verma
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International Journal of Stochastic Analysis, Volume 2004, Issue 3, Page 235-244, 2004., 2004 We consider a new class of equilibrium problems, known as hemiequilibrium problems. Using the auxiliary principle technique, we suggest and analyze a class of iterative algorithms for solving hemiequilibrium problems, the convergence of which requires either pseudomonotonicity or partially relaxed strong monotonicity. As a special case, we obtain a new
Muhammad Aslam Noor
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On some inequalities for relative semi-convex functions
, 2013 We consider and study a new class of convex functions that are called relative semi-convex functions. Some Hermite-Hadamard inequalities for the relative semi-convex function and its variant forms are derived.
M. Noor, M. U. Awan, K. Noor
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A‐monotonicity and applications to nonlinear variational inclusion problems
International Journal of Stochastic Analysis, Volume 2004, Issue 2, Page 193-195, 2004., 2004 A new notion of the A‐monotonicity is introduced, which generalizes the H‐monotonicity. Since the A‐monotonicity originates from hemivariational inequalities, and hemivariational inequalities are connected with nonconvex energy functions, it turns out to be a useful tool proving the existence of solutions of nonconvex constrained problems as well.
Ram U. Verma
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, 2012 Recently, Colao et al. (J Math Anal Appl 344:340-352, 2008) introduced a hybrid viscosity approximation method for finding a common element of the set of solutions of an equilibrium problem and the set of fixed points of a finite family of nonexpansive ...
L. Ceng, S. Guu, Jen-Chih Yao
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Nonlinear variational inequalities on reflexive Banach spaces and topological vector spaces
International Journal of Mathematics and Mathematical Sciences, Volume 2003, Issue 4, Page 199-207, 2003., 2003 The purpose of this paper is to introduce and study a class of nonlinear variational inequalities in reflexive Banach spaces and topological vector spaces. Based on the KKM technique, the solvability of this kind of nonlinear variational inequalities is presented.
Zeqing Liu +2 more
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Optimal control for cooperative systems involving fractional Laplace operators
Journal of Inequalities and Applications, 2021 In this work, the elliptic 2 × 2 $2\times 2$ cooperative systems involving fractional Laplace operators are studied. Due to the nonlocality of the fractional Laplace operator, we reformulate the problem into a local problem by an extension problem. Then,
H. M. Serag +2 more
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