Results 11 to 20 of about 45 (45)
On capacity and torsional rigidity
Bulletin of the London Mathematical Society, Volume 53, Issue 2, Page 347-359, April 2021., 2021 Abstract We investigate extremal properties of shape functionals which are products of Newtonian capacity cap(Ω¯), and powers of the torsional rigidity T(Ω), for an open set Ω⊂Rd with compact closure Ω¯, and prescribed Lebesgue measure. It is shown that if Ω is convex, then cap(Ω¯)Tq(Ω) is (i) bounded from above if and only if q⩾1, and (ii) bounded ...
M. van den Berg, G. Buttazzo
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Iterative approximation of a solution of a general variational‐like inclusion in Banach spaces
International Journal of Mathematics and Mathematical Sciences, Volume 2004, Issue 22, Page 1159-1168, 2004., 2004 We introduce a class of η‐accretive mappings in a real Banach space and show that the η‐proximal point mapping for η‐m‐accretive mapping is Lipschitz continuous. Further, we develop an iterative algorithm for a class of general variational‐like inclusions involving η‐accretive mappings in real Banach space, and discuss its convergence criteria.
C. E. Chidume, K. R. Kazmi, H. Zegeye
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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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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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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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KKM theorem with applications to lower and upper bounds equilibrium problem in G‐convex spaces
International Journal of Mathematics and Mathematical Sciences, Volume 2003, Issue 51, Page 3267-3276, 2003., 2003 We give some new versions of KKM theorem for generalized convex spaces. As an application, we answer a question posed by Isac et al. (1999) for the lower and upper bounds equilibrium problem.
M. Fakhar, J. Zafarani
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Existence results for general inequality problems with constraints
Abstract and Applied Analysis, Volume 2003, Issue 10, Page 601-619, 2003., 2003 This paper is concerned with existence results for inequality problems of type F0(u; v) + Ψ′(u; v) ≥ 0, for all v ∈ X, where X is a Banach space, F : X → ℝ is locally Lipschitz, and Ψ : X → (−∞ + ∞] is proper, convex, and lower semicontinuous. Here F0 stands for the generalized directional derivative of F and Ψ′ denotes the directional derivative of Ψ.
George Dincă +2 more
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Completely generalized multivalued nonlinear quasi‐variational inclusions
International Journal of Mathematics and Mathematical Sciences, Volume 30, Issue 10, Page 593-604, 2002., 2002 We introduce and study a new class of completely generalized multivalued nonlinear quasi‐variational inclusions. Using the resolvent operator technique for maximal monotone mappings, we suggest two kinds of iterative algorithms for solving the completely generalized multivalued nonlinear quasi‐variational inclusions.
Zeqing Liu +3 more
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Mixed variational inequalities and economic equilibrium problems
Journal of Applied Mathematics, Volume 2, Issue 6, Page 289-314, 2002., 2002 We consider rather broad classes of general economic equilibrium problems and oligopolistic equilibrium problems which can be formulated as mixed variational inequality problems. Such problems involve a continuous mapping and a convex, but not necessarily differentiable function. We present existence and uniqueness results of solutions under weakened P‐
I. V. Konnov, E. O. Volotskaya
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Evolutionary quasi-variational and variational inequalities with constraints on the derivatives
Advances in Nonlinear Analysis, 2018 This paper considers a general framework for the study of the existence of quasi-variational and variational solutions to a class of nonlinear evolution systems in convex sets of Banach spaces describing constraints on a linear combination of partial ...
Miranda Fernando +2 more
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