Variational inequalities and the principle of virtual displacements by N. A. Demyankov

“…The existence of a solution of the inclusion 0 ε A(x) + NQ(X) is provexl, in which A is a multivaluexl pseudomonotone operator from the reflexive space V to the conjugate space to it V*, NQ is a normal cone to the weakly compacct and, generally speaking, not convex set Q С V, with nonzero euler characcterization Ӽ(Q).…”
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THE WEAK DROP PROPERTY AND THE DE LA VALL´EE POUSSIN THEOREM by Hemanta Kalita

“…We prove that a closed bounded convex set is uniformly integrable if and only if it has the weak drop property. …”
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Efficiency and Generalized Convex Duality for Nondifferentiable Multiobjective Programs by Bae KwanDeok, Kang YoungMin, Kim DoSang

“…<p/> <p>We introduce nondifferentiable multiobjective programming problems involving the support function of a compact convex set and linear functions. The concept of (properly) efficient solutions are presented. …”
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On the closedness of sets with the fixed point property for contractions by Mira-Cristiana Anisiu, Valeriu Anisiu

“…In a Banach space, a convex set with nonvoid interior having the fixed point property for contractions is necessarily closed.…”
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On the closedness of sets with the fixed point property for contractions by Mira-Cristiana Anisiu, Valeriu Anisiu

“…In a Banach space, a convex set with nonvoid interior having the fixed point property for contractions is necessarily closed.…”
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Bishop-Phelps Theorem for Normed Cones by Ildar Sadeghi, Ali Hassanzadeh

“…Conclusion In this paper the notion of support points of convex sets in normed cones is introduced and it is shown that in a continuous normed cone, under the appropriate conditions, the set of support points of a bounded Scott-closed convex set is nonempty. …”
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A new method for global optimization by Kosolap Anatolii

“…We use exact quadratic regularization for the transformation of the multimodal problems to a problem of a maximum norm vector on a convex set. Quadratic regularization often allows you to convert a multimodal problem into a unimodal problem. …”
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Bound sets and two-point boundary value problems for second order differential systems by Jean Mawhin, Katarzyna Szymańska-Dębowska

“…The special cases where the bound set is a ball, a parallelotope or a bounded convex set are considered.…”
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On a variational principle for shape optimization and elliptic free boundary problems by Raúl B. González De Paz

“…The relaxed Energy functional is concave and it is defined on a convex set, so that the minimizing points are characteristic functions of sets. …”
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M-Structure and the space A(K,E) by T.S.S.R.K. RAO

“…For a compact convex set K and a Banach space E, under some natural M-structure theoretic conditions on K and E, we show that if the space of affine E-valued continuous functions on K is isometric to the space of E-valued continuous functions on some compact space, then K is a Bauer simplex. …”
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Quantitative stability for the Brunn–Minkowski inequality by Figalli, Alessio, Jerison, David

“…© 2016 We prove a quantitative stability result for the Brunn–Minkowski inequality: if |A|=|B|=1, t∈[τ,1−τ] with τ>0, and |tA+(1−t)B|1/n≤1+δ for some small δ, then, up to a translation, both A and B are quantitatively close (in terms of δ) to a convex set K.…”
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A branch and bound algorithm for the global optimization of Hessian Lipschitz continuous functions by Fowkes, J, Gould, N, Farmer, C

“…We present a branch and bound algorithm for the global optimization of a twice differentiable nonconvex objective function with a Lipschitz continuous Hessian over a compact, convex set. The algorithm is based on applying cubic regularisation techniques to the objective function within an overlapping branch and bound algorithm for convex constrained global optimization. …”

Optimality Conditions in Nondifferentiable G-Invex Multiobjective Programming by Do Sang Kim, Ho Jung Kim, You Young Seo

“…We consider a class of nondifferentiable multiobjective programs with inequality and equality constraints in which each component of the objective function contains a term involving the support function of a compact convex set. We introduce G-Karush-Kuhn-Tucker conditions and G-Fritz John conditions for our nondifferentiable multiobjective programs. …”
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Convexity and Order in Probabilistic Call-by-Name FPC by Mathys Rennela

“…Kegelspitzen are mathematical structures coined by Keimel and Plotkin, in order to encompass the structure of a convex set and the structure of a dcpo. In this paper, we ask ourselves what are Kegelspitzen the model of. …”
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Number of Spinal-Convex Polyominoes by Mustafa A. Sabri, Eman F. Mohomme

“…Keywords—: Polyominoes, Spinal-convex, Set column sequence, enumerating.…”
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Optimality Conditions in Nondifferentiable G-Invex Multiobjective Programming by Kim HoJung, Seo YouYoung, Kim DoSang

“…<p/> <p>We consider a class of nondifferentiable multiobjective programs with inequality and equality constraints in which each component of the objective function contains a term involving the support function of a compact convex set. We introduce G-Karush-Kuhn-Tucker conditions and G-Fritz John conditions for our nondifferentiable multiobjective programs. …”
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A Modified Form of Inertial Viscosity Projection Methods for Variational Inequality and Fixed Point Problems by Watanjeet Singh, Sumit Chandok

“…This paper aims to introduce an iterative algorithm based on an inertial technique that uses the minimum number of projections onto a nonempty, closed, and convex set. We show that the algorithm generates a sequence that converges strongly to the common solution of a variational inequality involving inverse strongly monotone mapping and fixed point problems for a countable family of nonexpansive mappings in the setting of real Hilbert space. …”
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ANALISIS MASALAH EKSTREM FUNGSI PADA RUANG BERNORMA by , QURRATUL AINI, , Dr. Ch. Rini

“…At first, we introduce the convex sets and the convex functions on normed space. …”

A Branch and Bound Algorithm for the Global Optimization of Hessian Lipschitz Continuous Functions by Fowkes, J, Gould, N, Farmer, C

“…We present a branch and bound algorithm for the global optimization of a twice differentiable nonconvex objective function with a Lipschitz continuous Hessian over a compact, convex set. The algorithm is based on applying cubic regularisation techniques to the objective function within an overlapping branch and bound algorithm for convex constrained global optimization. …”

Gauss Lucas theorem and Bernstein-type inequalities for polynomials by Ali Liyaqat, Rather N. A., Gulzar Suhail

“…According to Gauss-Lucas theorem, every convex set containing all the zeros of a polynomial also contains all its critical points. …”
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