Results 271 to 280 of about 68,947 (308)
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On the convexity of functional splines
Computer Aided Geometric Design, 1993We prove the convexity of large classes of functional splines with help of results on quasiconcave and pseudoconcave functions. The method developed for functional splines can also be used for smooth approximations of convex polyhedrons and some other convex surfaces.
Erich Hartmann, Yu Yu Feng 0001
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Mathematical Programming, 1972
A family of real functions, calledr-convex functions, which represents a generalization of the notion of convexity is introduced. This family properly includes the family of convex functions and is included in the family of quasiconvex functions.
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A family of real functions, calledr-convex functions, which represents a generalization of the notion of convexity is introduced. This family properly includes the family of convex functions and is included in the family of quasiconvex functions.
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Mathematics of the USSR-Sbornik, 1972
Let (x) be a convex downwards function, A > 0 a selfadjoint operator in a Hilbert space H, P an orthogonal projector in H; suppose DA PH is dense in PH, and let Ap be the Friedrichs extension of the operator PAP defined on DA PH. The inequality tr (Ap) ≤ tr (PAP) is proved. An estimate for the Jacobi θ-function and a distant generalization of the Szasz
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Let (x) be a convex downwards function, A > 0 a selfadjoint operator in a Hilbert space H, P an orthogonal projector in H; suppose DA PH is dense in PH, and let Ap be the Friedrichs extension of the operator PAP defined on DA PH. The inequality tr (Ap) ≤ tr (PAP) is proved. An estimate for the Jacobi θ-function and a distant generalization of the Szasz
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Commentationes Mathematicae, 2017
Summary: We introduce a new class of generalized convex functions called the \(\kappa\)-convex functions, based on Korenblum's concept of \(\kappa\)-decreasing functions, where \(\kappa\) is an entropy (distortion) function. We study continuity and differentiability properties of these functions, and we discuss a special subclass which is a counterpart
Lopez, Lorena Maria +2 more
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Summary: We introduce a new class of generalized convex functions called the \(\kappa\)-convex functions, based on Korenblum's concept of \(\kappa\)-decreasing functions, where \(\kappa\) is an entropy (distortion) function. We study continuity and differentiability properties of these functions, and we discuss a special subclass which is a counterpart
Lopez, Lorena Maria +2 more
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Archiv der Mathematik, 1992
Due to N. Kuhn, a function \(f: D\to R\), where \(D\) is an open convex subset of a real linear space and \(a\), \(b\) belong to (0,1), is called \((a,b)\)-convex if \[ f(ax+(1-a)y)\leq b\cdot f(x)+(1-b)\cdot f(y) \] for all \(x\), \(y\) in \(D\). Main result of the paper is the Theorem.
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Due to N. Kuhn, a function \(f: D\to R\), where \(D\) is an open convex subset of a real linear space and \(a\), \(b\) belong to (0,1), is called \((a,b)\)-convex if \[ f(ax+(1-a)y)\leq b\cdot f(x)+(1-b)\cdot f(y) \] for all \(x\), \(y\) in \(D\). Main result of the paper is the Theorem.
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Riemannian convexity of functionals
Journal of Global Optimization, 2011zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Constantin Udriste, Andreea Bejenaru
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Canadian Journal of Mathematics, 1970
In what follows, we suppose that ƒ(z) = Σ0∞anzn is regular for |z| < 1. LetandThen (see, for example, [6, pp. 235-236]), for 0 ≦ r < ρ < 1, we have:The following results are well known.
Başgöze, T. +2 more
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In what follows, we suppose that ƒ(z) = Σ0∞anzn is regular for |z| < 1. LetandThen (see, for example, [6, pp. 235-236]), for 0 ≦ r < ρ < 1, we have:The following results are well known.
Başgöze, T. +2 more
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Journal of the Society for Industrial and Applied Mathematics Series A Control, 1965
The purpose of this work is to, introduce pseudo-convex functions and to describe some of their properties and applications. The class of all pseudo-convex functions over a convex set C includes the class of all differentiable convex functions on C and is included in the class of all differentiable quasi-convex functions on C.
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The purpose of this work is to, introduce pseudo-convex functions and to describe some of their properties and applications. The class of all pseudo-convex functions over a convex set C includes the class of all differentiable convex functions on C and is included in the class of all differentiable quasi-convex functions on C.
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Convex Functions and Generalized Convex Functions
2023Giorgio Giorgi +2 more
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Submodular functions and convexity
1983In “continuous” optimization convex functions play a central role. Besides elementary tools like differentiation, various methods for finding the minimum of a convex function constitute the main body of nonlinear optimization. But even linear programming may be viewed as the optimization of very special (linear) objective functions over very special ...
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