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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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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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Convex Functions and Generalized Convex Functions
2023Giorgio Giorgi +2 more
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Computational optimization and applications, 2016
Xingju Cai, Deren Han, Xiaoming Yuan
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Xingju Cai, Deren Han, Xiaoming Yuan
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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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Random Gradient-Free Minimization of Convex Functions
Foundations of Computational Mathematics, 2015Y. Nesterov, V. Spokoiny
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On the Hermite–Hadamard-type inequalities for co-ordinated convex function via fractional integrals
, 2014M. Sarıkaya
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Semi-Infinite Optimization under Convex Function Perturbations: Lipschitz Stability
Journal of Optimization Theory and Applications, 2011Nguyen Quang Huy, Jen-Chih Yao
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Canadian Journal of Mathematics, 1949
Since the classical work of Minkowski and Jensen it is well known that many of the inequalities used in analysis may be considered as consequences of the convexity of certain functions. In several of these inequalities pairs of “conjugate” functions occur, for instance pairs of powers with exponents a and a related by 1/a + 1/a = 1.
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Since the classical work of Minkowski and Jensen it is well known that many of the inequalities used in analysis may be considered as consequences of the convexity of certain functions. In several of these inequalities pairs of “conjugate” functions occur, for instance pairs of powers with exponents a and a related by 1/a + 1/a = 1.
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