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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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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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The application of convex function and GA-convex function
Theoretical and Natural ScienceA convex function is a function that maps from a convex subset of a vector space to the set of real numbers. Convex functions have some important properties, such as non-negativity, monotonicity, and convexity, which can help us derive and prove inequalities.
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