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Minimization of an M-convex function
Discrete Applied Mathematics, 1998 A function \(f : \mathbb{Z}^n \rightarrow \mathbb{R}\cup \{ \infty \}\) is called \(M\)-convex if for any two vectors \(x,y \in\mathbb{Z}^n\), such that \(f(x) , f(y) \neq \infty\), and any unit vector \(e_i\) in a direction where \(x - y\) is positive there is a unit vector \(e_j\) in a direction where \(x-y\) is negative, such that \(f(x) + f(y) \geq
Akiyoshi Shioura
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M-Convex Function on Generalized Polymatroid [PDF]
Mathematics of Operations Research, 1999 The concept of M-convex function, introduced by Murota (1996), is a quantitative generalization of the set of integral points in an integral base polyhedron as well as an extension of valuated matroid of Dress and Wenzel (1990). In this paper, we extend this concept to functions on generalized polymatroids with a view to providing a unified framework ...
Kazuo Murota, Akiyoshi Shioura
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m-Convexity and Functional Equations [PDF]
Moroccan Journal of Pure and Applied Analysis, 2017 AbstractIn this research we aim to explore some properties of m-convex functions from the point of view of functional equations or better, functional inequalities. So far studies of m- convexity have been devoted mainly to establish properties, inequalities and examples on the topic, but not to look at the problem from the perspective of functional ...
Lara Teodoro +2 more
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On $\mathscr{M}$-convex functions
AIMS Mathematics, 2020 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Muhammad Uzair Awan +3 more
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Azerbaijan Journal of Mathematics, 2023 Summary: The theory of \(m\)-convex \((m-cv)\) functions is a new direction in the theory of real geometry. However, for \(m=1\) this class coincides with the class of convex functions, and for \(m=n\) it coincides with the class of subharmonic functions, which, as is known, have been well studied (A. Aleksandrov, I. Bakelman, A.
Sharipov, R. A., Ismoilov, M. B.
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The most important inequalities of $m$-convex functions [PDF]
TURKISH JOURNAL OF MATHEMATICS, 2017 The intention of this article is to investigate the most important inequalities of m-convex functions without using their derivatives. The article also provides a brief survey of general properties of m-convex functions.
Pavić, Zlatko, Avci Ardiç, Merve
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Hermite–Hadamard type inequalities for m-convex and $( \alpha , m)$-convex functions [PDF]
Journal of Inequalities and Applications, 2020 AbstractIn this paper, some new inequalities of the Hermite–Hadamard type for the classes of functions whose derivatives’ absolute values arem-convex and$( \alpha , m) $(α,m)-convex are obtained. The results obtained in this work extend and improve the corresponding ones in the literature.
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Hadamard type inequalities for m–convex and (α, m)–convex functions via fractional integrals [PDF]
AIP Conference Proceedings, 2018 In this paper, we established some new Hadamard-type integral inequalities for functions whose derivatives of absolute values are m-convex and (α,m)-convex functions via Riemann-Liouville fractional integrals.
Ozdemir, M. Emin +3 more
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Sandwich theorem for m-convex functions
Journal of Mathematical Analysis and Applications, 2017 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Matkowski, Janusz, Wróbel, Małgorzata
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A note on M-convex functions on jump systems
Discrete Applied Mathematics, 2021 A jump system is defined as a set of integer points (vectors) with a certain exchange property, generalizing the concepts of matroids, delta-matroids, and base polyhedra of integral polymatroids (or submodular systems). A discrete convexity concept is defined for functions on constant-parity jump systems and it has been used in graph theory and algebra.
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