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Hermite–Hadamard type inequalities for m-convex and ( α , m ) $( \alpha , m)$ -convex functions [PDF]
Journal of Inequalities and Applications, 2020 In this paper, some new inequalities of the Hermite–Hadamard type for the classes of functions whose derivatives’ absolute values are m-convex and ( α , m ) $( \alpha , m) $ -convex are obtained.
Serap Özcan
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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 ...
Akiyoshi Shioura, Kazuo Murota
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Moroccan Journal of Pure and Applied Analysis, 2019 In this research we lay the concept of log m-convex functions defined on real intervals containing the origin, some algebraic properties are exhibit, in the same token discrete Jensen type inequalities and integral inequalities are set and shown.
Lara Teodoro, Rosales Edgar
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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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Some new integral inequalities for (s, m)-convex and (α, m)-convex functions
Қарағанды университетінің хабаршысы. Математика сериясы, 2019 The paper considers several new integral inequalities for functions the second derivatives of which, with respect to the absolute value, are ( s,m )-convex and ( α,m )-convex functions.
B. Bayraktar, V.Ch. Kudaev
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Journal of Inequalities and Applications, 2018 In this paper some new general fractional integral inequalities for convex and m-convex functions by involving an extended Mittag-Leffler function are presented. These results produce inequalities for several kinds of fractional integral operators.
G. Farid +4 more
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Fractional Exponentially m-Convex Functions and Inequalities
International Journal of Analysis and Applications, 2019 In this article, we introduce a new class of convex functions involving m ∈ [0, 1], which is called exponentially m-convex function. Some new Hermite-Hadamard inequalities for exponentially m-convex functions via Reimann-Liouville fractional integral are
Saima Rashid +2 more
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Axioms, 2023 Research in this paper aims to explore the concept of generalized exponentially (s,m)-convex functions, and to determine some properties of these functions.
Wedad Saleh, Adem Kılıçman
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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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Advances in Difference Equations, 2021 Some new integral inequalities for strongly ( α , h − m ) $(\alpha ,h-m)$ -convex functions via generalized Riemann–Liouville fractional integrals are established.
Ghulam Farid +4 more
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