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COMPLEMENTARY RESULTS FOR h -CONVEX FUNCTIONS WITH APPLICATIONS
2023In this paper, we present several new properties of h -convex functions in a way that complements those known properties for convex functions. The obtained results include, but are not limited to, Mercer-type inequalities, gradient inequalities, Jensen-type inequalities, Mean-like bounds, Hermite ...
Sababheh, Mohammad +3 more
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Continuity of h-convex functions
Asian-European Journal of Mathematics, 2019In this paper, a condition which implies the continuity of an [Formula: see text]-convex function is investigated. In fact, any [Formula: see text]-convex function bounded from above is continuous if the function [Formula: see text] satisfies a certain condition which is called pre-continuity condition.
M. Rostamian Delavar, S. S. Dragomir
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Some inequalities for operator (φ,h)-convex functions
Rocky Mountain Journal of Mathematics, 2021zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Marghzar, Sima Hashemi +2 more
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Jensen–Mercer Type Inequalities for Operator h-Convex Functions
Bulletin of the Iranian Mathematical Society, 2021zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Abbasi, Mostafa +2 more
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LIPSCHITZ CONTINUITY FOR H-CONVEX FUNCTIONS IN CARNOT GROUPS
Communications in Contemporary Mathematics, 2006For a Carnot group G of step two, we prove that H-convex functions are locally bounded from above. Therefore, H-convex functions on a Carnot group G of step two are locally Lipschitz continuous by using recent results by Magnani.
Sun, Mingbao, Yang, Xiaoping
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Milne-Type Inequalities for $h$-Convex Functions
Real Analysis ExchangeIn this paper the authors utilized the concept of \(h\)-convex functions and conformable fractional integrals operators to derived and proved the Milne-type inequalities for \(h\)-convex functions. Several consequences of their results inform of Corollaries and Remarks were given and the connection with known results of this type in the literature were
Benaissa, Bouharket +1 more
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Some integral inequalities for harmonic h-convex functions involving hypergeometric functions
Applied Mathematics and Computation, 2015zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Marcela V. Mihai +3 more
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On the H-cone-functions for H-convex sets [PDF]
, 2019 Given a compact and H-convex subset K of the Heisenberg group H, with the origin e in its interior, we are interested in finding a homogeneous H-convex function f such that f(e) = 0 and f|∂K= 1; we will call this function f the H-cone-function of vertex e and base ∂K.
Calogero, A., Pini, R.
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Lipschitz continuity, Aleksandrov theorem and characterizations for H-convex functions
Mathematische Annalen, 2005The author proves that in stratified groups \(H\)-convex functions locally bounded from above are locally Lipschitz; moreover, he proves that the class of \(v\)-convex functions corresponds to the class of \(H\)-convex functions that are upper semicontinuous, and then they are also Lipschitz. In the class of step 2 groups a more precise result is given;
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Lifting of convex functions on Carnot groups and lack of convexity for a gauge function
Archiv der Mathematik, 2009Let \((\mathbb G,*)\) be a Carnot group, i.e., a connected and simply connected Lie group whose Lie algebra \({\mathbf g}\) admits a stratification \({\mathbf g}=V_{1}\oplus \cdot \cdot \cdot \oplus V_{r}\) with \( [V_{1},V_{i}]=V_{i+1}\) for \(i\leq r-1\) and \([V_{1},V_{r}]=\{0\}.\) A function \(u:\mathbb G\to\mathbb R\) is called horizontally convex
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