On h-convexity

By S. Varošanec. 2007

565 citations recorded by the source corpus.

Subfields: Applied Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/2228218cc902b1163d7c5e86b761870e1a1ff370

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In Applied Mathematics

In Geometry and Topology

Citations in the corpus

Some New Hermite-Hadamard Integral Inequalities for Convex functions (2014, unknown): “Definition 1.6 (Varošanec 2007).”
On new inequalities for h-convex functions via Riemann-Liouville fractional integration (2012, background): “ y = b and h is superadditive, we get (2.7) f(ta+(1 −t)b)+f((1−t)a +tb) ≤ h(1)[f(a)+f(b)]. Then multiplying both sides of (2.7) by tα−1 and integrating the resulting inequality with respect to t over [0,1], we get Z1 0 tα−1 [f(ta+(1−t)b) +f((1−t)a+tb)]dt ≤ Z1 0 tα−1h(1)[f(a) +f(b)]dt, Γ(α) (b −a)α [”
Some Hermite–Hadamard type inequalities for log-h-convex functions (2013, methodology): “1 ([15]) Let h W J ! R be a non-negative function.”
ON h m CONVEXITY AND HADAMARD TYPE INEQUALITIES (2011, background): “≤ 2 b− a ∫ b a f(x)dx ≤ 2[f(a) + f(b)] On all of these, in [5], Varošanec defined h−convex functions and gave some properties of this class of functions.”
ON SOME HADAMARD-TYPE INEQUALITIES FOR h-CONVEX FUNCTIONS (2008, background): “[11] Let h : J ⊆ R → R be a positive function .”
Integral Majorization Type Inequalities for the Functions in the Sense of Strong Convexity (2019, background): “In recent years there is a growing interest in generalized convex functions (such as quasi-convex function [1], strongly convex function [2–4], s-convex function [5], approximately convex function [6], logarithmically convex function [7, 8], midconvex function [9], pseudo-convex function [10], φ-con”
ON tgs-CONVEX FUNCTION AND THEIR INEQUALITIES (2015, background): “Namely, Definition of t s-convex function may be regarded as a special case of h-convex function (see [25]).”
Generalized Convexity and Integral Inequalities (2015, background): “…relativ convex functions, relativeh-convex functions, fractional integrals, Hermite-Hadamard inequality 2010 AMS Subject Classification:26D15, 26A51, 26A33, 49J40, 90C33 1 Introduction It is well known [29] that modern analysis directly or indirectly involve the applications of convexity.”
On hermite-hadamard inequalities for h-preinvex functions (2014, methodology): “Using the technique of Varosanec [32], we prove that the product of two h-preinvex functions is again a h-preinvex function.”
On some Hadamard-type inequalities for product of two s-convex functions on the co-ordinates (2012, background): “Varosanec in [19] (see [19] for further properties of  h convex functions).”