Related papers: A new treatment of convex functions
Generalized matrix-fractional (GMF) functions are a class of matrix support functions introduced by Burke and Hoheisel as a tool for unifying a range of seemingly divergent matrix optimization problems associated with inverse problems,…
In this paper, we derive new estimates for the remainder term of the midpoint, trapezoid, and Simpson formulae for functions whose derivatives in absolute value at certain power are quasi-convex. Some applications to special means of real…
In this paper several inequalities of the right-hand side of Hermite-Hadamard inequality are obtained for the class of functions whose derivatives in absolutely value at certain powers are ({\alpha},m)-convex.Some applications to special…
A new version of the Hadwiger theorem on convex functions is established and an explicit representation of functional intrinsic volumes is found using new functional Cauchy-Kubota formulas. In addition, connections between functional…
In this paper, two new lemmas are proved and inequalities are established for co-ordinated convex functions and co-ordinated s-convex functions.
In this paper, we extend some estimates of the left hand side of a Hermite- Hadamard type inequality for nonconvex functions whose derivatives absolute values are preinvex and log-preinvex.
This manuscript introduces the idea of GS-exponential kind of convex functions and some of their algebraic features, and we introduce a new class GS-exponential kind of convex sets. In addition, we describe certain fundamental…
This paper studies the convexity properties of nonsmooth extended-real-valued weakly convex functions, a class of functions that is central to modern optimization and its applications. We establish new characterizations of convexity using…
In this paper we established new Hadamard-type inequalities for functions that co-ordinated Godunova-Levin functions and co-ordinated P-convex functions, therefore we proved a new inequality involving product of convex functions and…
In this paper, we derive new estimates for the remainder term of the midpoint, trapezoid, and Simpson formulae for functions whose derivatives in absolute value at certain power are ({\alpha},m)-convex.
In this paper several inequalities of the right-hand side of Hermite-Hadamard's inequality are obtained for the class of functions whose derivatives in absolutely value at certain powers are strongly {\varphi}-convex with modulus c>0.
In this paper, we consider a new class of convex functions which is called $\lambda$-preinvex functions. We prove several Hermite-Hadamard type inequalities for differentiable $\lambda$-preinvex functions via Fractional Integrals. Some…
In this note we extend some new estimates of the integral $\int_a^b (x-a)^p(b-x)^qf(x)dx$ for functions when a power of the absolute value is $P-$convex.
In this study, the author establish some inequalities of Hadamard like based on convex and s-convexity in the second sense. Some applications to special means of positive real numbers are also given.
In a recent work of the authors, we showed some general inequalities governing numerical radius inequalities using convex functions. In this article, we present results that complement the aforementioned inequalities. In particular, the new…
We show how the recent improvement of the Hermite-Hadamard inequality can be applied to some (not necessarily convex) planar figures and three-dimensional bodies satisfying some kind of regularity.
In this paper, firstly we have established Hermite-Hadamard's inequalities for s-convex functions in the second sense and m-convex functions via fractional integrals. Secondly, a Hadamard type integral inequality for the fractional…
Two kinds of novel generalizations of Nesbitt's inequality are explored in various cases regarding dimensions and parameters in this article. Some other cases are also discussed elaborately by using the semiconcave-semiconvex theorem. The…
Integrally convex functions constitute a fundamental function class in discrete convex analysis, including M-convex functions, L-convex functions, and many others. This paper aims at a rather comprehensive survey of recent results on…
We provide extensions of geometric inequalities about sections and projections of convex bodies to the setting of integrable log-concave functions. Namely, we consider suitable generalizations of the affine and dual affine quermassintegrals…