Related papers: More on deviations from Mean Value
A generalised trapezoid inequality for convex functions and applications for quadrature rules are given. A refinement and a counterpart result for the Hermite-Hadamard inequalities are obtained and some inequalities for pdf's and…
This paper discusses basic results and recent developments on variational regularization methods, as developed for inverse problems. In a typical setup we review basic properties needed to obtain a convergent regularization scheme 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.
Recent results concerning solutions of the modified Helmholtz equation are reviewed; namely, various mean value properties and their corollaries, converse and inverse of these properties, and relations between these solutions and harmonic…
We consider the differentiation of the value function for parametric optimization problems. Such problems are ubiquitous in Machine Learning applications such as structured support vector machines, matrix factorization and min-min or…
A refinement of the Hardy inequality has been presented by use of superquadratic function.
Inspired by the recent work by R.Pal et al., we give further refined inequalities for a convex Riemann integrable function, applying the standard Hermite-Hadamard inequality. Our approach is different from their one in \cite{PSMA2016}. As…
In this paper, we are interested in investigating a weighted variant of Hermite-Hadamard type inequalities involving convex functionals. The approach undertaken makes it possible to refine and reverse certain inequalities already known in…
We study some properties convex functions fulfill. Among the conclusions we obtain from such result, we are able to prove some nontrivial inequalities among real numbers, and we give an improvement of the reverse triangle inequality in the…
Results involving various mean value properties are reviewed for harmonic, biharmonic and metaharmonic functions. It is also considered how the standard mean value property can be weakened to imply harmonicity and belonging to other classes…
We begin by shortly recalling a generalized mean value inequality for subharmonic functions, and two applications of it: first a weighted boundary behavior result (with some new references and remarks), and then a borderline case result to…
In this paper, we establish some new integral inequalities for $(\alpha, m)-$convex functions and quasi-convex functions, respectively. Our results in special cases recapture known results.
For convex univalent functions we give instances where the sharp bound for various coefficient functionals are identical to those for the corresponding bound for the inverse function. We give instances where the sharp bounds differ and also…
Matrix inequalities that extend certain scalar ones have been at the center of numerous researchers' attention. In this article, we explore the celebrated subadditive inequality for matrices via concave functions and present a reversed…
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, a new identity for convex functions is derived. A consequence of the identity is that we can derive new estimates for the remainder term of the midpoint, trapezoid, and Simpson formulae for functions whose derivatives in…
Some mathematical inequalities among various weighted means are studied. Inequalities on weighted logarithmic mean are given. Besides, the gap in Jensen's inequality is studied as a convex function approach. Consequently, some non-trivial…
Some new Hermite-Hadamard's inequalities for h-convex functions are proved, generalizing and unifying a number of known results. Some new applications for special Means of real numbers are also derived.
We study Whitney-type estimates for approximation of convex functions in the uniform norm on various convex multivariate domains while paying a particular attention to the dependence of the involved constants on the dimension and the…
In this paper we give refinements of some convex and log-convex moment inequalities of the first and second order using a special kind of positive semi-definite form. An open problem concerning eight parameter refinement of second order is…