相关论文: Some New Inequalities Between Important Means
In this paper, a general integral identity for convex functions is derived. Then, we establish new some inequalities of the Simpson and the Hermite-Hadamard's type for functions whose absolute values of derivatives are convex. Some…
In this paper, we prove some new inequalities of Hadamard-type for convex functions on the co-ordinates.
In this paper, we establish several new inequalities for some twice differantiable mappings that are connected with the celebrated Hermite-Hadamard integral inequality. Some applications for special means of real numbers are also provided.
It is well-known that if a real valued function acting on a convex set satisfies the $n$-variable Jensen inequality, for some natural number $n\geq 2$, then, for all $k\in\{1,\dots, n\}$, it fulfills the $k$-variable Jensen inequality as…
Convex analysis is fundamental to proving inequalities that have a wide variety of applications in economics and mathematics. In this paper we provide Jensen-type inequalities for functions that are, intuitively, "very" convex. These…
This paper is mainly devoted to studying operator Jensen inequality. More precisely, a new generalization of Jensen inequality and its reverse version for convex (not necessary operator convex) functions have been proved. Several special…
Some q-analysis variants of Hardy type inequalities of the form \int_0^b (x^{\alpha-1} \int_0^x t^{-\alpha} f(t) d_qt)^p d_qx \leq C \int_0^b f^p(t) d_qt with sharp constant C are proved and discussed. A similar result with the…
The theory of abstract convexity, also known as convexity without linearity, is an extension of the classical convex analysis. There are a number of remarkable results, mostly concerning duality, and some numerical methods, however, this…
In this article, we obtain two interesting general inequalities concerning Riemman sums of convex functions, which in particular, sharpen Alzer's inequality and give a suitable converse for it.
In this article, we present several inequalities treating operator means and the Cauchy-Schwarz inequality. In particular, we present some new comparisons between operator Heron and Heinz means, several generalizations of the difference…
In the paper, by finding linear relations of differences between some means, the authors supply a unified proof of some double inequalities for bounding Neuman-S\'andor means in terms of the arithmetic, harmonic, and contra-harmonic means…
In this paper, the connection between the functional inequalities $$ f\Big(\frac{x+y}{2}\Big)\leq\frac{f(x)+f(y)}{2}+\alpha_J(x-y) \qquad (x,y\in D)$$ and $$ \int_0^1f\big(tx+(1-t)y\big)\rho(t)dt \leq\lambda f(x)+(1-\lambda)f(y)…
In this paper, we first prove two new identities for multiplicative differentiable functions. Based on this identity, we establish a midpoint and trapezoid type inequalities for multiplicatively convex functions. Applications to special…
In the paper, we introduce the generalized convex function on fractal sets of real line numbers and study the properties of the generalized convex function. Based on these properties, we establish the generalized Jensen inequality and…
In the paper, the authors find some new integral inequalities of Hermite-Hadamard type for functions whose derivatives of the $n$-th order are $(\alpha,m)$-convex and deduce some known results. As applications of the newly-established…
We study the convexity/concavity properties of the generalized $p$-trigonometric functions in the sense of P. Lindqvist with respect to the power means.
Mercer inequality for convex functions is a variant of Jensen's inequality, with an operator version that is still valid without operator convexity. This paper is two folded. First, we present a Mercer-type inequality for operators without…
In this paper, we prove some new inequalities of Simpson's type for functions whose derivatives of absolute values are h-convex and h-concave functions. Some new estimations are obtained. Also we give some sophisticated results for some…
In this paper functions $f:D\to\mathbb{R}$ satisfying the inequality \[ f\Big(\frac{x+y}{2}\Big)\leq\frac12f(x)+\frac12f(y) +\varphi\Big(\frac{x-y}{2}\Big) \qquad(x,y\in D) \] are studied, where $D$ is a nonempty convex subset of a real…
The aim of this article is to establish new two-functions minimax inequalities extending classical results such as Simons' minimax theorem. Our results will be proved in a non-compact setting. We also prove, under general conditions, that…