凸函数和凹函数的幂平均不等式

文 [1 ]获得了当 α≥ 1时的凸函数的幂平均不等式 (3)、(4 ) [1] .本文指出文 [1 ]中的一个错误 ,并且得到了 α≤ 1时的凹函数的幂平均不等式 .修正和充实了文 [1 ]的定理 .同时讨论了当 α取其它值时不等式的情况 .     

与Gamma函数有关的对数完全单调函数及其应用

为了完善函数G_(α,β)(x)(其中参数α∈R,β≥0)及函数1/G_(α,β)(x)在区间(0,∞)上的对数完全单调性和相关不等式,利用Taylor展开式、Gamma函数、Psi函数的级数表达式和积分表达式研究了函数G_(α,β)(x)和函数1/G_(α,β)(x)数的对数完全单调性,将函数G_(α,β)(x)和函数1/G_(α,β)(x)对数完全单调的充分条件扩大;利用对数完全单调性得到新的不等式,并通过对特殊情形的研究,得到一个形式简单对称的双边不等式,该不等式对阶乘数之乘积与∏nk=1k~k的商做出估计.     

关于凸函数的一个控制不等式

关于凸函数的一个控制不等式续铁权（青岛教育学院数学系２６６０７１）设ｆ（ｘ）在［ａ，ｂ］上定义，０＜ｔ＜１，若称ｆ（ｘ）是［ａ，ｂ］上的凸函数，若当时严格不等式成立，称ｆ（ｘ）是严格凸函数．若不等式反向，称ｆ（ｘ）是凹函数和严格凹函数．本文研究凸函数...     

HG-凸函数及其Jensen型不等式

给出了HG-凸函数概念及其判定定理,建立了HG-凸函数的Jensen型不等式,并给出它的应用.     

关于p-凸函数的Hadamard型不等式

对于P-凸函数在给定连续区间上的算术平均问题,通过P-凸函数理论将其转化为定积分问题,利用定积分的定义计算和定积分运算,建立了P-凸函数的Hadamard 型不等式,给出了证明和发现不等式的实例.     

基于r-凸函数的Choquet积分不等式

本文研究了r-凸函数的Choquet积分的Hadamard不等式和詹森不等式。首先,针对单调r-凸函数,研究了其Choquet积分的类似Hadamard型不等式;接着,分别在扭曲勒贝格测度和非可加测度下,估计了r-凸函数的Choquet积分的上界;最后,在非可加测度是凹的情形下,给出了两个r-凸函数的Choquet积分的詹森不等式,其可用来估计Choquet积分的下界。另外,在扭曲勒贝格测度下,对文中所有结果进行了例证。     

GA-凸函数的Hadamard型不等式的改进和应用

通过研究函数的凸性、单调性及相关理论,建立了关于GA-凸函数的一些新的Hadamard型不等式,这些不等式推广了最近文献中的有关结果.     

p-凸函数与几类不等式

研究p-凸函数的一些新的性质及判别准则,并建立p-凸函数的Jensen型、Rado型及Hadamard型不等式.     

与GA-凸函数有关的若干单调函数

利用GA-凸函数的定义及其Hermite-Hadamard型不等式,得到与GA-凸函数有关的若干单调函数.     

s-对数凸函数的Hermite-Hadamard型积分不等式

该文定义了"s-对数凸函数"的概念,并给出了可微s-对数凸函数的若干个HermiteHadamard型积分不等式,作为应用给出了平均数的几个不等式.     

Integral inequalities for coordinated Harmonically convex functions

In this paper, we introduce the notion of coordinated harmonically convex functions. We derive some new integral inequalities of Hermite–Hadamard type for coordinated Harmonically convex functions. The interested readers are encouraged to find the applications of harmonically convex functions in pure and applied sciences.     

Integral inequalities for some special functions

Several integral inequalities for the classical hypergeometric, confluent hypergeometric, and confluent hypergeometric limit functions are given. The related results for Bessel and Whittaker functions as well as for Laguerre, Hermite, and Jacobi polynomials are discussed.     

Simpson and Newton type inequalities for convex functions via newly defined quantum integrals

We first establish two new identities, based on the kernel functions with either two section or three sections, involving quantum integrals by using new definition of quantum derivative. Then, some new inequalities related to Simpson's 1/3 formula for convex mappings are provided. In addition, Newton type inequalities, for functions whose quantum derivatives in modulus or their powers are convex, are deduced. We also mention that the results in this work generalize inequalities given in earlier study.     

Generalized convex functions and vector variational inequalities

In this paper, (, ,Q)-invexity is introduced, where :X ×X intR _m ⁺ , :X ×X X,X is a Banach space,Q is a convex cone ofR ^m . This unifies the properties of many classes of functions, such asQ-convexity, pseudo-linearity, representation condition, null space condition, andV-invexity. A generalized vector variational inequality is considered, and its equivalence with a multi-objective programming problem is discussed using (, ,Q)-invexity. An existence theorem for the solution of a generalized vector variational inequality is proved. Some applications of (, ,Q)-invexity to multi-objective programming problems and to a special kind of generalized vector variational inequality are given.The author is indebted to Dr. V. Jeyakumar for his constant encouragement and useful discussion and to Professor P. L. Yu for encouragement and valuable comments about this paper.     

关于伽玛函数和不完全伽玛函数单调性的注记

利用含有两参数拓广加权平均值的单调性和不等式,我们证明了三类比的伽玛函数在条件r＞0,s＞0和x＞0下是递增的,Γ(s),Γ(s,x)和γ(s,x)分别表示伽玛函数和不完全伽玛函数.据此关于伽玛函数和不完全伽玛函数的单调性结果和不等式被推广了,同时给出了伽玛函数一些结果的证明.     

On some inequalities for the incomplete gamma function

Let be a positive real number. We determine all real numbers and such that the inequalities

are valid for all . And, we determine all real numbers and such that

hold for all .

     

Inequalities for the Gamma function and estimates for the volume of sections of

Let and let be a -dimensional subspace of . We prove that , for and whenever . We also consider and other related cases. We obtain sharp inequalities involving Gamma function in order to get these results.

     

Some inequalities for the gamma function

Several inequalities involving gamma function are obtained. They are established using elementary properties of logarithmically convex functions.     

Hermite‐Hadamard‐type inequalities for interval‐valued coordinated convex functions involving generalized fractional integrals

In this paper, we define interval‐valued left‐sided and right‐sided generalized fractional double integrals. We establish inequalities of Hermite‐Hadamard like for coordinated interval‐valued convex functions by applying our newly defined integrals.