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1.
Jensen-Steffensen type inequalities for P-convex functions and functions with nondecreasing increments are presented. The obtained results are used to prove a generalization of ?eby?ev’s inequality and several variants of Hölder’s inequality with weights satisfying the conditions as in the Jensen-Steffensen inequality. A few well-known inequalities for quasi-arithmetic means are generalized. 相似文献
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X.Q. Yang 《Journal of Optimization Theory and Applications》2003,116(2):437-452
Gap functions play a crucial role in transforming a variational inequality problem into an optimization problem. Then, methods solving an optimization problem can be exploited for finding a solution of a variational inequality problem. It is known that the so-called prevariational inequality is closely related to some generalized convex functions, such as linear fractional functions. In this paper, gap functions for several kinds of prevariational inequalities are investigated. More specifically, prevariational inequalities, extended prevariational inequalities, and extended weak vector prevariational inequalities are considered. Furthermore, a class of gap functions for inequality constrained prevariational inequalities is investigated via a nonlinear Lagrangian. 相似文献
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The operator convex functions of several variables are characterized in terms of a non-commutative generalization of Jensen's inequality, extending previous results of F. Hansen and G.K. Pedersen for functions of one variable and of F. Hansen for functions of two variables.
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A. Barani 《Journal of Mathematical Analysis and Applications》2007,328(2):767-779
The concept of a geodesic invex subset of a Riemannian manifold is introduced. Geodesic invex and preinvex functions on a geodesic invex set with respect to particular maps are defined. The relation between geodesic invexity and preinvexity of functions on manifolds is studied. Using proximal subdifferential, certain results concerning extremum points of a non smooth geodesic preinvex function on a geodesic invex set are obtained. The main value inequality and the mean value theorem in invexity analysis are extended to Cartan-Hadamard manifolds. 相似文献
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S. Schaible 《Journal of Optimization Theory and Applications》1981,35(3):303-338
The purpose of this paper is twofold. Firstly, criteria for quasiconvex and pseudoconvex quadratic functions in nonnegative variables of Cottle, Ferland, and Martos are derived by specializing criteria proved by the author. We do not make use of the concept of positive subdefinite matrices. Instead, we are specializing criteria that were derived for quadratic functions on arbitrary convex sets to the special case of quadratic functions in nonnegative variables. The second purpose of this paper is to present several new criteria involving also strictly pseudoconvex quadratic functions.The author wishes to thank Professor R. W. Cottle for helpful discussions. 相似文献
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The present paper gives a survey of up-to-date results of holomorphic almost-periodic functions and mappings in one and several complex variables. 相似文献
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The aim of the present paper is to define a notion of weakly differentiable cochain in the generality of metric measure spaces and to study basic properties of such cochains. Our cochains are (sub)additive functionals on a subspace of chains, and a suitable notion of chains in metric spaces is given by Ambrosio–Kirchheim?s theory of metric currents. The notion of weak differentiability we introduce is in analogy with Heinonen–Koskela?s concept of upper gradients of functions. In one of the main results of our paper, we prove continuity estimates for cochains with p-integrable upper gradient in n-dimensional Lie groups endowed with a left-invariant Finsler metric. Our result generalizes the well-known Morrey–Sobolev inequality for Sobolev functions. Finally, we prove several results relating capacity and modulus to Hausdorff dimension. 相似文献
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In this paper we prove a rearrangement inequality that generalizes inequalities given in the book by Hardy, Littlewood and Pólya1 and by Luttinger and Friedberg.2 The inequality for an integral of a product of functions of one variable is further extended to the case of functions of several variables. 相似文献
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Qin Deng 《Applied mathematics and computation》2011,217(12):5889-5894
The objective of the present paper is to study the logarithmic coefficients of Bazilevic? functions. We obtain the inequality ∣γn∣ ? An−1logn (A is an absolute constant) which holds for Bazilevic? functions. 相似文献
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周从会 《纯粹数学与应用数学》2010,26(1):51-55,72
摘要:引入α-凸函数的一个子类M(α;A,B),讨论了这个函数类上的Fekete-Szego不等式,得到了准确的结果,推广了一些作者的结果.最后,给出了不等式在利用Hadamard积定义的函数类上的两个应用. 相似文献
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A. Perotti 《Journal of Mathematical Analysis and Applications》2008,337(1):107-115
In this paper the Dirichlet problem for pluriholomorphic functions of two complex variables is investigated. The key point is the relation between pluriholomorphic functions and pluriharmonic functions. The link is constituted by the Fueter-regular functions of one quaternionic variable. Previous results about the boundary values of pluriharmonic functions and new results on L2 traces of regular functions are applied to obtain a characterization of the traces of pluriholomorphic functions. 相似文献
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The generalized trigonometric functions occur as an eigenfunction of the Dirichlet problem for the one-dimensional p-Laplacian. The generalized hyperbolic functions are defined similarly. Some classical inequalities for trigonometric and hyperbolic functions, such as Mitrinovi?–Adamovi?’s inequality, Lazarevi?’s inequality, Huygens-type inequalities, Wilker-type inequalities, and Cusa–Huygens-type inequalities, are generalized to the case of generalized functions. 相似文献
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Given an analytic function of one complex variable f, we investigate the arithmetic nature of the values of f at algebraic points. A typical question is whether f() is a transcendental number for each algebraic number . Since there exist transcendental entire functions f such that
for any t0 and any algebraic number , one needs to restrict the situation by adding hypotheses, either on the functions, or on the points, or else on the set of values.
Among the topics we discuss are recent results due to Andrea Surroca on the number of algebraic points where a transcendental analytic function takes algebraic values, new transcendence criteria by Daniel Delbos concerning entire functions of one or several complex variables, and Diophantine properties of special values of polylogarithms. 相似文献
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We unify the three distinct inequality sequences (Abramowitz and Stegun (1972) [1, 9.5.2]) of positive real zeros of Bessel functions into a single one. 相似文献
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Radu Ioan Bo? Ioan Bogdan Hodrea 《Journal of Mathematical Analysis and Applications》2006,322(1):316-328
We present some Farkas-type results for inequality systems involving finitely many functions. Therefore we use a conjugate duality approach applied to an optimization problem with a composed convex objective function and convex inequality constraints. Some recently obtained results are rediscovered as special cases of our main result. 相似文献
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S.S. Dragomir 《Linear and Multilinear Algebra》2016,64(9):1800-1813
Some trace operator inequalities for synchronous functions that are related to the ?eby?ev inequality for sequences of real numbers are given. 相似文献
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We present an outline of the theory of Bessel-like functions with more than one index and one or more variables. Their link with other types of functions is discussed and their use in applications is touched on. 相似文献