m at h . C A ] 9 J an 2 00 7 GENERALIZED CONVEXITY AND INEQUALITIES
نویسنده
چکیده
Let R+ = (0,∞) and let M be the family of all mean values of two numbers in R+ (some examples are the arithmetic, geometric, and harmonic means). Given m1, m2 ∈ M, we say that a function f : R+ → R+ is (m1, m2)-convex if f(m1(x, y)) ≤ m2(f(x), f(y)) for all x, y ∈ R+. The usual convexity is the special case when both mean values are arithmetic means. We study the dependence of (m1, m2)-convexity on m1 and m2 and give sufficient conditions for (m1, m2)-convexity of functions defined by Maclaurin series. The criteria involve the Maclaurin coefficients. Our results yield a class of new inequalities for several special functions such as the Gaussian hypergeometric function and a generalized Bessel function.
منابع مشابه
Pseudoconvex Multiobjective Continuous-time Problems and Vector Variational Inequalities
In this paper, the concept of pseudoconvexity and quasiconvexity for continuous~-time functions are studied and an equivalence condition for pseudoconvexity is obtained. Moreover, under pseudoconvexity assumptions, some relationships between Minty and Stampacchia vector variational inequalities and continuous-time programming problems are presented. Finally, some characterizations of the soluti...
متن کاملSome existence results for generalized vector quasi-equilibrium problems
In this paper, we introduce and study a class of generalized vector quasi-equilibrium problem, which includes many vector equilibrium problems, equilibrium problems, vector variational inequalities and variational inequalities as special cases. Using one person game theorems, the concept of escaping sequences and without convexity assumptions, we prove some existence results for ...
متن کاملSchur convexity of the generalized geometric Bonferroni mean and the relevant inequalities
In this paper, we discuss the Schur convexity, Schur geometric convexity and Schur harmonic convexity of the generalized geometric Bonferroni mean. Some inequalities related to the generalized geometric Bonferroni mean are established to illustrate the applications of the obtained results.
متن کاملar X iv : m at h / 03 11 27 5 v 1 [ m at h . A P ] 1 7 N ov 2 00 3 REPRESENTATION OF MULTIVARIATE FUNCTIONS VIA THE POTENTIAL THEORY
t− a if a ≤ t ≤ x t− b if x < t ≤ b . In the last decade, many authors (see for example [2] and the references therein) have extended the above result for different classes of functions defined on a compact interval, including: functions of bounded variation, monotonic functions, convex functions, n-time differentiable functions whose derivatives are absolutely continuous or satisfy different c...
متن کاملOpial–type Inequalities for Fractional Integral Operator Involving Mittag––leffler Function
In this paper we give generalization of Opial-type inequalities by using generalized fractional integral operator involving generalized Mittag–Leffler function. We deduce some results which already have been proved. Also we consider n -exponential convexity of some non-negative differences of inequalities involving Mittag-Leffler function and deduce their exponential convexity and log-convexity.
متن کامل