Search

In this paper, we establish some inequalities of Hermite-Hadamard type for convex functions and convex functions on the co-ordinates defined in a rectangle from the plane. Keywords and Phrases: Hermite-Hadamard inequality, Convex function, Convex function on the co-ordinates., 1. Introduction Let I be an interval in R, f: I [??] R [right arrow] R be a convex function and a, b [member of] I with a < b. [...]

A sharp bound for some Euler-Gruss type inequalities are established and some applications are given. Keywords and Phrases: Euler formulae, Bernoulli polynomials, Gruss inequality, Simpson's rule., 1. Introduction Let f: [a,b][right arrow]R be such that [f.sup.(n)] (n[greater than or equal to]1) is continuous on [a,b] and [m.sub.n][less than or equal to][f.sup.(n)](t)[less than or equal to][M.sub.n], t [...]

In this paper, we establish some inequalities of Fejer type for g-convex dominated functions. Keywords and Phrases: Hermite-Hadamard inequality, Fejer inequality, g-Convex dominated functions., 1. Introduction The inequality f([a + b]/2) [less than or equal to] [1/[b-a]][[integral].sub.a.sup.b]f(x)dx [less than or equal to] [[f(a) + f(b)]/2], (1.1) which holds for all convex functions f: [a, [...]

In this note, we establish some multivariate Ostrowski type inequalities involving several functions. Keywords and Phrases: Multivariate, Ostrowski type inequalities, n-fold integral., 1. Introduction Throughout, R and [R.sup.n] denote the set of real numbers and the n--dimensional Euclidean space, respectively. Let D = {([x.sub.1], ..., [x.sub.n])∈ [R.sup.n]: [a.sub.i] < [x.sub.i] < [b.sub.i] [...]

Abstract In this paper, we establish some Ostrowski-Gruss-Cebysev type inequalities involving several functions whose modulus of the derivatives are convex functions. Keywords and Phrases: Ostrowski inequality, Gruss inequality, Cebysev inequality, [...]

Abstract In this paper, we establish some new Opial type finite difference inequalities. Keywords and Phrases: Opial type inequality, Finite difference inequalities, Forward differences, Holder's inequality, Nondecreasing functions of several [...]