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In this paper we establish some natural consequences of the Wirtinger integral inequality. Applications related to the trapezoid unweighted and weighted inequalities, of Fej'er's inequality for convex functions and of Gr¨uss' type inequalities are also provided. [ABSTRACT FROM AUTHOR]

In this paper, is defined the operator Dλ,ν,nα,β : A → A, given by Dλ,ν,nα,β f(z) = (1 - α - β)RνDnf(z) + αRνΩλzf(z) + βDnΩλzf(z), for z ∈ U, where Rν is the Ruscheweyh derivative, Dn is the Sălăgean operator, Ωλz is a fractional differintegral operator introduced by S. Owa and H. M. Srivastava, A = {f ∈ H(U) : f(z) = z + a2z² + a3z³ + ..., z ∈ U}, α, β ≥ 0, ν > -1, n ∈ N0 = {0, 1, 2, 3, ...}, -∞ < λ < 2. A certain subclass of analytic functions in the open unit disk, Rλ,ν,nα,β (δ), where 0 ≤ δ ≤ 1, is introduced using the new operator. Are obtained some properties of the class Rλ,ν,nα,β (δ) and some differential subordinations using the operator Dλ,ν,nα,β. [ABSTRACT FROM AUTHOR]

In this article we present a method to get upper bound for some integrals. The method is in connection with on a generalized trapezoidal quadrature formula. Applications for upper bounds of the elliptical integral of the first kind are presented. We compare these bounds with some previous results from the literature. [ABSTRACT FROM AUTHOR]