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formula MSC 2010: 26D10, 30E10, 41A55 || Andrea Aglić Aljinović: Department of Applied Mathematics, Faculty of Electrical Engineering and Computing, University of Zagreb, Unska 3, 10 000 Zagreb, Croatia, e-mail: andrea.aglic@fer.hr 1 Introduction TheMellin transformM(f) of a Lebesgue integrable mapping f : [0,∞⟩ → ℝ is dened by M(f)(z) = ∞ ∫ 0 f(t)tz−1dt (1.1) for every z ∈ ℂ for which the integral on the right hand side of (1.1) exists, i.e. !!!!∫ ∞ 0 f(t)t z−1dt!!!! <∞. The Mellin transform is widely used not only in various branches of mathematics (for instance for

, invex set, preinvex function, Hölder’s integral inequality MSC 2010: Primary 26D15; secondary 26A51, 26B12, 41A55 || Muhammad Amer Latif: School of Computational and Applied Mathematics, University of the Witwatersrand, Private Bag 3, Wits 2050, Johannesburg, South Africa, e-mail: m_amer_latif@hotmail.com Sever Silvestru Dragomir: School of Engineering and Science, Victoria University, PO Box 14428, Melbourne City, MC 8001, Australia; and School of Computational and Applied Mathematics, University of the Witwatersrand, Private Bag 3, Wits 2050, Johannesburg, South

DOI 10.1515/anly-2012-1235 | Analysis 2014; 34 (4):379–389 Research Article Muhammad Amer Latif New Hermite–Hadamard type integral inequalities for GA-convex functions with applications Abstract: In this paper, some renements of Hermite–Hadamard type inequali- ties for GA-convex functions are obtained. Applications of the obtained results to special means are given. Keywords: Hermite–Hadamard’s inequality, convex function, GA-convex func- tion, Hölder’s inequality MSC 2010: Primary 26D15; secondary 26A51, 26E60, 41A55 || Muhammad Amer Latif: School of

Abstract

Asymptotic expressions for remainder terms of the mid-point, trapezoid and Simpson’s rules are given. Corresponding formulas with finite sums are also given.

Abstract

In the paper there are presented and evaluated for effectiveness three methods of accuracy increase of fractional order derivatives and integrals computations for application with the Riemann-Liouville/Caputo formulas. They are based on the ideas of either transforming difficult integrand in the formulas to high-accuracy computations requirements of a applied method of numerical integration or adapting a numerical method of integration to handle with high-accuracy a difficult feature in the integrand. Additional accuracy gain is obtained by incorporating increased precision into computations. The actual accuracy improvement by applying presented methods is compared with the capabilities of wide range of available methods of integration.

Abstract

In this work, we construct a new general two-point quadrature rules for the Riemann–Stieltjes integral abf(t)du(t), where the integrand f is assumed to be satisfied with the Hölder condition on [a, b] and the integrator u is of bounded variation on [a, b]. The dual formulas under the same assumption are proved. Some sharp error Lp–Error estimates for the proposed quadrature rules are also obtained.

Abstract

We establish two Ostrowski type inequalities for double integrals of second order partial derivable functions which are bounded. Then, we deduce some inequalities of Hermite-Hadamard type for double integrals of functions whose partial derivatives in absolute value are convex on the co-ordinates on rectangle from the plane. Finally, some applications in Numerical Analysis in connection with cubature formula are given.

Abstract

In this work, Lp-error estimates of general two and three point quadrature rules for Riemann-Stieltjes integrals are given. The presented proofs depend on new triangle type inequalities of Riemann-Stieltjes integrals.

Abstract

A sharp companion of Ostrowski’s inequality for the Riemann-Stieltjes integral abf(t)du(t), where f is assumed to be of r-H-Hölder type on [a, b] and u is of bounded variation on [a, b], is proved. Applications to the approximation problem of the Riemann-Stieltjes integral in terms of Riemann-Stieltjes sums are also pointed out.

Abstract.

In the paper, the authors obtain some Hermite–Hadamard type integral inequalities for extended s-convex functions on the co-ordinates in a rectangle.