Chebyshev–Grüss type inequalities via Euler type and Fink identities

Euler-type Identities for Integer Compositions via Zig-zag Graphs

This paper is devoted to a systematic study of combinatorial identities which assert the equality of different sets of compositions, or ordered partitions, of integers. The proofs are based on properties of zig-zag graphs the graphical representations of compositions introduced by Percy A. MacMahon in his classic book Combinatory Analysis. In particular it is demonstrated, by means of general t...

New Inequalities of Shafer-Fink Type for Arc Hyperbolic Sine

On Shafer-Fink-Type Inequality

Algorithms for Some Euler-Type Identities for Multiple Zeta Values

. . . , s k are positive integers with s 1 > 1. For k ≤ n, let E(2n, k) be the sum of all multiple zeta values with even arguments whose weight is 2n and whose depth is k. The well-known result E(2n, 2) = 3ζ(2n)/4was extended to E(2n, 3) and E(2n, 4) by Z. Shen and T. Cai. Applying the theory of symmetric functions, Hoffman gave an explicit generating function for the numbers E(2n, k) and then ...

Some extended Simpson-type inequalities and applications

‎In this paper‎, ‎we shall establish some extended Simpson-type inequalities‎ ‎for differentiable convex functions and differentiable concave functions‎ ‎which are connected with Hermite-Hadamard inequality‎. ‎Some error estimates‎ ‎for the midpoint‎, ‎trapezoidal and Simpson formula are also given‎.