In this paper, we introduce a new function class called n-fractional polynomial convex function and their some algebric properties. We obtain some refinements of the right-hand side of Hermite-Hadamard inequality for the class of functions whose derivatives in absolutely value at certain powers are n-fractional polynomial convex. Also, we compare the results obtained with both Hölder, Hölder-İşcan inequalities and power-mean, improved-power-mean integral inequalities and show that the result obtained with Hölder-İşcan and improved power-mean inequalities give better approach than the others. Some applications to special means of real numbers are also given. [ABSTRACT FROM AUTHOR]
The main object of this paper is to study an old problem concerning the hyper-sums of powers of integers. First, we establish some important properties of this problem (generating function, explicit formula, congruence). Finally, an explicit formula for the hyper-sums of powers of integers involving the generalized Bernoulli polynomials are also given. [ABSTRACT FROM AUTHOR]
In this paper we introduce r-parameter Srivastava polynomials in r-variable by inserting new indices. These polynomials include the Lagrange polynomials in several variables, which are also known as Chan-Chyan-Srivastava polynomials (W.-C.C. Chan, C.-J. Chyan and H.M. Srivastava, The Lagrange polynomials in several variables, Integral Transforms and Special Functions, 12 (2001) 139-148). We prove several two sided linear generating relations between r-variable and (r-1)-variable Chan-Chyan-Srivastava polynomials. Some special cases of the main results are also presented. [ABSTRACT FROM AUTHOR]