On an extended Hardy-Littlewood-Polya’s inequality

Abstract

By utilization of the weight coefficients, the idea of introducing parameters and Euler-Maclaurin summation formula, an extended Hardy-Littlewood-Polya’s inequality and its equivalent form are established. The equivalent statements of the best possible constant factor involving several parameters, and some particular cases are provided. The operator expressions of the obtained results are also considered.

Keywords

• weight coefficient
• hardy-littlewood-polya’s inequality
• euler-maclaurin summation formula
• equivalent statement
• parameter