Power series inequalities via Young’s inequality with applications

Abstract

In this paper, we establish some inequalities for power series with real coefficients by utilizing Young's inequality for sequences of complex numbers. Some applications for special functions such as polylogarithm, hypergeometric and Bessel functions are also presented. MSC: 26D15

Inequalities for Power Series with Nonnegative Coefficients via Reverses of Jensen Inequality

“…For other recent results for power series with nonnegative coefficients, see [9] and [10]. For more results on power series inequalities, see [2] and [5]- [8].…”

Further inequalities for power series with nonnegative coefficients via a reverse of Jensen inequality

“…For some similar exponential and logarithmic inequalities see [5]. For other recent results for power series with nonnegative coefficients, see [2], [7], [11] and [12]. For more results on power series inequalities, see [2] and [7]- [10].…”

Some new results for power means

“…For example, in [9], Ibrahim and Dragomir established inequalities by utilizing power series and Young's inequality. In [10], Kouba used classical analysis to obtain some new inequalities.…”