Some Hardy-type integral inequalities with sharp constant involving monotone functions

In this work, we present some Hardy-type integral inequalities for 0 < p < 1 via a second parameter q > 0 with sharp constant. This inequalities are new generalizations to the inequalities given below.

___

  • Benaissa, B., Budak, H., On Hardy-type integral inequalities with negative parameter,Turkish Journal of Inequalities, 5(2) (2021), 42-47.
  • Benaissa, B., Sarikaya, M. Z., Senouci, A., On some new Hardy-type inequalities, J. Math. Meth. Appl. Sci., 43 (2020), 8488-8495. https/doi.org/10.1002/mma.6503
  • Yang, B., On a new Hardy type integral inequalities, Int. Math. Forum., 67(2) (2007), 3317–3322.
  • Burenkov, V. I., On the best constant in Hardy’s inequality with 0 < p < 1 for monotone functions, Proc. Steklov Inst. Math., 194 (1993), 59-63.
  • Sulaiman, W. T., Some Hardy type integral inequalities, Appl. Math. Lett, 25 (2012), 520-525. https://doi.org/10.1016/j.aml.2011.09.050
  • Kufner, A., Maligranda, L., Person, L. E., The Hardy Inequality: About Its History and Some Related Results, Vydavatelsky Servis Publishing House, Pilsen, 2007.
  • Banyat, S., More on some Hardy type integral inequalities, J. Math. Inequal., 8(3) (2014), 497–501.