Some generalizations of integral inequalities for quasimonotone functions in weighted variable exponent Lebesgue space with $0<p(x)<1$

The aim of the talk is to obtain some generalizations of the weighted Hardy inequalities obtained in (V.I. Burenkov, T.V.Tararykova, { About Holder's inequality in Lebesgue space with variable summability}. Contemporary Mathematics. Fundamental Directions, 67 (2021), no. 3, 472-482 (in Russian); A. Senouci, A. Zanou, Some integral inequalities for quasi-monotone functions in weighted variable exponent Lebesgue spaces with 0<p(x)<1. Eurasian Math. Journal 4 (2020), no. 4, 58-65.) for quasi-monotone functions in weighted variable exponent Lebesgue space with $0<p(x)<1$.