HALF-DISCRETE HILBERT'S INEQUALITY FOR THREE VARIABLES WITH HYPERBOLIC SINE FUNCTION

Abstract

For three variables of the half-discrete Hilbert's inequality and using the hyperbolic sine function, we present two new forms of the half-discrete Hilbert's inequality in thisstudy. We also demonstrate that the constants on the right-hand side of the inequality arethe best. The equivalence forms of the two inequalities are also introduced.