by the method of weight coefficients, techniques of real analysis andhermite-hadamard's inequality, a half-discrete hardy-hilbert-type inequalityrelated to the kernel of the hyperbolic cosecant function with the best possibleconstant factor expressed in terms of the extended riemann-zeta function is proved.the more accurate equivalent forms, the operator expressions with the norm,the reverses a...

We prove two kinds of Lyapunov type inequalities for pseudo-integrals. One discusses pseudo-integrals where pseudo-operations are given by a monotone and continuous function g. The other one focuses on the pseudo-integrals based on a semiring 0; 1 ½ Š; sup; ð Þ , where the pseudo-multiplication is generated. Some examples are given to illustrate the validity of these inequalities. As a generali...