We reproduce masses of the self-conjugate and
non-self-conjugate mesons in the context of the spinless Salpeter
equation taking into account the relativistic kinematics and the quark
spins. The hyperfine splittings for the 2S charmonium and 1S bottomonium
are also calculated. Further, the pseudoscalar and vector decay
constants of the Bc meson and the unperturbed radial wave
function at the origin are also calculated. We have obtained a local
equation with a complete relativistic corrections to a class of three
attractive static interaction potentials of the general form V(r) = -Ar-β + κrβ + V0, with β = 1, 1/2, 3/4 decomposed into scalar and vector parts in the form VV(r) = -Ar-β + (1-∊)κrβ and VS(r) = ∊κrβ + V0;
where 0≤∊≤1. We have used the shifted large-N-expansion technique
(SLNET) to solve the reduced equation for the scalar (∊ = 1), equal
mixture of scalar-vector (∊ = 1/2), and vector (∊ = 0) confinement
interaction kernels. The energy eigenvalues are carried out up to the
third order approximation.