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 IS bottomonium are also calculated. Further, the pseudoscalar and vector decay constants of the Be 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-beta+kappa r(beta)+V-0, with beta= 1, 1/2, 3/4 decomposed into scalar and vector parts in the form Vv(r) = -Ar-beta + (1 - epsilon)kappa r(beta) and V-S(r) = epsilon kappa r(beta) + Vo; where 0 <= epsilon <= 1. We have used the shifted large-N-expansion technique (SLNET) to solve the reduced equation for the scalar (epsilon = 1), equal mixture of scalar-vector (epsilon = 1/2), and vector (epsilon = 0) confinement interaction kernels. The energy eigenvalues are carried out up to the third order approximation.