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The one-dimensional spinless Salpeter equation has been solved for thePT-symmetric generalized Hulth\'{e}n potential. The Nikiforov-Uvarov {NU)method which is based on solving the second-order linear differential equationsby reduction to a generalized equation of hypergeometric type is used to obtainexact energy eigenvalues and corresponding eigenfunctions. We have investigatedthe positive and negative exact bound states of the s-states for differenttypes of complex generalized Hulthen potentials.Comment: 24 page

BOUND-STATES OF A SEMI-RELATIVISTIC EQUATION FOR THE ${\cal PT}$-SYMMETRIC GENERALIZED HULTHÉN POTENTIAL BY THE NIKIFOROV–UVAROV METHOD