We report new measurements of the production cross sections of pairs of
charged pions and kaons as a function of their fractional energies using
various fractional-energy definitions. Two different fractional-energy
definitions were used and compared to the conventional fractional-energy
definition reported previously. The new variables aim at either identifying
dihadron cross sections in terms of single-hadron fragmentation functions, or
to provide a means of characterizing the transverse momentum created in the
fragmentation process. The results were obtained applying the updated
initial-state radiation correction used in other recent Belle publications on
light-hadron production cross sections. In addition, production cross sections
of single charged pions, kaons, and protons were also updated using this
initial-state radiation correction. The cross sections are obtained from a
$558\,{\rm fb}^{-1}$ data sample collected at the $\Upsilon(4S)$ resonance with
the Belle detector at the KEKB asymmetric-energy $e^+ e^-$ collider.