Symmetry, cilt.15, sa.4, 2023 (SCI-Expanded)
The main purpose of this paper is to define multiple alternative q-harmonic numbers, (Formula presented.) and multi-generalized q-hyperharmonic numbers of order r, (Formula presented.) by using q-multiple zeta star values (q-MZSVs). We obtain some finite sum identities and give some applications of them for certain combinations of q-multiple polylogarithms (Formula presented.) with the help of generating functions. Additionally, one of the applications is the sum involving q-Stirling numbers and q-Bernoulli numbers.