​In this work, using the concepts of q -calculus, we first define the q -Jung-Kim-Srivastava and q -Bernardi integral operators for multivalent functions. Then, we use these operators to establish the generalized integral operator {{\mathcal{ {\mathcal B} }}}_{q,p}^{-m-\lambda }f\left(z) for multivalent functions. By using the newly defined operator {{\mathcal{ {\mathcal B} }}}_{q,p}^{-m-\lambda }f\left(z) , we define a new class of multivalent analytic functions and diskuss various interesting features of the functions belonging to this class. Certain interesting examples of our developments are also considered. Furthermore, we explore the applications of the Carathéodory lemma in the form of specific results.​​​