Due to its significance in reconstructing signals, the theory of dual frames has attracted the interest of many mathematicians. In this paper, we introduce the concept of approximate Q-oblique dual g-frames. We characterize the approximate Q-oblique dual g-frames of an arbitrarily given g-frame; present a method for constructing approximate Q-oblique dual g-frame pairs that have better approximation from a given approximate Q-oblique dual g-frame pair; and investigate the stability of approximate Q-oblique dual g-frame pairs under the analysis, synthesis and frame operator-perturbation, the gap-perturbation, and the 𝓁2 operator portrait-perturbation. Finally, as an application of the above results, we obtain some new results on usual frames which cover some existing results.

Characterization and Construction of Approximate Q -Oblique Dual g-Frames