To complement the property of Q-order of convergence we introduce the notions of Q-superorder and Q-suborder of convergence. A new definition of exact Q-order of convergence given in this note generalizes one given by Potra. The definitions of exact Q-superorder and exact Q-suborder of convergence are also introduced. These concepts allow the characterization of any sequence converging with Q-o...

A combinatorial study of multiple q-integrals is developed. This includes a q-volume of a convex polytope, which depends upon the order of q-integration. A multiple q-integral over an order polytope of a poset is interpreted as a generating function of linear extensions of the poset. Specific modifications of posets are shown to give predictable changes in q-integrals over their respective orde...

By making use of a higher-order q-derivative operator, certain families meromorphic q-starlike functions and q-convex are introduced studied. Several sufficient conditions coefficient inequalities for in these subclasses derived. The results presented this article extend generalize number previous results.

Abstract The fast growing solutions of the following linear differential equation $$(*)$$ ( ∗ ) is investigated by using a more general scale $${[p,q]_{,\varphi }}$$ [ p , <mml:m...