On q-statistical convergence and statistical solution of q-Cauchy problem

In this paper, we present the concept of q-statistical convergence for any sequence of real-valued functions. Several characteristics of q-statistical convergence for sequences of functions with real values are examined. Further, we introduce the notion of q-statistical convergence for sequences of Jackson integrable functions. Finally, we determine the q-statistical solution of q-differential equations that involve non-uniquely solvable Cauchy problems.