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

Abstract

In this paper, we introduce $\mathfrak{q}$-statistical convergences for any sequence of real valued functions. Several properties of $\mathfrak{q}$-statistical convergences
for any sequence of real valued functions are discussed. Furthermore, we introduce the idea of $\mathfrak{q}$-statistical convergence for sequences of Jackson integrable functions. Further, we find $\mathfrak{q}$-statistical solution of $\mathfrak{q}$-differentiable equations with non-uniquely solvable Cauchy problems.