The sets of \(\left( \alpha ,\beta \right) \)-statistically convergent and \(\left( \alpha ,\beta \right) \)-statistically bounded sequences of order \(\gamma \) defined by modulus functions

In this research paper, our aim is to introduce the concepts of \(\varvec{\left( \alpha ,\beta \right) }\) $\left(\mathit{\alpha },\mathbf{,},\mathit{\beta }\right)$ -statistical convergence of order \(\varvec{\gamma } \) $\mathit{\gamma }$ and \(\varvec{\left( \alpha ,\beta \right) }\) $\left(\mathit{\alpha },\mathbf{,},\mathit{\beta }\right)$ -statistical boundedness of order \(\varvec{\gamma } \) $\mathit{\gamma }$ by using unbounded modulus functions in metric spaces. Furthermore, we obtain some relations between these concepts, and we provide some counterexamples to support our results.