Statistical Convergence via <em>q</em>-Calculus and a Korovkin’s Type Approximation Theorem

Abstract

In this paper, we define and study q-statistical limit point, q-statistical cluster point, q-statistically Cauchy, q-strongly Cesàro and statistically C1q-summable sequences. We establish relationships of q-statistical convergence with q-statistically Cauchy, q-strongly Cesàro and statistically C1q-summable sequences. Further, we apply q-statistical convergence to prove a Korovkin type approximation theorem.

Keywords

• statistical convergence
• <i>q</i>-integers
• <i>q</i>-Cesàro matrix
• <i>q</i>-statistical convergence
• <i>q</i>-statistical limit point
• <i>q</i>-statistical cluster point