On logarithmic q-statistical convergence and Korovkin approximation theorem

Abstract

Recently, the notion of q-Cesàro summability has been introduced as a new summability method. In this work, we make use of q-calculus and harmonic summability to define logarithmic q-density and logarithmic q-statistical convergence and establish its relation with H1q-summability. Further, we discuss how logarithmic q-statistical convergence and [H1q, p]-summability are related to each other. Finally, we use this new summability method in proving a Korovkin type theorem.