On logarithmic q-statistical convergence and Korovkin approximation theorem

Abstract

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 $H_{q}^{1}$-summability. Further, we discuss how logarithmic $q$-statistical convergence and $[H_{q}^{1},p]$-summability are related to each other. Finally, we use this new summability method in proving a Korovkin type theorem.