Korovkin Type Approximation Theorems via Lacunary Equistatistical Convergence

Abstract

H. Aktuğlu and H. Gezer [Central European J. Math. 7 (2009), 558--567] introduced the concepts of lacunary equistatistical convergence, lacunary statistical pointwise convergence and lacunary statistical uniform convergence for sequences of functions. In this paper, we apply the notion of lacunary equistatistical convergence to prove a Korovkin type approximation theorem by using test functions 1,(x/(1-x)),((x/(1-x)))².