On some properties of IK-convergence.

In 2011 M. Macaj and M. Sleziak first introduced the concept of I^K convergence mainly as a generalization of statistical convergence. In this paper, we introduce and investigate a few interesting properties of I^K convergence of real sequences. We also study some implication relations between I, I*, and I^K-convergence of such sequences. Further, we find the conditions under which (i) I^K-convergence implies K-convergence, (ii) I^K-convergence implies I-convergence, (iii) I-convergence implies I^K-convergence, and (iv) K^I-convergence implies I^K-convergence. [ABSTRACT FROM AUTHOR]