I∗-α CONVERGENCE AND I∗-EXHAUSTIVENESS OF SEQUENCES OF METRIC FUNCTIONS

Abstract

By a metric function, we mean a function from a metric space $(X,d)$ into a metric space $(Y,\rho )$. We introduce and study the notions of ${\mathcal{I}}^{\ast }\text{-}\alpha$ convergence and ${\mathcal{I}}^{\ast }$-exhaustiveness of sequences of metric functions, and we establish an inter-relationship between these two concepts. Moreover, we establish some relationship between our concepts with some well-established concepts such as $\mathcal{I}\text{-}\alpha$ convergence and $\mathcal{I}$-exhaustiveness of sequences of metric functions.