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 $\mathcal I^{*}\text{-}\alpha$ convergence and $\mathcal I^*$-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.

Keywords: $\mathcal I^{*}\text{-}\alpha$ convergence; $\mathcal I^*$-exhaustiveness; sequence of metric functions; ideal convergence.

MSC: 40A35, 26A03

Pages:  110$-$118     

Volume  74 ,  Issue  2 ,  2022