$\boldsymbol{\mathcal I^{*}\text{-}\alpha}$ CONVERGENCE AND $\boldsymbol{\mathcal I^*}$-EXHAUSTIVENESS OF SEQUENCES OF METRIC FUNCTIONS

Authors

  • A. Ghosh Department of Mathematics, Brainware University, Barasat, Kolkata-700125, India Author

Keywords:

$\mathcal I^{*}\text{-}\alpha$ convergence, $\mathcal I^*$-exhaustiveness, sequence of metric functions, ideal convergence

Subjects:

40A35, 26A03

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.

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Published

2022-04-15