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Over the last few years, numerous researchers have contributed significantly to summability theory by connecting various notions of convergence concepts of sequences. In this paper, we introduce the concepts ofℐ{\mathcal{I}}-statistical supremum andℐ{\mathcal{I}}-statistical infimum of a real-valued sequence and study some fundamental features of the newly introduced notions. We also introduce the concept ofℐ{\mathcal{I}}-statistical monotonicity and establish the condition under which anℐ{\mathcal{I}}-statistical monotonic sequence isℐ{\mathcal{I}}-statistical convergent. We end up giving a necessary and a sufficient condition for theℐ{\mathcal{I}}-statistical convergence of a real-valued sequence.

Certain aspects of ℐ-statistical supremum and ℐ-statistical infimum of real-valued sequences