What question did this study set out to answer?

The aim is to define and explore the concepts of strongly lacunary convergence and Cauchy sequences in double sequences of functions.

May 24, 2026Open Access

STRONGLY LACUNARY I₂-CONVERGENCE OF DOUBLE SEQUENCES OF FUNCTIONS

Key Points

The aim is to define and explore the concepts of strongly lacunary convergence and Cauchy sequences in double sequences of functions.
Defined strongly lacunary convergence, $ ext{I}_2$-convergence, and $ ext{I}^ ext{*}$-convergence of double sequences of functions.
Investigated relationships between these convergence types and corresponding Cauchy sequences.
Identified clear relationships among strongly lacunary convergence, Cauchy sequences, and variations of the $ ext{I}_2$ and $ ext{I}^ ext{*}$ definitions.

Abstract

In this paper, firstly, we define the concepts of strongly lacunary convergence, strongly lacunary I-convergence and strongly lacunary I^-convergence of double sequence of functions, and also we investigate the relations between them. Then, we define the concepts of strongly lacunary Cauchy sequence, strongly lacunary I₂-Cauchy sequence and and strongly lacunary I^₂-Cauchy sequence of functions, and also we investigate the relations among strongly lacunary I₂-convergence, strongly lacunary I₂-Cauchy sequence and strongly lacunary I^₂-Cauchy sequence.

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