f-asymptotically lacunary ideal equivalence of double sequences

Abstract

Abstract In this study, we present the notions of f-asymptotically I2 $\mathcal{I}_{2}$-equivalence, strongly f-asymptotically I2 $\mathcal{I}_{2}$-equivalence, f-asymptotically lacunary I2 $\mathcal{I}_{2}$-equivalence, and strongly f-asymptotically lacunary I2 $\mathcal{I}_{2}$-equivalence of double sequences and investigate some relationships between them. Also, we examine some relationships between strongly f-asymptotically I2 $\mathcal{I}_{2}$-equivalence and asymptotically I2 $\mathcal{I}_{2}$-statistical equivalence and between strongly f-asymptotically lacunary I2 $\mathcal{I}_{2}$-equivalence and asymptotically lacunary I2 $\mathcal{I}_{2}$-statistical equivalence of double sequences.

Keywords

• Asymptotically equivalence
• Lacunary sequence
• I 2 $\mathcal{I}_{2}$ -equivalence
• Double sequence
• Modulus function