• Honam Mathematical Journal
• /
• v.44 no.4
• /
• pp.560-571
• /
• 2022

In this paper, firstly we introduce the concepts of deferred Cesàro summable and deferred statistically convergent function, and secondly we introduce the concepts of deferred almost summable and deferred almost statistically convergent functions. Furthermore, we investigate the relations between these concepts.

• Kyungpook Mathematical Journal
• /
• v.64 no.2
• /
• pp.235-244
• /
• 2024

In this paper, we establish relations between the sets of strongly Cesàro summable sequences of complex numbers for modulus functions f and g satisfying various conditions. Furthermore, for some special modulus functions, we obtain relations between the sets of strongly Cesàro summable and statistically convergent sequences of complex numbers.

• Journal of Applied and Pure Mathematics
• /
• v.5 no.3_4
• /
• pp.265-279
• /
• 2023

In this paper, we firstly presented the definitions of arithmetic ${\mathcal{I}}$-statistically convergence, ${\mathcal{I}}$-lacunary arithmetic statistically convergence, strongly ${\mathcal{I}}$-lacunary arithmetic convergence, ${\mathcal{I}}$-Cesàro arithmetic summable and strongly ${\mathcal{I}}$-Cesàro arithmetic summable using weighted density via Orlicz function ${\tilde{\phi}}$. Then, we proved some theorems associated with these concepts, and we examined the relationship between them. Finally, we establish some sequential properties of ${\mathcal{I}}$-lacunary arithmetic statistical continuity.

• Kyungpook Mathematical Journal
• /
• v.52 no.2
• /
• pp.137-147
• /
• 2012

In this paper we introduce some new double sequence spaces via ideal convergence and an Orlicz function in $n$-normed spaces and examine some properties of the resulting spaces.

• Kyungpook Mathematical Journal
• /
• v.58 no.1
• /
• pp.91-103
• /
• 2018

In this paper, we generalize the concept of deferred density to that of deferred f-density, where f is an unbounded modulus and introduce a new non-matrix convergence method, namely deferred f-statistical convergence or $S^f_{p,q}$-convergence. Apart from studying the $K{\ddot{o}}the$-Toeplitz duals of $S^f_{p,q}$, the space of deferred f-statistically convergent sequences, a decomposition theorem is also established. We also introduce a notion of strongly deferred $Ces{\grave{a}}ro$ summable sequences defined by modulus f and investigate the relationship between deferred f-statistical convergence and strongly deferred $Ces{\grave{a}}ro$ summable sequences defined by f.