• Kyungpook Mathematical Journal
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• v.64 no.2
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• pp.235-244
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• 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 mathematics & informatics
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• v.37 no.5_6
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• pp.459-467
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• 2019

In this work, via Orlicz functions, we have obtained a generalization of rough statistical convergence of asymptotically equivalent triple sequences a new non-matrix convergence method, which is intermediate between the ordinary convergence and the rough statistical convergence. We also have examined some inclusion relations related to this concept. We obtain the results are non negative real numbers with respect to the partial order on the set of real numbers.

• Kyungpook Mathematical Journal
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• v.58 no.2
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• pp.271-289
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• 2018

Let 0 < q < ${\infty}$. In this study, we introduce the spaces ${\mathcal{BV}}_q$ and ${\mathcal{LS}}_q$ of q-bounded variation double sequences and q-summable double series as the domain of four-dimensional backward difference matrix ${\Delta}$ and summation matrix S in the space ${\mathcal{L}}_q$ of absolutely q-summable double sequences, respectively. Also, we determine their ${\alpha}$- and ${\beta}-duals$ and give the characterizations of some classes of four-dimensional matrix transformations in the case 0 < q ${\leq}$ 1.

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

• Journal of applied mathematics & informatics
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• v.42 no.2
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• pp.245-256
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• 2024

This article introduces the notion of almost deferred weighted convergence, statistical deferred weighted almost convergence and almost deferred weighted statistical convergence for real valued sequences. Further, with the aid of interesting examples, we investigated some relationships among our proposed methods. Moreover, we prove a new type of approximation theorem and demonstrated that our theorem effectively extends and improves most of the earlier existing results. Finally, we have presented an example which proves that our theorem is a stronger than its classical versions.