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494 results on '"Savas, Ekrem"'

1. The novel Tauberian conditions associated with the $(\overline{N},p,q)$ summability of double sequences

Author

Önder, Zerrin, Savaş, Ekrem, and Çanak, İbrahim

Subjects
Mathematics - General Mathematics, 40A05, 40E05, 40G99
Abstract

In this paper, our primary objective is to provide a fresh perspective on the relationship between the $(\overline{N},p,q)$ method, which is a product of relevant one-dimensional summability methods, and $P$-convergence for double sequences. To accomplish this objective, we establish certain Tauberian conditions that control the behavior of a double sequence in terms of both $O_L$-oscillation and $O$-oscillation in certain senses, building a bridge between $(\overline{N},p,q)$ summability and $P$-convergence, while imposing certain restrictions on the weight sequences. As special circumstances of our findings, we demonstrate that Landau-type $O_L$ condition with respect to $(P_m)$ and $(Q_n),$ as well as Hardy-type $O$ condition with respect to $(P_m)$ and $(Q_n),$ serve as Tauberian conditions for $(\overline{N},p,q)$ summability under particular additional conditions. Consequently, these results encompass all classical Tauberian theorems, including conditions such as slow decrease or slow oscillation in certain senses.

Published
2023

2. Measure theoretic results for approximation by neural networks with limited weights

Author

Ismailov, Vugar and Savas, Ekrem

Subjects
Computer Science - Machine Learning, Mathematics - Functional Analysis, 41A30, 41A63, 92B20
Abstract

In this paper, we study approximation properties of single hidden layer neural networks with weights varying on finitely many directions and thresholds from an open interval. We obtain a necessary and at the same time sufficient measure theoretic condition for density of such networks in the space of continuous functions. Further, we prove a density result for neural networks with a specifically constructed activation function and a fixed number of neurons., Comment: 12 pages

Published
2023
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3. On Some Sequence Spaces in Fuzzy

Author

Savas, Ekrem, Kacprzyk, Janusz, Series Editor, Gomide, Fernando, Advisory Editor, Kaynak, Okyay, Advisory Editor, Liu, Derong, Advisory Editor, Pedrycz, Witold, Advisory Editor, Polycarpou, Marios M., Advisory Editor, Rudas, Imre J., Advisory Editor, Wang, Jun, Advisory Editor, Giri, Debasis, editor, Vaidya, Jaideep, editor, Ponnusamy, S., editor, Lin, Zhiqiang, editor, Joshi, Karuna Pande, editor, and Yegnanarayanan, V., editor

Published
2024
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6. Some Sequence Spaces of Weight f

Author

Savaş, Ekrem, Kacprzyk, Janusz, Series Editor, Pal, Nikhil R., Advisory Editor, Bello Perez, Rafael, Advisory Editor, Corchado, Emilio S., Advisory Editor, Hagras, Hani, Advisory Editor, Kóczy, László T., Advisory Editor, Kreinovich, Vladik, Advisory Editor, Lin, Chin-Teng, Advisory Editor, Lu, Jie, Advisory Editor, Melin, Patricia, Advisory Editor, Nedjah, Nadia, Advisory Editor, Nguyen, Ngoc Thanh, Advisory Editor, Wang, Jun, Advisory Editor, Giri, Debasis, editor, Raymond Choo, Kim-Kwang, editor, Ponnusamy, Saminathan, editor, Meng, Weizhi, editor, Akleylek, Sedat, editor, and Prasad Maity, Santi, editor

Published
2022
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8. Generalized Double Statistical Convergence in Topological Groups

Author

Savas, Ekrem, Kacprzyk, Janusz, Series Editor, Pal, Nikhil R., Advisory Editor, Bello Perez, Rafael, Advisory Editor, Corchado, Emilio S., Advisory Editor, Hagras, Hani, Advisory Editor, Kóczy, László T., Advisory Editor, Kreinovich, Vladik, Advisory Editor, Lin, Chin-Teng, Advisory Editor, Lu, Jie, Advisory Editor, Melin, Patricia, Advisory Editor, Nedjah, Nadia, Advisory Editor, Nguyen, Ngoc Thanh, Advisory Editor, Wang, Jun, Advisory Editor, Giri, Debasis, editor, Buyya, Rajkumar, editor, Ponnusamy, S., editor, De, Debashis, editor, Adamatzky, Andrew, editor, and Abawajy, Jemal H., editor

Published
2021
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9. Double Lacunary Statistical Convergence of Weight via Ideal in Topological Groups

Author

Savaş, Ekrem, Kacprzyk, Janusz, Series Editor, Pal, Nikhil R., Advisory Editor, Bello Perez, Rafael, Advisory Editor, Corchado, Emilio S., Advisory Editor, Hagras, Hani, Advisory Editor, Kóczy, László T., Advisory Editor, Kreinovich, Vladik, Advisory Editor, Lin, Chin-Teng, Advisory Editor, Lu, Jie, Advisory Editor, Melin, Patricia, Advisory Editor, Nedjah, Nadia, Advisory Editor, Nguyen, Ngoc Thanh, Advisory Editor, Wang, Jun, Advisory Editor, Giri, Debasis, editor, Ho, Anthony T. S., editor, Ponnusamy, S., editor, and Lo, Nai-Wei, editor

Published
2021
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10. On -Ideal Statistical Convergence of Weighted h for Multiple Sequences

Author

Savaş, Ekrem, Kacprzyk, Janusz, Series Editor, Pal, Nikhil R., Advisory Editor, Bello Perez, Rafael, Advisory Editor, Corchado, Emilio S., Advisory Editor, Hagras, Hani, Advisory Editor, Kóczy, László T., Advisory Editor, Kreinovich, Vladik, Advisory Editor, Lin, Chin-Teng, Advisory Editor, Lu, Jie, Advisory Editor, Melin, Patricia, Advisory Editor, Nedjah, Nadia, Advisory Editor, Nguyen, Ngoc Thanh, Advisory Editor, Wang, Jun, Advisory Editor, Giri, Debasis, editor, Ho, Anthony T. S., editor, Ponnusamy, S., editor, and Lo, Nai-Wei, editor

Published
2021
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13. [Untitled]

Author

Savaş, Ekrem, Kacprzyk, Janusz, Series Editor, Pal, Nikhil R., Advisory Editor, Bello Perez, Rafael, Advisory Editor, Corchado, Emilio S., Advisory Editor, Hagras, Hani, Advisory Editor, Kóczy, László T., Advisory Editor, Kreinovich, Vladik, Advisory Editor, Lin, Chin-Teng, Advisory Editor, Lu, Jie, Advisory Editor, Melin, Patricia, Advisory Editor, Nedjah, Nadia, Advisory Editor, Nguyen, Ngoc Thanh, Advisory Editor, Wang, Jun, Advisory Editor, Dutta, Hemen, editor, Hammouch, Zakia, editor, Bulut, Hasan, editor, and Baskonus, Haci Mehmet, editor

Published
2020
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16. Some new lacunary $f$-statistical $A$-convergent sequence spaces of order $\alpha$

Author

Savas, Ekrem and Borgohain, Stuti

Subjects
Mathematics - Functional Analysis
Abstract

We study the concept of density for sets of natural numbers in some lacunary $A$-convergent sequence spaces. Also we are trying to investigate some relation between the ordinary convergence and module statistical convergence for evey unbounded modulus function. Morever we also study some results on the newly defined lacunary $f$-statistically $A$-convergent sequence spaces with respect to some Musielak-Orlicz function., Comment: Conference paper. arXiv admin note: text overlap with arXiv:1506.05452

Published
2015
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17. Measures of noncompactness in some new lacunary difference sequence spaces

Author

Savas, Ekrem and Borgohain, Stuti

Subjects
Mathematics - Functional Analysis
Abstract

In this research article, we establish some identities and estimates for the operator norms and the Hausdorff measures of noncompactness of certain operators on some lacunary difference sequence spaces defined by Orlicz function. Moreover, we apply our results to characterize some classes of compact operators on those spaces by using the Hausdorff measure of noncompactness., Comment: communicated

Published
2015

18. Note on $f_\lambda$-statistical convergence

Author

Borgohain, Stuti and Savas, Ekrem

Subjects
Mathematics - Functional Analysis
Abstract

In this article, we study about the $\lambda$-statistical convergence with respect to the density of moduli and find some results related to statistical convergence as well. Also we introduce the concept of $f_\lambda$-summable sequence and try to investigate some relation between the $f_\lambda$-summability and module $% \lambda$-statistical convergence., Comment: Communicated

Published
2015

19. On strongly almost lacunary statistical $A$-convergence defined by Musielak-Orlicz function

Author

Savas, Ekrem and Borgohain, Stuti

Subjects
Mathematics - Functional Analysis
Abstract

We study some new strongly almost lacunary statistical $A$-convergent sequence space of order $\alpha$ defined by a Musielak-Orlicz function. We also give some inclusion relations between the newly introduced class of sequences with the spaces of strongly almost lacunary $A$-convergent sequence of order $\alpha$. Moreover we have examined some results on Musielak-Orlicz function with respect to these spaces., Comment: Communicated

Published
2015

20. Generalized Statistical Convergence for Sequences of Function in Random 2-Normed Spaces

Author

Savaş, Ekrem, Gürdal, Mehmet, Barbosa, Simone Diniz Junqueira, Series Editor, Chen, Phoebe, Series Editor, Filipe, Joaquim, Series Editor, Kotenko, Igor, Series Editor, Sivalingam, Krishna M., Series Editor, Washio, Takashi, Series Editor, Yuan, Junsong, Series Editor, Zhou, Lizhu, Series Editor, Ghosh, Debdas, editor, Giri, Debasis, editor, Mohapatra, Ram N., editor, Savas, Ekrem, editor, Sakurai, Kouichi, editor, and Singh, L. P., editor

Published
2018
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27. Some Geometric and Topological Properties of a New Sequence Space Defined by De la Vallee-Poussin Mean

Author

Simsek, Necip, Savas, Ekrem, and Karakaya, Vatan

Subjects
Mathematics - Functional Analysis, 46A45, 46B20, 46B45 (Primary)
Abstract

The main purpose of this paper is to introduce a new sequence space by using de la Vallee-Poussin mean and investigate both the modular structure with some geometric properties and some topological properties with respect to the Luxemburg norm., Comment: 12 pages

Published
2009

29. -double Statistically Convergent Sequences in Topological Groups

Author

Savaş, Ekrem, Chen, Phoebe, Series editor, Du, Xiaoyong, Series editor, Filipe, Joaquim, Series editor, Kara, Orhun, Series editor, Kotenko, Igor, Series editor, Liu, Ting, Series editor, Sivalingam, Krishna M., Series editor, Washio, Takashi, Series editor, Giri, Debasis, editor, Mohapatra, Ram N., editor, Begehr, Heinrich, editor, and Obaidat, Mohammad S., editor

Published
2017
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30. Necessary and sufficient conditions for inclusion relations for absolute summability

Author

Rhoades, B E and Savas, Ekrem

Subjects
Mathematics - Classical Analysis and ODEs, 47H10
Abstract

We obtain a set of necessary and sufficient conditions for $| \bar{N}, p_{n} |_{k} $ to imply $|\bar{N}, q_{n} |_{s}$ for $1 < k \leq s < \infty$. Using this result we establish several inclusion theorems as well as conditions for the equivalence of $| \bar {N}, p_{n} |_{k}$ and $|\bar{N},q_{n} |_{s}$., Comment: 8 pages, no figures

Published
2003

34. Some novel approaches on the (N̅, p, q) summability of double sequences of fuzzy numbers and its applications.

Author

Onder, Zerrin, Savas, Ekrem, and Canak, Ibrahim

Subjects
*FUZZY numbers, *SUMMABILITY theory, *POSITIVE operators, *LINEAR operators
Abstract

In this paper, our aim is to make a novel interpretation of relation between (N̅,p,q) method and P-convergence for double sequences of fuzzy numbers. In accordance with this aim, we derive some Tauberian conditions, controlling O-oscillatory behavior of a double sequence of fuzzy numbers in certain senses, from (N̅,p,q) summability to P- convergence with some restrictions on the weight sequences. As special cases, we indicate that O-condition of Hardy type with respect to (Pm) and Qn are Tauberian conditions for (N̅,p,q) summability under some additional conditions. In the sequel, we prove a fuzzy Korovkin-type approximation theorem by using the (N̅,p,q) summability method for fuzzy positive linear operators. [ABSTRACT FROM AUTHOR]

Published
2023
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40. Preface

Author

Kočinac, Ljubiša D.R. and Savaş, Ekrem

Published
2016

48. On I-Statistical φ-Limit Superior and I-Statistical φ-Limit Inferior.

Author

Savas, Ekrem, Debnath, Shyamal, and Choudhury, Chiranjib

Subjects
*REAL numbers
Abstract

In this paper, we have extended the concepts of I-statistical limit superior and I-statistical limit inferior to I-statistical φ-limit superior and I-statistical φ-limit inferior and studied some of their properties for sequence of real numbers. [ABSTRACT FROM AUTHOR]

Published
2023

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