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A category theorem for double sequences
AbstractThe goal of this paper is to present the following multidimensional category theorem for double sequences via four-dimensional matrix transformations. The set of second category double subsequences of the double sequence (sk,l) is summable by a four-dimensional RH-regular matrix A=(am,n,k,l) if and only if (sk,l) is P-convergent.
Patterson, Richard F., Savas, Ekrem
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According to the definition of sequence shadowing property and regularly recurrent point in the inverse limit space, we introduce the concept of sequence shadowing property and regularly recurrent point in the double inverse limit space and study their ...
Zhan jiang Ji
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In the field of pattern recognition, clustering groups the data into different clusters on the basis of similarity among them. Many a time, the similarity level between data points is derived through a distance measure; so, a number of clustering ...
Mohd Shoaib Khan, QM Danish Lohani
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KOROVKIN THEOREM VIA STATISTICAL e-MODULAR CONVERGENCE OF DOUBLE SEQUENCES
In the present paper, we obtain an abstract version of the Korovkin type theorem via the concept of statistical e-convergence in modular spaces for double sequences of positive linear operators.
Sevda Yıldız
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Double Path Networks for Sequence to Sequence Learning
Encoder-decoder based Sequence to Sequence learning (S2S) has made remarkable progress in recent years. Different network architectures have been used in the encoder/decoder. Among them, Convolutional Neural Networks (CNN) and Self Attention Networks (SAN) are the prominent ones. The two architectures achieve similar performances but use very different
Kaitao Song +5 more
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Double sequence spaces characterized by lacunary sequences
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Savaş, Ekrem, Patterson, Richard F.
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The (weak) wedgeness for FK-spaces was first defined by Bennett in 1974. Then, some results of Bennett (1974) were improved by İnce (2002) and Daˇgadur (2004) for all (weak) wedge FK spaces.
Sezgek Şeyda, Dağadur İlhan
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Approximation theorems using the method of $\mathcal{I}_{2}$-statistical convergence
In this study, we utilize the concept of $\mathcal{I}$-statistical convergence for double sequences to establish a general approximation theorem of Korovkin-type for double sequences of positive linear operators $(PLOs)$ mapping from $H_{\omega }\left( X\
Sevda Yıldız +2 more
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In this paper we introduce the strongly generalized difference sequence spaces of modulus function and is a non-negative four dimensional matrix of complex numbers and (pi(mn)) is a sequence of positive real numbers.
Subramanian Nagarajan, Umakanta Misra
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Matrix Transformations of Double Convergent Sequences with Powers for the Pringsheim Convergence
In 2004–2006, the corresponding double sequence spaces were defined for the Pringsheim and the bounded Pringsheim convergence by Gokhan and Colak. In 2009, Colak and Mursaleen characterized some classes of matrix transformations transforming the space of
Maria Zeltser, Şeyda Sezgek
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