TY  - JOUR
T1  - On the Generalized Weighted Statistical Convergence
TT  - On the Generalized Weighted Statistical Convergence
AU  - Bayram, Erdal
AU  - Bektaş, Çiğdem
PY  - 2024
DA  - November
Y2  - 2024
DO  - 10.34248/bsengineering.1553162
JF  - Black Sea Journal of Engineering and Science
JO  - BSJ Eng. Sci.
PB  - Karyay Karadeniz Yayımcılık Ve Organizasyon Ticaret Limited Şirketi
WT  - DergiPark
SN  - 2619-8991
SP  - 1310
EP  - 1314
VL  - 7
IS  - 6
LA  - en
AB  - Statistical convergence and summability represent a significant generalization of traditional convergence for sequences of real or complex values, allowing for a broader interpretation of convergence phenomena. This concept has been extensively examined by numerous researchers using various mathematical tools and applied to different mathematical structures over time, revealing its relevance across multiple disciplines. In the present study, a generalized definition of the concepts of statistical convergence and summability, termed (△_v^m )_u-generalized weighted statistical convergence and (△_v^m )_u-generalized weighted by [¯N_t ]-summability for real sequences, is introduced using the weighted density and generalized difference operator. Based on this definition, several fundamental properties and inclusion results, obtained by differentiating the components used in the definitions, are provided.
KW  - Generalized difference sequence
KW  - Weighted density
KW  - Weighted statistical convergence
KW  - Weighted summability
N2  - Statistical convergence and summability represent a significant generalization of traditional convergence for sequences of real or complex values, allowing for a broader interpretation of convergence phenomena. This concept has been extensively examined by numerous researchers using various mathematical tools and applied to different mathematical structures over time, revealing its relevance across multiple disciplines. In the present study, a generalized definition of the concepts of statistical convergence and summability, termed (△_v^m )_u-generalized weighted statistical convergence and (△_v^m )_u-generalized weighted by [¯N_t ]-summability for real sequences, is introduced using the weighted density and generalized difference operator. Based on this definition, several fundamental properties and inclusion results, obtained by differentiating the components used in the definitions, are provided.
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UR  - https://doi.org/10.34248/bsengineering.1553162
L1  - http://dergipark.org.tr/tr/download/article-file/4228060
ER  -