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g-METRIC SPACES AND ASYMPTOTICALLY LACUNARY STATISTICAL EQUIVALENT SEQUENCES
( Saime Kolanci ),( Mehmet Gürdal ),( Ömer Kişi ) 호남수학회 2023 호남수학학술지 Vol.45 No.3
In the present article, we introduce the concepts of strongly asymptotically lacunary equivalence, asymptotically statistical equivalence, and asymptotically lacunary statistical equivalence for sequences in g-metric spaces. We investigate some properties and relationships among these new concepts.
BEREZIN NUMBER INEQUALITIES VIA YOUNG INEQUALITY
( HAMDULLAH BAŞARAN ),( Mehmet Gürdal ) 호남수학회 2021 호남수학학술지 Vol.43 No.3
In this paper, we obtain some new inequalities for the Berezin number of operators on reproducing kernel Hilbert spaces by using the Hölder-McCarthy operator inequality. Also, we give refine generalized inequalities involving powers of the Berezin number for sums and products of operators on the reproducing kernel Hilbert spaces.
ON ASYMPTOTICALLY LACUNARY STATISTICAL EQUIVALENT TRIPLE SEQUENCES VIA IDEALS AND ORLICZ FUNCTION
( Mualla Birgül Huban ),( Mehmet Gürdal ),( Hamza Baytürk ) 호남수학회 2021 호남수학학술지 Vol.43 No.2
In the present paper, we introduce the concepts of I-asymptotically statistical ф-equivalence and I-asymptotically lacunary statistical ф-equivalence for triple sequences. Moreover, we give the relations between these new notions.
STATISTICALLY LOCALIZED SEQUENCES IN 2-NORMED SPACES
( Ulaş Yamanci ),( Anar Adiloglu Nabiev ),( Mehmet Gürdal ) 호남수학회 2020 호남수학학술지 Vol.42 No.1
We introduce statistically localized sequences in 2-normed spaces and give some main properties of statistically localized sequences. Also, we prove that a sequence is statistically Cauchy sequence if and only if its statistical barrier is equal to zero. Moreover, we define the uniformly statistically localized sequences on 2-normed spaces and investigate its relationship with statistically Cauchy sequences.