I-Statistical Rough Convergence of Order α

Yıl 2022, Sayı: 38, 34 - 41, 31.03.2022

Sevcan Bulut , Aykut Or

https://doi.org/10.53570/jnt.1062253

Cited By: 2

Öz

The aim of this paper is to define the concept of I-statistical (I-st) rough convergence of order α (0 < α ≤ 1). It proposes the concept of I-st bounded of order α. Moreover, the necessary and sufficient condition for a sequence (x_k) to be I-st bounded of order α is studied. In addition, the necessary and sufficient condition for a sequence (x_k) to be I-st convergent of order α is examined. Finally, the need for further research studies is discussed.

Anahtar Kelimeler

Ideal rough convergence, Ideal statistical rough convergence, Ideal statistical rough convergence of order α.

Kaynakça

• H. Fast, Sur la Convergence Statistique, Colloquium Mathematicae 2 (1951) 241–244.
• H. Steinhaus, Sur la Convergence Ordinaire et la Convergence Asymptotique, Colloquium Mathematicae 2 (1951) 73–74.
• I. J. Schoenberg, The Integrability of Certain Functions and Related Summability Methods, American Mathematical Monthly 66 (1959) 361–375.
• T. Salat, On Statistically Convergent Sequences of Real Numbers, Mathematica Slovaca 30 (1980) 139–150.
• A. R. Freedman, J. J. Sember, Densities and Summability, Pacific Journal of Mathematics 95 (1981) 293–305.
• J. A. Fridy, On Statistical Convergence, Analysis 5 (1985) 301–313.
• J. S. Connor, The Statistical and Strong p-Cesaro Convergence of Sequences, Analysis 8 (1988) 47–63.
• E. Kolk, Matrix Summability of Statistically Convergent Sequences, Analysis 13 (1993) 77–83.
• J. A. Fridy, C. Orhan, Lacunary Statistical Convergence, Pacific Journal of Mathematics 160 (1993) 43–51.
• J. A. Fridy, C. Orhan, Statistical Limit Superior and Limit Inferior, American Mathematical Society 125(12) (1997) 3625–3631.
• P. Kostroyko, T. Salat, W. Wilezynski, I-Convergence, Real Analysis Exchange 26(2) (2000) 669–686.
• A. D. Gadjiev, C. Orhan, Some Approximation Theorems via Statistical Convergence, Rocky Mountain Journal of Mathematics 32 (2002) 129–138.
• R. Çolak, Statistical Convergence of Order α, in: M. Mursaleen (Ed.), Modern Methods in Analysis and Its Applications, New Delhi, India, 2010, pp. 121–129.
• P. Das, E. Savaş, On I-Statistical and I-Lacunary Statistical Convergence of Order Alpha, Bulletin of the Iranian Mathematical Society 40 (2014) 459–472.
• H. X. Phu, Rough Convergence in Normed Linear Spaces, Numerical Functional Analysis and Optimization 22 (2001) 199–222.
• S. Aytar, Rough Statistical Convergence, Numerical Functional Analysis and Optimization 29(3) (2008) 283–290.
• S. Aytar, The Rough Limit Set and The Core of A Real Sequence, Numerical Functional Analysis and Optimization 29(3-4) (2008) 291–303.
• S. Aytar, Rough Statistical Cluster Points, Filomat 31(16) (2017) 5295–2304.
• S. K. Pal, D. Chandra, S. Dutta, Rough Ideal Convergence, Hacettepe Journal of Mathematics and Statistics 42(6) (2013) 633–640.
• E. Dündar, C. Çakan, Rough I-Convergence, Gulf Journal of Mathematics 2(1) (2014) 45–51.
• E. Savaş, S. Debnath, D. Rakshit, On I-Statisticaly Rough Convergence, Publications De L’institut Matematique 105(119) (2019) 145–150.
• M. Maity, A Note on Rough Statistical Convergence of Order Alpha, arXiv:1603.00183v1 2016.
• P. Das, E. Savaş, A Generalized Statistical Convergence via Ideals, Applied Mathematics Letters 24 (2011) 826–830.
• M. Mursaleen, S. Debnath, D. Rakshit, I-Statistical Limit Superior and I-Statistical Limit Inferior, Filomat 31(7) (2017) 2103–2108.