Weighted Lacunary I-Statistical Convergence

Öz

In this paper, we defne the concepts of weighted lacunary �-statistical convergence or S ( ) R,θ ( ) I
-convergence and[ ] R, pr ,θ I-summability, and investigate some inclusion relations

Anahtar Kelimeler

• I-statistical convergence,ideal convergence,Riesz mean,weighted

Ağırlıklı Lacunary I-İstatistiksel Yakınsaklık

Öz

Bu makalede,
S( ) R,θ ( ) I veya ağırlıklı lacunary I-istatistiksel yakınsaklık ile[ ] R pr θ I-toplanabilirlik
kavramları tanımlanmıştır ve bazı kapsama bağıntıları araştırılmıştır.

Anahtar Kelimeler

• Ağırlık,I-istatiksel yakınsaklık,İdeal yakınsaklık,Riesz ortalama

Kaynakça

1. Altundağ S, Sözbir B, 2015. Weighted I-statistical convergence and its application to Korovkin type approximation theorem. International Journal of Mathematics Science and Engineering Applications, 9 (2): 63-76.
2. Başarır M, Konca Ş, 2014. On some spaces of lacunary convergent sequences derived by Nörlund-type mean and weighted lacunary statistical convergence. Arab Journal of Mathematics and Science, 20 (2): 250-263.
3. Das P, Savaş E, Ghosal K, 2011. On generalizations of certain summability methods using ideals. Applied Mathematics Letters, 24: 1509-1514.
4. Fast H, 1951. Sur la convergence statistique. Colloquium Mathematicum, 2 (3–4): 241–244.
5. Fridy JA, Orhan C, 1993. Lacunary statistical convergence. Pacific Journal of Mathematics, 160:43-51.
6. Hazarika B, Savaş E, 2011. Some I-convergent lambda-summable difference sequence spaces of fuzzy real numbers defined by a sequence of Orlicz function. Mathematical and Computer Modelling, 54: 2986–2998.
7. Korovkin PP, 1960. Linear Operators and Approximation Theory, Hindustan Publishing Corporation, Delhi.
8. Kostyrko P, Salat T, Wilczynski W, 2000–2001. I-convergence. Real Analysis Exchange, 26 (2): 669–686.

9. Kostyrko P, Macaj M, Salat T, Sleziak M, 2005. I-convergence and extremal I-limit points. Mathematica Slovaca, 55: 443-464.
10. Kumar S, Kumar S, Bhatia SS, 2013. On ideal version of lacunary statistical convergence of double sequences. General Mathematics Notes, 17 (1): 32-44.
11. Lahiri BK, Das P, 2005. I and I*-convergence in topological spaces, Mathematica Bohemica, 130 (2): 153-160.
12. Moricz F, Orhan C, 2004. Tauberian conditions under which statistical convergence follows from statistical summability by weighted means, Studia Scientiarum Mathematicarum Hungarica, 41: 391-403.
13. Salat T, Tripathy BC, Ziman B, 2004. On some properties of I-convergence. Tatra Mountains Mathematical Publications, 28: 279–286.
14. Schoenberg IJ, 1959. The integrability of certain functions and related summability methods. American Mathematical Monthly, 66: 361–375.
15. Steinhaus H, 1951. Sur la convergence ordinate et al convergence asymptotique. Colloquium Mathematicum, 2: 73–84.
16. Tripathy BC, Hazarika B, Choudhary B, 2012. Lacunary I-convergent sequences. Kyungpook Mathematical Journal, 52 (4): 473-482.