Abstract
We establish some core inequalities for complex bounded sequences using the concept of
statistical
We establish some core inequalities for complex bounded sequences using the concept of
statistical
H. Fast, “Sur la convergence statistique,” Colloquium Mathematicum, vol. 2, pp. 241–244, 1951.
View at: Google Scholar | Zentralblatt MATH | MathSciNetT. Šalát, “On statistically convergent sequences of real numbers,” Mathematica Slovaca, vol. 30, no. 2, pp. 139–150, 1980.
View at: Google Scholar | MathSciNetJ. A. Fridy, “On statistical convergence,” Analysis, vol. 5, no. 4, pp. 301–313, 1985.
View at: Google Scholar | Zentralblatt MATH | MathSciNetM. Mursaleen and O. H. H. Edely, “Statistical convergence of double sequences,” Journal of Mathematical Analysis and Applications, vol. 288, no. 1, pp. 223–231, 2003.
View at: Publisher Site | Google Scholar | Zentralblatt MATH | MathSciNetF. Móricz, “Statistical convergence of multiple sequences,” Archiv der Mathematik, vol. 81, no. 1, pp. 82–89, 2003.
View at: Google Scholar | Zentralblatt MATH | MathSciNetF. Móricz, “Tauberian conditions, under which statistical convergence follows from statistical summability ,” Journal of Mathematical Analysis and Applications, vol. 275, no. 1, pp. 277–287, 2002.
View at: Google Scholar | Zentralblatt MATH | MathSciNetA. A. Scherbakov, “Kernals of sequences of complex numbers and their regular transformations,” Mathematical Notes, vol. 22, pp. 948–953, 1977.
View at: Google ScholarJ. A. Fridy and C. Orhan, “Statistical core theorems,” Journal of Mathematical Analysis and Applications, vol. 208, no. 2, pp. 520–527, 1997.
View at: Publisher Site | Google Scholar | Zentralblatt MATH | MathSciNetR. P. Agnew, “Cores of complex sequences and of their transforms,” American Journal of Mathematics, vol. 61, no. 1, pp. 178–186, 1939.
View at: Publisher Site | Google Scholar | Zentralblatt MATH | MathSciNetB. Choudhary, “An extension of Knopp's core theorem,” Journal of Mathematical Analysis and Applications, vol. 132, no. 1, pp. 226–233, 1988.
View at: Publisher Site | Google Scholar | Zentralblatt MATH | MathSciNetH. Çoşkun, C. Çakan, and M. Mursaleen, “On the statistical and -cores,” Studia Mathematica, vol. 154, no. 1, pp. 29–35, 2003.
View at: Google Scholar | Zentralblatt MATH | MathSciNetI. J. Maddox, “Some analogues of Knopp's core theorem,” International Journal of Mathematics and Mathematical Sciences, vol. 2, no. 4, pp. 605–614, 1979.
View at: Publisher Site | Google Scholar | Zentralblatt MATH | MathSciNetM. Mursaleen and O. H. H. Edely, “On some statistical core theorems,” Analysis, vol. 22, no. 3, pp. 265–276, 2002.
View at: Google Scholar | Zentralblatt MATH | MathSciNetM. Mursaleen and O. H. H. Edely, “Statistically strongly regular matrices and some core theorems,” International Journal of Mathematics and Mathematical Sciences, no. 18, pp. 1145–1153, 2003.
View at: Publisher Site | Google Scholar | Zentralblatt MATH | MathSciNetP. N. Natarajan, “On the core of a sequence over valued fields,” The Journal of the Indian Mathematical Society, vol. 55, no. 1–4, pp. 189–198, 1990.
View at: Google Scholar | Zentralblatt MATH | MathSciNetC. Çakan and B. Altay, “Statistically boundedness and statistical core of double sequences,” Journal of Mathematical Analysis and Applications, vol. 317, no. 2, pp. 690–697, 2006.
View at: Google Scholar | MathSciNetM. Mursaleen, “Almost strongly regular matrices and a core theorem for double sequences,” Journal of Mathematical Analysis and Applications, vol. 293, no. 2, pp. 523–531, 2004.
View at: Publisher Site | Google Scholar | Zentralblatt MATH | MathSciNetM. Mursaleen and O. H. H. Edely, “Almost convergence and a core theorem for double sequences,” Journal of Mathematical Analysis and Applications, vol. 293, no. 2, pp. 532–540, 2004.
View at: Publisher Site | Google Scholar | Zentralblatt MATH | MathSciNetM. Mursaleen and E. Savaş, “Almost regular matrices for double sequences,” Studia Scientiarum Mathematicarum Hungarica, vol. 40, no. 1-2, pp. 205–212, 2003.
View at: Publisher Site | Google Scholar | Zentralblatt MATH | MathSciNetR. F. Patterson, “Double sequence core theorems,” International Journal of Mathematics and Mathematical Sciences, vol. 22, no. 4, pp. 785–793, 1999.
View at: Publisher Site | Google Scholar | Zentralblatt MATH | MathSciNetS. Simons, “Banach limits, infinite matrices and sublinear functionals,” Journal of Mathematical Analysis and Applications, vol. 26, pp. 640–655, 1969.
View at: Publisher Site | Google Scholar | Zentralblatt MATH | MathSciNetE. Kolk, “Matrix maps into the space of statistically convergent bounded sequences,” Proceedings of the Estonian Academy of Sciences. Physics, Mathematics, vol. 45, no. 2-3, pp. 187–192, 1996, Problems of pure and applied mathematics (Tallinn, 1995).
View at: Google Scholar | Zentralblatt MATH | MathSciNetJ. A. Fridy and C. Orhan, “Statistical limit superior and limit inferior,” Proceedings of the American Mathematical Society, vol. 125, no. 12, pp. 3625–3631, 1997.
View at: Publisher Site | Google Scholar | Zentralblatt MATH | MathSciNetI. J. Schoenberg, “The integrability of certain functions and related summability methods,” The American Mathematical Monthly, vol. 66, pp. 361–375, 1959.
View at: Publisher Site | Google Scholar | Zentralblatt MATH | MathSciNetJ. Li and J. A. Fridy, “Matrix transformations of statistical cores of complex sequences,” Analysis, vol. 20, no. 1, pp. 15–34, 2000.
View at: Google Scholar | Zentralblatt MATH | MathSciNet