On weighted weak statistical convergence

Yıl 2018, Cilt: 6 Sayı: 2, 194 - 199, 15.10.2018

Sinan Ercan

Öz

The purpose of the present work is to introduce extended notion of weak statistical convergence on normed spaces. Furthermore, some certain properties of this mode of convergence are given.

Anahtar Kelimeler

weighted statistical convergence, statistical convergence

Kaynakça

• [1] A. Zygmund, Trigonometric Series, Cambridge University Press, New York, NY, USA, 1959.
• [2] H. Fast, Sur la convergence statistique, Colloq. Math. 2 (1951) 241-244.
• [3] H. Steinhaus, Sur la convergence ordinaire et la convergence asymptotique, Colloq. Math. 2 (1951) 73-74.
• [4] A. R. Freedman, J. J. Sember, M. Raphael, Some Ces`aro-type summability spaces, Proc. Lond. Math. Soc. 37(3) (1978) 508-520.
• [5] D. Rath, B. C. Tripathy, On statistically convergent and statistically Cauchy sequences, Indian J. Pure. Appl. Math. 25(4) (1994) 381-386. [6] T. ˇ Sal´at, On statistically convergent sequences of real numbers, Math. Slovaca 30 (1980) 139-150.
• [7] J. Connor, M. Ganichev, V. Kadets, A characterization of Banach spaces with separable duals via weak statistical convergence, J. Math. Anal. Appl. 244 (2000) 251-261.
• [8] V.K. Bhardwaj, I. Bala, On weak statistical convergence, Int. J. Math. Math. Sci. Art. ID 38530, (2007) 9 pp.
• [9] Meenakshi, M. S. Saroa , V. Kumar, Weak statistical convergence defined by de la Vall´ee-Poussin mean, Bull. Calcutta Math. Soc. 106 no.3 (2014) 215-224
• [10] V. Karakaya, T. A. Chishti, Weighted statistical convergence, Iran. J. Sci. Technol. Trans. A Sci. 33 (2009) 219-223.
• [11] M. K¨uc¸ ¨ukaslan, Weighted statistical convergence, International Journal of Science and Technology, 2 (2012) 2-10.
• [12] M. Mursaleen, V. Karakaya, M. Ert¨urk, F. G¨ursoy, Weighted statistical convergence and its application to Korovkin type aprroximation theorem, Appl. Math. Comput. 218, (2012) 9132-9137.
• [13] S. Ghosal, Weighted statistical convergence of order a and its applications, J. Egyptian Math. Soc. 24 no. 1 (2016) 60-67.
• [14] K. H. Karlsen, Notes on weak convergence, University of Oslo, Norway, 2006
• [15] I. J. Maddox, Statistical convergence in a locally convex space, Math. Proc. Cambridge Phil. Soc. 104 (1988) 141-145.
• [16] M. İlkhan, E. E. Kara, A new type of statistical Cauchy sequence and its relation to Bourbaki completeness, Cogent Mathematics & Statistics, (2018) 5:1487500.