IDEAL LIMIT SUPERIOR-INFERIOR

Yıl 2017, Cilt: 30 Sayı: 1, 401 - 411, 14.03.2017

Mehmet Küçükaslan Maya Altınok

Öz

In this paper the notation of ideal supremum and ideal inmum
of real valued sequences is dened. Besides the main properties, it is shown that equality of ideal sup and ideal inf of the sequence is necessary but not sucient for to existence of usual limit of it. On the other hand, the equality of them is necessary and sucient for to existence of ideal limit.

Anahtar Kelimeler

statistical limit superior and inferior, statistical supremum and inmum, I-limit

Kaynakça

• Altnok M. and Kucukaslan M., Statistical supremum-inmum and statistical convergence", The Aligarh Bulletin of Mathematics, 32: 1-16, (2013).
• Altnok M. and Kucukaslan M., A-statistical supremum-inmum and A-statistical convergence", Azerbaijan Journal of Mathematics, 4,2: 31-42, (2014).
• Buck R.C., The measure theoretic approch to density", Amer. J. Math., , 68: 560-580, (1946).
• Connor J.S., R-type summability methods, Cauchy criteria, p-sets, and statistical convergence", Proc. Amer. Math. Soc., , 115: 319-327, (1992).
• Connor J.S., The statistical and strong p-Cesaro convergence of sequences", Analysis., , 8: 47-63, (1988).
• Demirci K., I-limit superior and limit inferior", Mathematical Communications, 6: 165-172, (2001).
• Erdos P. and Tenenbaum G., Sur les densities de certaines suites d'entries", Proc. London Math. Soc., , 59: 417-438, (1989).
• Fast H., Sur la convergece statistique", Colloq. Math., 2: 241-244, (1951).
• Fridy J.A., On statistical convergence", Analysis, , 5: 301-313, (1985).
• Fridy J.A. and Miller H.I., A matrix characterization of statistical convergence", Analysis, 11: 59-66, (1991).
• Fridy J.A. and Orhan C., Statistical limit superior and limit inferior", Proc. Amer. Math. Socaity, 125, 12: 3625-3631, (1997).
• Kaya E., Kucukaslan M. and Wagner R.,"On Statistical Convergence and Statistical Monotonicity", Annales Univ. Sci. Budapest. Sect. Comp., 39: 257-270, (2013).
• Kostyrko P., Macaj and Salat T., Statistical convergence and I-convergence", to appear in Real Anal. Exchange.
• Kostyrko P., Salat T. and Wiezynski T. W., I-Convergence,", Real Analysis Exchange, 26,2: 669-680, (2000/2001).
• Kuratowski C., Topologie I ", PWN, Warszawa, (1958).
• Lahiri B. K. and Das P. Further results on I-limit superior and limit inferior ", Mathematical Communications, 8: 151-156, (2003).
• Nagata J., Modern General Topology"North-Holland Publ. Comp., Amsterdam-London, (1974).
• Schoenberg I.J.,The integrability of certain functions and related summability methods ", Amer. Math. Monthly, 66: 361-375, (1959).
• Steinhaus H., Sur la convergence ordinaire et la convergence asymtotique", Colloq. Math., 2: 73-74, (1951).