Pancaroglu, Nimet; Nuray, Fatih Invariant statistical convergence of sequences of sets with respect to a modulus function. (English) Zbl 1474.40014 Abstr. Appl. Anal. 2014, Article ID 818020, 5 p. (2014). Summary: We introduce and study the concept of invariant convergence for sequences of sets with respect to modulus function \(f\) and give some inclusion relations. Cited in 1 Document MSC: 40A35 Ideal and statistical convergence PDF BibTeX XML Cite \textit{N. Pancaroglu} and \textit{F. Nuray}, Abstr. Appl. Anal. 2014, Article ID 818020, 5 p. (2014; Zbl 1474.40014) Full Text: DOI References: [1] Fast, H., Sur la convergence statistique, Colloquium Mathematicae, 2, 3-4, 241-244 (1951) · Zbl 0044.33605 [2] Šalát, T., On statistically convergent sequences of real numbers, Mathematica Slovaca, 30, 2, 139-150 (1980) · Zbl 0437.40003 [3] Beer, G., Convergence of continuous linear functionals and their level sets, Archiv der Mathematik, 52, 5, 482-491 (1989) · Zbl 0662.46015 [4] Aubin, J. P.; Frankowska, H., Set Valued Analysis (1990), Boston, Mass, USA: Birkhäuser, Boston, Mass, USA [5] Baronti, M.; Papini, P. L., Convergence of sequences of sets, Methods of Functional Analysis in Approximation Theory, 76, 135-155 (1986), Basel, Switzerland: Birkhäuser, Basel, Switzerland · Zbl 0606.54006 [6] Nuray, F.; Rhoades, B. E., Statistical convergence of sequences of sets, Fasciculi Mathematici, 49, 87-99 (2012) · Zbl 1287.40004 [7] Ulusu, U.; Nuray, F., Lacunary statistical convergence sequences of sets, Progress in Applied Mathematics, 4, 2, 99-109 (2012) [8] Pancaroglu, N.; Nuray, F., On invariant statistically convergence and lacu-nary invariant statistically convergence of sequences of sets, Progress in Applied Mathematics, 5, 2, 23-29 (2013) [9] Nakano, H., Concave modulars, Journal of the Mathematical Society of Japan, 5, 1, 29-49 (1953) · Zbl 0050.33402 [10] Ruckle, W. H., \(F K\) spaces in which the sequence of coordinate vectors is bounded, Canadian Journal of Mathematics, 25, 973-978 (1973) · Zbl 0267.46008 [11] Maddox, I. J., Sequence spaces defined by a modulus, Mathematical Proceedings of the Cambridge Philosophical Society, 100, 1, 161-166 (1986) · Zbl 0631.46010 [12] Connor, J., On strong matrix summability with respect to a modulus and statistical convergence, Canadian Mathematical Bulletin, 32, 2, 194-198 (1989) · Zbl 0693.40007 [13] Nuray, F.; Savaş, E., Some new sequence spaces defined by a modulus function, Indian Journal of Pure and Applied Mathematics, 24, 11, 657-663 (1993) · Zbl 0805.40004 [14] Savaş, E., Strongly \(\sigma \)-convergent sequences, Bulletin of the Calcutta Mathematical Society, 81, 4, 295-300 (1989) · Zbl 0716.40006 [15] Savaş, E., On strong almost \(A\)-summability with respect to a modulus and statistical convergence, Indian Journal of Pure and Applied Mathematics, 23, 3, 217-222 (1992) · Zbl 0756.40004 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.