Modes of continuity involving almost and ideal convergence

Antonio Boccuto; Xenofon Dimitriou; Nicolas Papanastassiou

doi:10.2478/v10127-012-0032-x

.blurhash-client-img { display: none !important; }

Modes of continuity involving almost and ideal convergence

Tatra Mountains Mathematical Publications

Volume 52 (2012): Issue 1 (August 2012)

By: Antonio Boccuto, Xenofon Dimitriou and Nicolas Papanastassiou

Open Access

|Nov 2012

Abstract

We investigate some properties of almost convergence and compare it with other kinds of convergence. Moreover, we present different modes of continuity considering almost, Single and ideal convergence, giving some relations between them and some examples. Finally, we pose some open problems.

References

[1] ACZEL, J.-DHOMBRES, J.: Functional Equations in Several Variables. Cambridge Univ. Press, Cambridge, 1987.
Search in Google Scholar
[2] ANTONI, J.: On the A-continuity of real functions II, Math. Slovaca 36 (1986), 283-288.
Search in Google Scholar
[3] ANTONI, J.-ˇSAL´AT, T.: On the A-continuity of real functions, Acta Math. Univ. Comenian. 39 (1980), 159-164.
Search in Google Scholar
[4] BALCERZAK, M.-DEMS, K.-KOMISARSKI, A.: Statistical convergence and idealconvergence for sequences of functions, J. Math. Anal. Appl. 328 (2007), 715-729.10.1016/j.jmaa.2006.05.040
Search in Google Scholar
[5] BOCCUTO, A.-DIMITRIOU, X.-PAPANASTASSIOU, N.-WILCZY´NSKI, W.: Onsome different types of ideal continuity, 2012 (preprint).
Search in Google Scholar
[6] BORS´IK, J.-ˇSAL´AT, T.: On F-continuity of real functions, Tatra Mt. Math. Publ. 2 (1993), 37-42.
Search in Google Scholar
[7] CONNOR, J.-GROSSE-ERDMANN, K. G.: Sequential definitions of continuity for realfunctions, Rocky Mountain J. Math. 33 (2003), 93-121.10.1216/rmjm/1181069988
Search in Google Scholar
[8] FAST, H.: Sur la convergence statistique, Colloq. Math. 2 (1951), 41-44.
Search in Google Scholar
[9] FREEDMAN, A. R.-SEMBER, J. J.: Densities and summability, Pacific J. Math. 95 (1981), 293-305.10.2140/pjm.1981.95.293
Search in Google Scholar
[10] KOLK, E.: Inclusion relations between the statistical convergence and strong summability, Acta Comment. Univ. Tartu. Math. 2 (1998), 39-54.
Search in Google Scholar
[11] KOSTYRKO, P.-ˇSAL´AT, T.-WILCZY´NSKI,W.: I-convergence, Real Anal. Exchange 26 (2000/2001), 669-685.10.2307/44154069
Search in Google Scholar
[12] LORENTZ, G. G.: A contribution to the theory of divergent sequences, Acta Math. 80 (1948), 167-190.10.1007/BF02393648
Search in Google Scholar
[13] M´ORICZ, F.-STADTM˝ULLER, U.: Summability of double sequences by weighted meanmethods and Tauberian conditions for convergence in Pringsheim’s sense, Int. J. Math. Math. Sci. 65 (2004), 3499-3511.10.1155/S0161171204403329
Search in Google Scholar
[14] PAPANASTASSIOU, N.: On a new type of convergence of sequences of functions, Atti Semin. Mat. Fis. Univ. Modena 50 (2002), 493-506.
Search in Google Scholar
[15] PETERSEN, G. M.: Regular Matrix Transformations. McGraw-Hill, London, 1966.
Search in Google Scholar
[16] SM´ITAL, J.: On Functions and Functional Equations. Adam Hilger, Bristol, UK, 1988.
Search in Google Scholar
[17] STEINHAUS, H.: Sur la convergence ordinaire et la convergence asymptotique, Colloq. Math. 2 (1951), 73-74.10.4064/cm-2-2-98-108
Search in Google Scholar

Articles in this issue

DOI: https://doi.org/10.2478/v10127-012-0032-x | Journal eISSN: 1338-9750 | Journal ISSN: 1210-3195

Journal RSS Feed

Language: English

Page range: 115 - 131

Published on: Nov 19, 2012

Published by: Slovak Academy of Sciences, Mathematical Institute

In partnership with: Paradigm Publishing Services

Publication frequency: 1 issue per year

Keywords:

almost convergence,

Single convergence,

ideal convergence,

Pringsheim-Single convergence,

(Lorentz) uniform equal convergence,

modes of continuity.

Related subjects:

Mathematics,

General mathematics

© 2012 Antonio Boccuto, Xenofon Dimitriou, Nicolas Papanastassiou, published by Slovak Academy of Sciences, Mathematical Institute
This work is licensed under the Creative Commons License.

Volume 52 (2012): Issue 1 (August 2012)