Some Results of Ideal Convergence of Double Sequences in Topological Spaces


Abstract views: 11 / PDF downloads: 13

Authors

  • Işıl Açık Demirci Burdur Mehmet Akif Ersoy University
  • Ömer Kişi Bartın University
  • Mehmet Gürdal Suleyman Demirel University

Keywords:

Ideal Convergence, Strong Convergence, Statistical Convergence, Topological Space

Abstract

Here, we provide statistical UI2-strong convergence and UT
I2-strong convergence, which, via a
certain class of special functions, expand UI2-strong convergence in Hausdorff topological spaces.
Furthermore, we give a characterization of UI2-statistical convergence and draw linkages between UI2
statistical convergence and UT
I2-strong convergence.

Downloads

Download data is not yet available.

Author Biographies

Işıl Açık Demirci, Burdur Mehmet Akif Ersoy University

Department of Mathematics, Burdur, Turkey

Ömer Kişi, Bartın University

Department of Mathematics, Bartın, Turkey

Mehmet Gürdal, Suleyman Demirel University

Department of Mathematics, Isparta, Turkey

References

R. Aldrovandi and J. G. Pereira, An Introduction to Geometrical Physics, World Scientific, 1995.

J. Boos, Classical and Modern Methods in Summability, Oxford Univ. Press, 2000.

H. Cakalli and M. K. Khan , “Summability in topological spaces,” Appl. Math. Lett., vol. 24, no. 3, pp. 348-352, 2011.

J. S. Connor, “The statistical and strong p-Cesaro convergence of sequences,” Analysis, vol. 8, pp. 47-63, 1988.

J. S. Connor, “On strong matrix summability with respect to a modulus and statistical convergence,” Canad. Math. Bull., vol. 32, no. 2, pp. 194-198, 1989.

J. S. Connor, “Two valued measures and summability,” Analysis, vol. 10, no. 4, pp. 373-385, 1990.

S. Dutta and R. Ghosh, “Strong ideal convergence in topological spaces,” to appear.

H. Fast, “Sur la convergence statistique,” Colloq. Math., vol. 2, pp. 241-244, 1951.

J. A. Fridy, “On statistical convergence,” Analysis, vol. 5, pp. 301-313, 1985.

O. H. H. Edely and M. Mursaleen, “On statistical A-summability,” Math. Comp. Model., vol. 49, no. 8, pp. 672-680, 2009.

M. K. Khan and C. Orhan, “Characterization of strong and statistical convergences,” Publ. Math. Debrecen, vol. 76, no. 1-2, pp. 77-88, 2010.

E. Kolk, “Matrix summability of Statistically convergent sequences,” Analysis, vol. 13, pp. 77-83, 1993.

E. Kolk, “maps into the space of statistically convergent bounded sequences,” Proc. Estonia Acad. Sci. Phys. Math., vol. 45, pp. 192-197, 1996.

P. Kostyrko, T. Šalát, W. Wilczyński, “I-convergence,” Real Anal. Exchange, vol. 26, no. 2, pp. 669-685, 2000/2001.

B. K. Lahiri and P. Das, “I and I^*-convergence in topological spaces,” Math. Bohemica, vol. 130, pp. 153-160, 2005.

G. Di Maio and L. D. R. Koc̃inac, “Statistical convergence in topology,” Topology Appl., vol. 156, no. 1, pp. 28-45, 2008.

M. Mursaleen and A. Alotaibi, “Statistical summability and approximation by de la Vallepoussin mean,” Appl. Math. Lett., vol. 24, pp. 672-680, 2011.

E. Savaş, P. Das, and S. Dutta, “A note on strong matrix summability via ideals,” Appl. Math. Lett., vol. 25, pp. 733-738, 2012.

E. Savaş, P. Das, and S. Dutta, “A note on some generalized summability methods,” Acta Math. Univ. Comenian.(N.S.), vol. 82, no. 2, pp. 297-304, 2013.

L. A. Steen and J. A. Seebach, Counterexamples in Topology, Springer-Verlag, New York, 1970.

Z. Tang and F. Lin, “Statistical versions of sequential and Frechet-Urysohn spaces,” Adv. Math. (China), vol. 44, no. 6, pp. 945-954, 2015.

M. Unver and S. Yardimci, “Strong Convergence in Topological Spaces,” Methods Funct. Anal. Topol., Vol. 24, no. 1, pp. 82-90, 2018.

Downloads

Published

2024-08-29

How to Cite

Açık Demirci, I., Kişi, Ömer, & Gürdal, M. (2024). Some Results of Ideal Convergence of Double Sequences in Topological Spaces . International Journal of Advanced Natural Sciences and Engineering Researches, 8(7), 89–97. Retrieved from https://as-proceeding.com/index.php/ijanser/article/view/1971

Issue

Section

Articles