I*-CONVERGENCE OF FUNCTION SEQUENCES IN ASYMMETRIC METRIC SPACE

Year 2024, Volume: 7 Issue: To memory "Assoc. Prof. Dr. Zeynep AKDEMİRCİ ŞANLI", 109 - 118, 29.12.2024

Kadriye Dilan Kolaç , Mehmet Küçükaslan

https://doi.org/10.33773/jum.1564703

Abstract

In this paper, by considering ideal which is special subfamily of power set of natural numbers I∗-convergence of sequence of functions in asymmetric metric spaces is defined and some results about new concept are given.Obtained results is supported some examples to show differences by the classical ones.

Keywords

Asymmetric Metric Space, Ideal Convergence, Ideal-α convergence, Ideal uniform convergence, Ideal exhaustiveness

References

• A.M. Aminpour, Some Results in Asymmetric Metric Spaces, Mathematica Aeterna, Vol. 2,pp.533 - 540,(2012).
• J.S. Connor, The Statistical and Strong p-Cesaro Convergence of Sequences, Analysis, Vol. 12,pp.47-63,(1988).
• G. Di Maio, L.D.R. Kocinac, Statistical convergence in topology, Topology and its Applications, Vol. 156, pp.28-45,(2008).
• D. Doitchinov, On Completeness in Quasi Metric Spaces, Topology and its Applications, Vol. 30,pp.127-148,(1988).
• R. Dutta, On Quasi b-Metric Space with index k and fixed point results, The Journal of Analysis, Vol. 30, pp.919-940 (2022).
• H. Fast, Sur la convergence statistique, Communications, Vol. 2., pp.241-244, (1951).
• R. Filipow, N. Mrozek, I. Reclaw, P. Szuca, Ideal Convergence of Bounded Sequences,The Journal of Symbolic Logic, Vol.72, pp.501-512, (2010).
• A.R. Freedman, J.J. Sember, Densities and Summability, Journal of Mathematics, Vol.95, pp.293-305,(1981). J.A. Fridy, On statistical convergence,Analysis, Vol.5,pp.1187-1192, (1985).
• A. Ghosh, A study on convergence of sequences of functions in asymmetric metric spaces using ideals,Novi Sad J. Math, Vol. 53,pp.97-116 ,(2023).
• A. Ghosh, I*alpha Convergence and I-Exhaustiveness of Sequences of Metric Functions,Matematicki Vesnik Matematiqkıvesnık, Vol.74(2),pp.110-118,(2022).
• M. İlkhan, E.E. Kara, On statistical convergence in quasi-metric spaces, Demonstratio Mathematica ,Vol.1 ,pp.225-236, (2019).
• P. Kostyrko, T. Salat, W. Wilczynki, I-convergence, Real Analysis Exchange ,Vol.26 (2), pp.669-686,(2000/2001).
• B.K. Lahiri, P. Das, I and I-convergence in topological spaces, Mathematica Bohemica, Vol. 130,pp.153-160, (2005).
• O.O. Otafudu, Maps that preserve left (right) K-Cauchy sequences,Hacettepe Journal of Mathematics and Statistics, Vol. 50 (5), pp.1466-1476,(2021).
• I.L. Reilly, P.V. Subrahmanyam, M.K. Vamanamurthy, Cauchy Sequences in Quasi-Pseudo-Metric Spaces, Monatshefte fur Mathematik, Vol.93,pp.127-140,(1982).
• H. Steinhaus, Sur la convergence ordinaine et la convergence asymptotique, Colloquium Mathematicum, Vol.2, pp.73-74,(1951)
• A. Sahiner, M. Gürdal, T. Yigit, Ideal convergence characterization of the completion of linear n-normed spaces, Computers and Mathematics with Applications, Vol.61, pp.683-689, (2011).