Abstract
In this present paper, we have considered the extension of the concept of strong Ces\(\grave{\text {a}}\)ro-type quasinormal convergence, strong lacunary-quasinormal convergence, statistical-quasinormal convergence, lacunary-statistical-quasinormal convergence for double sequence of functions and derived some inclusive relation between these notions.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Similar content being viewed by others
References
Bukovsk\(\acute{\text{a}}\), Z.: Quasinormal convergence. Math. Slov. 41(2), 137–146 (1991)
Bukovsk\(\acute{\text{y}}\), L., Reclaw, I., Repick\(\acute{\text{y}}\), M.: Spaces not distinguishing pointwise and quasinormal convergence of real functions. Topol. Appl. 41(1–2), 25–40 (1991)
Bukovsk\(\acute{\text{y}}\), L., Hale\(\hat{\text{s}}\), J.: QN-space, wQN-space and covering properties. Topol. Appl. 154(4), 848–858 (2007)
Çinar, M., Karakaş, M., Et, M.: On pointwise and uniform statistical convergence of order \(\alpha \) for sequences of functions. Fixed Point Theory Appl. 33, 11 (2013)
Cs\(\acute{\text{a}}\)sz\(\acute{\text{a}}\)r, \(\acute{\text{A}}\)., Laczkovich, M.: Discrete and equal convergence. Stud. Sci. Math. Hungar. 10, 463–472 (1975)
Cs\(\grave{\text{a}}\)sz\(\grave{\text{a}}\)r, \( \acute{\text{A}}\)., Laczkovich, M.: Some remarks on discrete Baire classes. Acta Math. Acad. Sci. Hungar. 33, 51–70 (1979)
Et, M., Çinar, M., Karakaş, M.: On \(\lambda \)-statistical convergence of order of sequences of function. J. Inequal. Appl. 204, 8 (2013)
Et, M., Şeng\(\ddot{\text{u}}\)l, H.: On pointwise lacunary statistical convergence of order of \( \alpha \) sequences of function. Proc. Natl. Acad. Sci. India Sect. A 85(2), 253–258 (2015)
Fast, H.: Sur la convergence statistique. Cooloq. Math. 2, 241–244 (1951)
Fridy, J.A.: On statistical convergence. Analysis 5, 301–313 (1985)
Freedman, A.R., Sember, J.J., Raphael, M.: Some Ces\(\grave{\text{a}}\)ro-type summability spaces. Proc. Lond. Math. Soc. 37(3), 508–520 (1978)
G\(\ddot{\text{o}}\)khan, A., G\(\ddot{\text{u}}\)ng\(\ddot{\text{o}}\)r, M.: On pointwise statistical convergence. Indian J. Pure Appl. Math. 33(9), 1379–1384 (2002)
G\(\ddot{\text{o}}\)khan, A., G\(\ddot{\text{u}}\)ng\(\ddot{\text{o}}\)r, M., Bulut, Y.: On the strong lacunary convergence and strong Ces\(\grave{\text{a}}\)ro summability of sequences of real-valued functions. Appl. Sci. 8, 70–77 (2006)
G\(\ddot{\text{o}}\)khan, A.: Lacunary statistical convergence of sequences of real-valued functions. J. Math. 4 (2013)
Fridy, J.A., Orhan, C.: Lacunary statistical summability. J. Math. Anal. Appl. 173, 497–504 (1993)
Fridy, J.A., Orhan, C.: Lacunary statistical convergence. Pac. J. Math. 160, 43–51 (1993)
Mursaleen, Edely, O.H.H.J.: Statistical convergence of double sequences. Math. Appl. 288, 223–231 (2003)
Nuray, F.: Some Ces\(\grave{\text{a}}\)ro-type quasinormal convergences. Creat. Math. Inform. 30(1), 75–80 (2021)
Prokaj, V.: A note on equal convergence. Acta Math. Hungar. 73(1–2), 155–158 (1996)
Schoenberg, I.J.: The integrability of certain functions and related summability methods. Am. Math. Mon. 66, 361–375 (1959)
Taş, E., Orhan, C.: Ces\(\grave{\text{a}}\)ro means of subsequences of double sequences. Sarajevo J. Math. 15(2), 169–179 (2019)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2023 The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd.
About this paper
Cite this paper
Sonker, S., Priyanka (2023). (C, 1, 1)-Quasinormal Convergence of Double Sequence of Functions. In: Sahni, M., Merigó, J.M., Hussain, W., León-Castro, E., Verma, R.K., Sahni, R. (eds) Mathematical Modeling, Computational Intelligence Techniques and Renewable Energy. Advances in Intelligent Systems and Computing, vol 1440. Springer, Singapore. https://doi.org/10.1007/978-981-19-9906-2_2
Download citation
DOI: https://doi.org/10.1007/978-981-19-9906-2_2
Published:
Publisher Name: Springer, Singapore
Print ISBN: 978-981-19-9905-5
Online ISBN: 978-981-19-9906-2
eBook Packages: Intelligent Technologies and RoboticsIntelligent Technologies and Robotics (R0)