Abstract
In this article, we introduce Chlodowsky Integral type operators with the help of generalized exponential function with two unbounded and non-negative real number sequences \(a_n\) and \(b_n\). We study their basic estimates and investigate local and global approximation results with the aid of second-order modulus of continuity, Peetre’s K-functional, Lipschitz-type class and rth-order Lipschitz-type maximal function. In the last, statistical approximation results are studied.
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
References
Altomare, F., Campiti, M.: Korovkin-Type Approximation Theory and Its Applications. De Gruyter Studies in Mathematics, Appendix A By Michael Pannenberg and Appendix B By Fendinand Beckho, vol. 17. Walter De Gruyter, Berlin (1994)
DeVore, R.A., Lorentz, G.G.: Constructive Approximation. Grudlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences]. Springer, Berlin (1993)
Duman, O., Orhan, C.: Statistical approximation by positive linear operators. Studio Math. 16(2), 187–197 (2004)
Ibikli, E., Gadjieva, E.A.: The order of approximation of some unbounded functions by the sequence of positive linear operators. Turkish J. Math. 19(3), 331–337 (1995)
Gadjiev, A.D.: The convergence problem for a sequence of positive linear operators on bounded sets and theorems analogous to that of P. P. Korovkin. Dokl. Akad. Nauk SSSR 218(5) (1974); Transl. in Soviest Math. Dokl. 15(5), 1433–1436 (1974)
Gadjiev, A.D., Orhan, C.: Some approximation theorems via statistical convergence. Rocky Mountain J. Math. 32(1), 129–138 (2007)
Wafi, A., Rao, N.: Sz\(\acute{a}\)sz-Durrmeyer operators based on Dunkl analogue. Complex Anal. Oper. Theory (2017). https://doi.org/10.1007/s11785-017-0647-7
Wafi, A., Rao, N.: textitSz\(\acute{a}\)sz-gamma operators based on Dunkl analogue. Iran J. Sci. Technol. Trans. Sci. https://doi.org/10.1007/s40995-017-0433-4
Milovanovic Gradimir, V., Mursaleen, M., Nasiruzzaman, M.: Modified Stancu type Dunkl generalization of Szasz-Kantorovich operators. Revista de la Real Academia de Ciencias Exactas, Fsicas y Naturales, Serie A. https://doi.org/10.1007/s13398-016-0369-0
Mursaleen, M., Nasiruzzaman, M., Alotaibi, A.: Dunkl, on modified, generalization of Szasz operators via q-calculus. J. Inequalities Appl. 2017, 38 (2017). https://doi.org/10.1186/s13660-017-1311-5
Mursaleen, M., Nasiruzzaman, M.: Dunkl generalization of Kantorovich type Szasz-Mirakjan operators via q- Calculus. Asian-Eur. J. Math. https://doi.org/10.1142/S1793557117500772.
Icoz, G, Cekim, B.: Dunkl generalization of Szsz operators via q-calculus. J. Inequal. Appl., 284 (2015)
Icoz, G., Cekim, B.: Stancu-type generalization of Dunkl analogue of Szsz-Kantorovich operators. Math. Met. Appl. Sci. https://doi.org/10.1002/mma.3602
Karaisa, A., Karakoc, F.: Stancu type generalization of Dunkl analogue of Szsz operators. Adv. Appl. Clifford Algebr. 26, 1235. https://doi.org/10.1007/s00006-016-0643-4
Kajla, A., Agrawal, P.N.: Szász-Durrmeyer type operators based on Charlier polynomials. Appl. Math. Comput. 268, 1001–1014 (2015)
Lenze, B.: On Lipschitz type maximal functions and their smoothness spaces. Nederl. Akad. Indag. Math. 50, 53–63 (1988)
Mazhar, S.M., Totik, V.: Approximation by modified Szász operators. Acta Sci. Math. (Szeged) 49(1–4), 257–269 (1985)
Mursaleen, M., Nasiruzzaman, M., Shrivastwa, H.M.: Approximation by bicomplex beta operators in compact \(\mathbb{(}B)\mathbb{C}\)-disks. Math. Met. Appl. Sci. (2016). https://doi.org/10.1002/mma.3739
Mursaleen, M., Nasiruzzaman, M., Shrivastwa, H.M.: Approximation properties for modified q-Bernstein-Kantorovich operators. Numer. Funct. Anal. Optim. 36(5), 1178–1197 (2015)
Mursaleen, M., Nasiruzzaman, M.: A Dunkl generalization of q-parametric Szász-Mirakjan operators (2015). arXiv:1511.06628 [math.CA]
Karaisa, A., Karakoç, F.: Stancu type generalization of Dunkl analogue of Szàsz operators. Adv. Appl. Clifford Algebr. 26, 1235 (2016). https://doi.org/10.1007/s00006-016-0643-4
Özarslan, M.A., Aktuğlu, H.: Local approximation for certain King type operators. Filomat. 27, 173–181 (2013)
Rosenblum, M.: Generalized Hermite polynomials and the Bose-like oscillator calculus. Oper. Theory Adv. Appl. 73, 369–396 (1994)
Shisha, O., Bond, B.: The degree of convergence of linear positive operators. Proc. Nat. Acad. Sci. USA 60, 1196–1200 (1968)
Sucu, S.: Dunkl analogue of Sz\(\acute{a}\)sz operators. Appl. Math. Comput. 244, 42–48 (2014)
Sz\(\acute{a}\)sz, O.: Generalization of S. Bernstein’s polynomials to the infinite interval. J. Research Nat. Bur. Standards. 45, 239–245 (1950)
Yüksel, I., Ispir, N.: Weighted approximation by a certain family of summation integral-type operators. Comput. Math. Appl. 52(10–11), 1463–1470 (2006)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2020 The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd.
About this paper
Cite this paper
Rao, N., Wafi, A., Khatoon, S. (2020). Better Rate of Convergence by Modified Integral Type Operators. In: Shahid, M., Ashraf, M., Al-Solamy, F., Kimura, Y., Vilcu, G. (eds) Differential Geometry, Algebra, and Analysis. ICDGAA 2016. Springer Proceedings in Mathematics & Statistics, vol 327. Springer, Singapore. https://doi.org/10.1007/978-981-15-5455-1_20
Download citation
DOI: https://doi.org/10.1007/978-981-15-5455-1_20
Published:
Publisher Name: Springer, Singapore
Print ISBN: 978-981-15-5454-4
Online ISBN: 978-981-15-5455-1
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)