AIMS Mathematics, 2020, 5(4): 3019-3034. doi: 10.3934/math.2020196.

Research article

Export file:

Format

• RIS(for EndNote,Reference Manager,ProCite)
• BibTex
• Text

Content

• Citation Only
• Citation and Abstract

Approximation of Jakimovski-Leviatan-Beta type integral operators via q-calculus

1 Operator Theory and Applications Research Group, Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah, Saudi Arabia
2 Department of Medical Research, China Medical University Hospital, China Medical University (Taiwan), Taichung, Taiwan
3 Department of Mathematics, Aligarh Muslim University, Aligarh 202002, India
4 Department of Computer Science and Information Engineering, Asia University, Taichung, Taiwan

## Abstract    Full Text(HTML)    Figure/Table

We construct Jakimovski-Leviatan-Beta type q-integral operators and show that these positive linear operators are uniformly convergent to a continuous functions. We obtain the Korovkin type results, the rate of convergence as well as some direct theorems.
Figure/Table
Supplementary
Article Metrics

Citation: Abdullah Alotaibi, M. Mursaleen. Approximation of Jakimovski-Leviatan-Beta type integral operators via q-calculus. AIMS Mathematics, 2020, 5(4): 3019-3034. doi: 10.3934/math.2020196

References

• 1. P. Appell, Une classe de polynômes, Ann. Sci. École Norm. Sup., 9 (1880), 119-144.
• 2. İ. Büyükyazıcı, H. Tanberkan, S. Serenbay, et al. Approximation by Chlodowsky type JakimovskiLeviatan operators, J. Comput. Appl. Math., 259 (2014), 153-163.
• 3. F. H. Jackson, On q-definite integrals, Quart. J. Pure Appl. Math., 41 (1910), 193-203.
• 4. V. Kac, P. Cheung, Quantum Calculus, Universitext, Springer-Verlag, New York, 2002.
• 5. V. Kac, A. De Sole, On integral representations of q-gamma and q-beta functions, Mathematica, 9 (2005), 11-29.
• 6. W. A. Al-Salam, q-Appell polynomials, Ann. Mat. Pura Appl., 4 (1967), 31-45.
• 7. M. E. Keleshteri, N. I. Mahmudov, A study on q-Appell polynomials from determinantal point of view, Appl. Math. Comput., 260 (2015), 351-369.
• 8. M. Mursaleen, K. J. Ansari, M. Nasiruzzaman, Approximation by q-analogue of JakimovskiLeviatan operators involving q-Appell polynomials, Iranian J. Sci. Tech. A, 41 (2017), 891-900.
• 9. M. Mursaleen, T. Khan, On approximation by Stancu type Jakimovski-Leviatan-Durrmeyer operators, Azerbaijan J. Math., 7 (2017), 16-26.
• 10. V. N. Mishra, P. Patel, On generalized integral Bernstein operators based on q-integers, Appl. Math. Comput., 242 (2014), 931-944.
• 11. M. Mursaleen, M. Ahasan, The Dunkl generalization of Stancu type q-Szász-Mirakjan-Kantrovich operators and some approximation results, Carpathian J. Math., 34 (2018) 363-370.
• 12. M. Mursaleen, S. Rahman, Dunkl generalization of q-Szász-Mirakjan operators which preserve x2, Filomat, 32 (2018), 733-747.
• 13. N. Rao, A. Wafi, A. M. Acu, q-Szász-Durrmeyer type operators based on Dunkl analogue, Complex Anal. Oper. Theory, 13 (2019), 915-934.
• 14. P. P. Korovkin, Linear Operators and Approximation Theory, Hindustan Publ. Co., Delhi 1960.
• 15. A. D. Gadžiev, A problem on the convergence of a sequence of positive linear operators on unbounded sets, and theorems that are analogous to P. P. Korovkin's theorem, Dokl. Akad. Nauk SSSR (Russian), 218 (1974), 1001-1004.
• 16. A. D. Gadžiev, Weighted approximation of continuous functions by positive linear operators on the whole real axis, Izv. Akad. Nauk Azerbaijan. SSR Ser. Fiz. Tehn. Mat. Nauk (Russian), 5 (1975), 41-45.
• 17. E. Ibikli, A. D. Gadžiev, The order of approximation of some unbounded functions by the sequence of positive linear operators, Turk. J. Math. 19 (1995), 331-337.
• 18. J. Peetre, Noteas de mathematica 39, Rio de Janeiro, Instituto de Mathematica Pura e Applicada, Conselho Nacional de Pesquidas, 1968.
• 19. A. Ciupa, A class of integral Favard-Szász type operators, Stud. Univ. Babeş-Bolyai, Math., 40 (1995), 39-47.
• 20. C. Atakut, N. Ispir, Approximation by modified Szász-Mirakjan operators on weighted spaces, Proc. Indian Acad. Sci. Math. Sci., 112 (2002), 571-578.