λ-Bernstein Operators Based on Pólya Distribution

References

• Eggenberger, F., Pólya, G. (1923). Uber die Statistik verkerter Vorgänge. Z. Angew. Math. Mech. 1:279–289. DOI: 10.1002/zamm.19230030407.
   Google Scholar
• Stancu, D. D. (1968). Approximation of functions by a new class of linear polynomial operators. Rev. Roumaine Math. Pures Appl. 13:1173–1194.
   Google Scholar
• Bernstein, S. N. (1912). Démonstration du théoréme de weierstrass fondée sur le calcul de probabilités. Commun. Sco. Math. Charkov. 13(2):1–2.
   Google Scholar
• Johnson, N. L., Kotz, S. (1969). Discrete Distributions. Boston: Houghton-Mifflin.
   Google Scholar
• Stancu, D. D. (1970). Two classes of positive linear operators. Anal. Univ. Timişoara, Ser. Matem. 8:213–220.
   Google Scholar
• Baskakov, V. A. (1957). An instance of a sequence of linear positive operators in the space of continuous functions. Dokl. Akad. Nauk. 113:249–251.
   Google Scholar
• Razi, Q. (1989). Approximation of a function by Kantorovich type operators. Mat. Vesnik. 41(3):183–192.
   Google Scholar
• Büyükyazici, İ. (2010). Approximation by Stancu-Chlodowsky polynomials. Comput. Math. Appl. 59(1):274–282. DOI: 10.1016/j.camwa.2009.07.054.
   Google Scholar
• Agrawal, P. N., Ispir, N., Kajla, A. (2015). Approximation properties of Bézier-summation-integral type operators based on Polya-Bernstein functions. Appl. Math. Comput. 259:533–539. DOI: 10.1016/j.amc.2015.03.014.
   Google Scholar
• Deo, N., Dhamija, M., Miclǎuş, D. (2016). Stancu-Kantorovich operators based on inverse Pólya-Eggenberger distribution. Appl. Math. Comput. 273(1):281–289. DOI: 10.1016/j.amc.2015.10.008.
   Google Scholar
• Aral, A., Gupta, V. (2016). Direct estimates for Lupas-Durrmeyer operators. Filomat. 30(1):191–199. DOI: 10.2298/FIL1601191A.
   Google Scholar
• Cárdenas-Morales, D., Gupta, V. (2014). Two families of Bernstein-Durrmeyer type operators. Appl. Math. Comput. 248:342–353. DOI: 10.1016/j.amc.2014.09.094.
   Google Scholar
• Dhamija, M., Deo, N. (2016). Jain-Durrmeyer operators associated with the inverse Pólya-Eggenberger distribution. Appl. Math. Comput. 286:15–22. DOI: 10.1016/j.amc.2016.03.015.
   Google Scholar
• Dhamija, M., Deo, N. (2017). Approximation by generalized positive linear Kantorovich operators. Filomat. 31(14):4353–4368. DOI: 10.2298/FIL1714353D.
   Google Scholar
• Dhamija, M., Deo, N., Pratap, R., Acu, A. M. (2022). Generalized Durrmeyer operators based on inverse Pólya-Eggenberger distribution. Afr. Mat. 33(1):1–13. DOI: 10.1007/s13370-021-00949-8.
   Google Scholar
• Deshwal, S., Agrawal, P. N., Araci, S. (2017). Modified Stancu operators based on inverse Pólya-Eggenberger distribution. J. Inequal. Appl. 2017(1):57. DOI: 10.1186/s13660-017-1328-9.
   PubMedGoogle Scholar
• Cai, Q. B., Lian, B. Y., Zhou, G. (2018). Approximation properties of. λ Bernstein operators. J. Inequal. Appl. 2018(1):61. DOI: 10.1186/s13660-018-1653-7.
   PubMedGoogle Scholar
• Acu, A. M., Manav, N., Sofonea, D. F. (2018). Approximation properties of λ-Kantorovich operators. J. Inequal. Appl. 2018(1):202. DOI: 10.1186/s13660-018-1795-7.
   PubMed Web of Science ®Google Scholar
• Rahman, S., Mursaleen, M., Acu, A. M. (2019). Approximation properties of λ-Bernstein-Kantorovich operators with shifted knots. Math. Methods Appl. Sci. 42(11):4042–4053. DOI: 10.1002/mma.5632.
   Web of Science ®Google Scholar
• Cai, Q. B. (2018). The Bézier variant of Kantorovich type λ-Bernstein operators. J. Inequal. Appl. 2018(1):90. DOI: 10.1186/s13660-018-1688-9.
   PubMed Web of Science ®Google Scholar
• Cai, Q. B., Zhou, G. (2018). Blending type approximation by GBS operators of bivariate tensor product of λ-Bernstein-Kantorovich type. J. Inequal. Appl. 2018(1):268. DOI: 10.1186/s13660-018-1862-0.
   Google Scholar
• Acu, A. M., Acar, T., Radu, V. A. (2019). Approximation by modified Unρ operators. RACSAM. 113:2715–2729. DOI: 10.1007/s13398-019-00655-y.
   Google Scholar
• Braha, N. L., Mansour, T., Mursaleen, M., Acar, T. (2021). Convergence of λ-Bernstein operators via power series summability method. Appl. Math. Comput. 65:125–146.
   Google Scholar
• Kajla, A., Acar, T. (2018). Blending type approximation by generalized Bernstein-Durrmeyer type operators. Miskolc Math. Notes. 19(1):319–336. DOI: 10.18514/MMN.2018.2216.
   Web of Science ®Google Scholar
• Kajla, A., Acar, T. (2018). A new modification of Durrmeyer type mixed hybrid operators. Carpathian J. Math. 34(1):47–56. DOI: 10.37193/CJM.2018.01.05.
   Google Scholar
• Kajla, A., Mursaleen, M., Acar, T. (2020). Durrmeyer-type generalization of parametric Bernstein operators. Symmetry. 12(7):1141. DOI: 10.3390/sym12071141.
   Google Scholar
• Ditzian, Z., Totik, V. (1987). Moduli of Smoothness. New York: Springer-Verlag.
   Google Scholar