Modified Lupaş-Jain operators
-
Murat Bodur
Abstract
The goal of this paper is to propose a modification of Lupaş-Jain operators based on a function ρ having some properties. Primarily, the convergence of given operators in weighted spaces is discussed. Then, order of approximation via weighted modulus of continuity is computed for these operators. Further, Voronovskaya type theorem in quantitative form is taken into consideration, as well. Ultimately, some graphical results that illustrate the convergence of investigated operators to f are given.
Communicated by Marcus Waurick
References
[1] Abel, U.—Ivan, M.: On a generalization of an approximation operator defined by A. Lupaş, Gen. Math. 15(1) (2007), 21–34.Search in Google Scholar
[2] Abel, U.—Agratini, O.: Asymptotic behaviour of Jain operators, Numer. Algorithms 71 (2016), 553–565.10.1007/s11075-015-0009-3Search in Google Scholar
[3] Acar, T.: Asymptotic formulas for generalized Szász-Mirakyan operators, Appl. Math. Comput. 263 (2015), 223–239.10.1016/j.amc.2015.04.060Search in Google Scholar
[4] Acar, T.—Aral, A.—Raşa, I.: Modified Bernstein-Durrmeyer operators, Gen. Math. 22(1) (2014), 27–41.Search in Google Scholar
[5] Agratini, O.: On a sequence of linear positive operators, Facta Univ. Ser. Math. Inform. 14 (1999), 41–48.Search in Google Scholar
[6] Agratini, O.: Approximation properties of a class of linear operators, Math. Methods Appl. Sci. 36(17) (2013), 2353–2358.10.1002/mma.2758Search in Google Scholar
[7] Aral, A.—Inoan, D.—Raşa, I.: On the generalized Szász-Mirakyan operators, Results Math. 65 (2014), 441–452.10.1007/s00025-013-0356-0Search in Google Scholar
[8] Aral, A.—Ari, D. A.—Cárdenas-Morales, D.: A note on Baskakov operators based on a function ν, Creat. Math. Inform. 25(1) (2016), 15–27.10.37193/CMI.2016.01.03Search in Google Scholar
[9] Başcanbaz-Tunca, G.—İnce İlarslan, H. G.—Erençİn, A.: Bivariate Bernstein type operators, Appl. Math. Comput. 273 (2016), 543–552.10.1016/j.amc.2015.10.037Search in Google Scholar
[10] Başcanbaz-Tunca, G.—Bodur, M.—Söylemez, D.: On Lupaş-Jain Operators, Stud. Univ. Babeş-Bolyai Math. 63(4) (2018), 525–537.10.24193/subbmath.2018.4.08Search in Google Scholar
[11] Başcanbaz-Tunca, G.—Erençİn, A.—İnce İLARSLAN H. G.: Quantitative estimates for modified Beta operators, Matematički Vesnik, in press.Search in Google Scholar
[12] Bodur, M.—Taşdelen, F.—Başcanbaz-Tunca, G.: On multivariate Lupaş operators, Hacet. J. Math. Stat. 47(4) (2018), 783–792.10.15672/HJMS.2017.500Search in Google Scholar
[13] Cárdenas-Morales, D.—Garrancho, P.—Raşa, I.: Bernstein-type operators which preserve polynomials, Comput. Math. Appl. 62 (2011), 158–163.10.1016/j.camwa.2011.04.063Search in Google Scholar
[14] Erençİn, A.—Olgun, A.—Taşdelen, F.: Generalized Baskakov type operators, Math. Slovaca 67(5) (2017), 1269–1277.10.1515/ms-2017-0048Search in Google Scholar
[15] Erençİn, A.—Başcanbaz-Tunca, G.—Taşdelen, F.: Some properties of the operators defined by Lupaş, Rev. Anal. Numér. Théor. Approx. 43(2) (2014), 158–164.Search in Google Scholar
[16] Farcaş, A.: An asymptotic formula for Jain’s operators, Stud. Univ. Babeş-Bolyai Math. 57(4) (2012), 511–517.Search in Google Scholar
[17] Finta, Z.: Quantitative estimates for some linear and positive operators, Stud. Univ. Babeş-Bolyai Math. 47(3) (2002), 71–84.Search in Google Scholar
[18] Gadjiev, A.D.: Theorems of the type of P. P. Korovkin type theorems, Math. Zametki 20(5) (1976), 781–786.10.1007/BF01146928Search in Google Scholar
[19] Holhoş, A.: Quantitative estimates for positive linear operators in weighted spaces, Gen. Math. 16 (2008), 99–110.Search in Google Scholar
[20] Jain, G.C.: Approximation of functions by a new class of linear operators, J. Austral. Math. Soc. 13(3) (1972), 271–276.10.1017/S1446788700013689Search in Google Scholar
[21] Lupaş, A.: The approximation by some positive linear operators. In: Proceedings of the International Dortmund Meeting on Approximation Theory (M. W. Muller et al., eds.), Akademie Verlag, Berlin 1995, pp. 201–229.Search in Google Scholar
[22] Olgun, A.—Taşdelen, F.—Erençİn, A.: A generalization of Jain’s operators, Appl. Math. Comput. 266 (2015), 6–11.10.1016/j.amc.2015.05.060Search in Google Scholar
[23] Patel, P.—Mishra, V. N.: On new class of linear and positive operators, Boll. Unione Mat. Ital. 8 (2015), 81–96.10.1007/s40574-015-0026-0Search in Google Scholar
[24] Patel, P.—Mishra, V. N.: Jain-Baskakov operators and its different generalization, Acta Math. Vietnam 40 (2015), 715–733.10.1007/s40306-014-0077-9Search in Google Scholar
[25] Sofonea, D. F.: On a sequence of linear and positive operators, Results Math. 53(3–4) (2009), 435–444.10.1007/s00025-008-0355-8Search in Google Scholar
[26] Söylemez, D.: Some properties of the generalized Bleimann, Butzer and Hahn operators, Commun. Fac. Sci. Univ. Ank. Sér. A1 Math. Stat. 64(2) (2015), 55–62.10.1501/Commua1_0000000733Search in Google Scholar
[27] Taşdelen Yeşİldal, F.—Bodur, M.: Bivariate Baskakov type operators, Rev. R. Acad. Cienc. Exactas Fís. Nat. Ser. A Math. RACSAM. 113(4) (2019), 3269–3281. https://doi.org/10.1007/s13398-019-00695-4.10.1007/s13398-019-00695-4Search in Google Scholar
© 2020 Mathematical Institute Slovak Academy of Sciences
Articles in the same Issue
- Regular papers
- Relatively residuated lattices and posets
- Strongly s-dense injective hull and Banaschewski’s theorems for acts
- Wild sets in global function fields
- Generators and integral points on elliptic curves associated with simplest quartic fields
- New Filbert and Lilbert matrices with asymmetric entries
- Returning functions with closed graph are continuous
- On sets of points of approximate continuity and ϱ-upper continuity
- Investigation of the fifth Hankel determinant for a family of functions with bounded turnings
- On solvability of some nonlocal boundary value problems for biharmonic equation
- The study of piecewise pseudo almost periodic solutions for impulsive Lasota-Wazewska model with discontinuous coefficients
- Strongly increasing solutions of higher-order quasilinear ordinary differential equations
- Oscillation of second order half-linear neutral differential equations with weaker restrictions on shifted arguments
- Filippov solutions of vector Dirichlet problems
- Sequences of positive homoclinic solutions to difference equations with variable exponent
- Modified Lupaş-Jain operators
- New fixed point results in bv(s)-metric spaces
- Improved Young and Heinz operator inequalities for unitarily invariant norms
- Scrutiny of some fixed point results by S-operators without triangular inequality
- The lattices of families of regular sets in topological spaces
- Iterated partial summations applied to finite-support discrete distributions
- Hamiltonicity of a class of toroidal graphs
Articles in the same Issue
- Regular papers
- Relatively residuated lattices and posets
- Strongly s-dense injective hull and Banaschewski’s theorems for acts
- Wild sets in global function fields
- Generators and integral points on elliptic curves associated with simplest quartic fields
- New Filbert and Lilbert matrices with asymmetric entries
- Returning functions with closed graph are continuous
- On sets of points of approximate continuity and ϱ-upper continuity
- Investigation of the fifth Hankel determinant for a family of functions with bounded turnings
- On solvability of some nonlocal boundary value problems for biharmonic equation
- The study of piecewise pseudo almost periodic solutions for impulsive Lasota-Wazewska model with discontinuous coefficients
- Strongly increasing solutions of higher-order quasilinear ordinary differential equations
- Oscillation of second order half-linear neutral differential equations with weaker restrictions on shifted arguments
- Filippov solutions of vector Dirichlet problems
- Sequences of positive homoclinic solutions to difference equations with variable exponent
- Modified Lupaş-Jain operators
- New fixed point results in bv(s)-metric spaces
- Improved Young and Heinz operator inequalities for unitarily invariant norms
- Scrutiny of some fixed point results by S-operators without triangular inequality
- The lattices of families of regular sets in topological spaces
- Iterated partial summations applied to finite-support discrete distributions
- Hamiltonicity of a class of toroidal graphs
