×
Kumar, Alok; Tapiawala, Dipti; Mishra, Lakshmi Narayan

Direct estimates for certain integral type operators. (English) Zbl 1413.41016

Eur. J. Pure Appl. Math. 11, No. 4, 958-975 (2018).
Summary: In this note, we study approximation properties of a family of linear positive operators and establish asymptotic formula, rate of convergence, local approximation theorem, global approximation theorem, weighted approximation theorem, and better approximation for this family of linear positive operators.

Cited in 2 Documents

MSC:

41A35 Approximation by operators (in particular, by integral operators)
26A15 Continuity and related questions (modulus of continuity, semicontinuity, discontinuities, etc.) for real functions in one variable
41A25 Rate of convergence, degree of approximation

Keywords:

global approximation; Voronovskaja-type theorem; \(K\)-functional; modulus of continuity; weighted approximation
PDF BibTeX XML Cite
\textit{A. Kumar} et al., Eur. J. Pure Appl. Math. 11, No. 4, 958--975 (2018; Zbl 1413.41016)
Full Text: Link

References:

[1] T. Acar, L.N. Mishra, V.N. Mishra, Simultaneous Approximation for Generalized Srivastava-Gupta Operators, Journal of Function Spaces Volume 2015, Article ID 936308, 11 pages. · Zbl 1321.41024
[2] R.A. DeVore, G.G. Lorentz, Constructive Approximation, Springer, Berlin (1993). · Zbl 0797.41016
[3] Z. Ditzian, V. Totik, Moduli of Smoothness, Springer-Verlag, New York, 1987. REFERENCES973 · Zbl 0666.41001
[4] A.R. Devdhara, V.N. Mishra, Local Approximation Results for Stancu Variant of Modified Szasz-Mirakjan Operators, Eur. J. Pure Appl. Math., Vol. 11, No. 2 (2018), 400-409. · Zbl 1413.41026
[5] E. Deniz, A. Aral, G. Ulusoy, New integral type operators, Filomat, 31:9 (2017), 2851-2865.
[6] A.D. Gadjiev, Theorems of the type of P.P. korovkin’s theorems, Matematicheskie Zametki, 20(5) (1976), 781-786.
[7] A.D. Gadjiev, 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 Soviet Math. Dokl. 15(5) (1974), 1433-1436. · Zbl 0312.41013
[8] A.D. Gadjiev, A. Aral, The Weighted Lp-approximation with positive linear operators on unbounded sets, Appl. Math. Letters, 20 (2007), 1046-1051. · Zbl 1132.41323
[9] A.R. Gairola, Deepmala, L.N. Mishra, On the q-derivatives of a certain linear positive operators, Iranian Journal of Science and Technology, Transactions A: Science, Vol. 42, No. 3, (2018), pp. 1409-1417. DOI 10.1007/s40995-017-0227-8. · Zbl 1397.41005
[10] A.R. Gairola, Deepmala, L.N. Mishra, Rate of Approximation by Finite Iterates of q-Durrmeyer Operators, Proc. Natl. Acad. Sci., India, Sect. A Phys. Sci. (April-June 2016) 86(2):229-234 (2016). doi: 10.1007/s40010-016-0267-z · Zbl 1381.41020
[11] V. Gupta, D. Agrawal, Approximation results by certain genuine operators of integral type, Kragujevac Journal of Mathematics, 42 (3) (2018), 335-348.
[12] R.B. Gandhi, Deepmala, V.N. Mishra, Local and global results for modified Sz´aszMirakjan operators, Math. Method. Appl. Sci., Vol. 40, Issue 7, (2017), pp. 2491-2504. DOI: 10.1002/mma.4171. · Zbl 1364.41014
[13] G.C. Jain, Approximation of functions by a new class of linear operators, J. Aust. Math. Soc., 13:3 (1972), 271-276. · Zbl 0232.41003
[14] A. Kajla, Direct estimates of certain Mihes.an-Durrmeyer type operators, Adv. Oper. Theory 2 (2017), no. 2, 16217178. http://doi.org/10.22034/aot.1612-1079
[15] A. Kajla, Approximation for a summation-integral type link operators, Khayyam. J. Math. 3 (2017), no. 1, 441760. DOI: 10.22034/kjm.2017.45322 · Zbl 1382.41016
[16] A. Kumar, Approximation by Stancu type generalized Srivastava-Gupta operators based on certain parameter, Khayyam J. Math., Vol. 3, no. 2 (2017), pp. 147-159. DOI: 10.22034/kjm.2017.49477 · Zbl 1384.41018
[17] A. Kumar, General Gamma type operators in Lpspaces, Palestine Journal of Mathematics, 7 (1) (2018), 73-79. REFERENCES974 · Zbl 1375.41012
[18] A. Kumar, Voronovskaja type asymptotic approximation by general Gamma type operators, Int. J. of Mathematics and its Applications, 3(4-B) (2015) 71-78.
[19] A. Kumar, D.K. Vishwakarma, Global approximation theorems for general Gamma type operators, Int. J. of Adv. in Appl. Math. and Mech. 3(2) (2015), 77-83. · Zbl 1359.41007
[20] A. Kumar,Vandana,Approximation by genuine Lupa¸s-Beta-Stancu operators, J. Appl. Math. and Informatics, Vol. 36 (2018), No. 1-2, pp. 15-28. https://doi.org/10.14317/jami.2018.015 · Zbl 1388.41016
[21] A. Kumar, Vandana, Some approximation properties of generalized integral type operators, Tbilisi Mathematical Journal, 11 (1) (2018), pp. 99-116. DOI 10.2478/tmj2018-0007. · Zbl 1384.41013
[22] A. Kumar, Vandana, Approximation properties of modified Srivastava-Gupta operators based on certain parameter, Bol. Soc. Paran. Mat., v. 38 (1) (2020), 41-53. doi:10.5269/bspm.v38i1.36907
[23] A. Kumar, L.N. Mishra, Approximation by modified Jain-Baskakov-Stancu operators, Tbilisi Mathematical Journal, 10(2) (2017), pp. 185-199. · Zbl 1371.41021
[24] A. Kumar, V.N. Mishra, Dipti Tapiawala, Stancu type generalization of modified Srivastava-Gupta operators, Eur. J. Pure Appl. Math., Vol. 10, No. 4 (2017), 890907. · Zbl 1370.41027
[25] A. Sathish Kumar, T. Acar, Approximation by generalized Baskakov-DurrmeyerStancu type operators, Rend.Circ.Mat. Palermo, 65 (3) (2016). DOI 10.1007/s12215016-0242-1 · Zbl 1354.41010
[26] J.P. King, Positive linear operators which preserve x2, Acta Math. Hungar., 99(3) (2003), 203-208. · Zbl 1027.41028
[27] Kejal Khatri, V.N. Mishra, Generalized Szasz-Mirakyan operators involving Brenke type polynomials, Appl. Math. Comp., 324 (2018), 228-238.
[28] C.P. May, On Phillips operators, J. Approx. Theory, 20 (1977), 315-332. · Zbl 0399.41021
[29] M. Mursaleen, T. Khan, On Approximation by Stancu Type Jakimovski-LeviatanDurrmeyer Operators, Azerbaijan Journal of Mathematics, V. 7, No 1 (2017), 16-26. · Zbl 1367.41019
[30] V.N. Mishra, Preeti Sharma, On approximation properties of Baskakov-Schurer-S´zasz operators, arXiv:1508.05292v1 [math.FA] 21 Aug 2015.
[31] V.N. Mishra, K. Khatri, L.N. Mishra, Some approximation properties of q-BaskakovBeta-Stancu type operators, Journal of Calculus of Variations, Volume 2013, Article ID 814824, 8 pages. REFERENCES975 · Zbl 1298.41039
[32] V.N. Mishra, K. Khatri, L.N. Mishra, Deepmala, Inverse result in simultaneous approximation by Baskakov-Durrmeyer-Stancu operators, Journal of Inequalities and Applications 2013, 2013:586. doi:10.1186/1029-242X-2013-586. · Zbl 1295.41013
[33] V.N. Mishra, Rajiv B. Gandhi, Ram N. Mohapatraa, Summation-Integral type modification of S´zasz-Mirakjan-Stancu operators, J. Numer. Anal. Approx. Theory, vol. 45, no.1 (2016), pp. 27-36. · Zbl 1399.41047
[34] V.N. Mishra, A.R. Devdhara, R.B. Gandhi,Global approximation theorems for the generalized Szasz-Mirakjan type operators in exponential weight spaces, Appl. Math. Comp., 336 (2018), 206-214.
[35] V.N. Mishra, H.H. Khan, Kejal Khatri and L.N. Mishra, Hypergeometric Representation for Baskakov-Durrmeyer-Stancu Type Operators, Bulletin of Mathematical Analysis and Applications, ISSN: 1821-129, Vol. 5, Issue 3, (2013), 18-26. · Zbl 1314.41013
[36] V.N. Mishra, Kejal Khatri and L.N. Mishra, Statistical approximation by Kantorovich type Discrete q-Beta operators, Advances in Difference Equations, 2013, 2013:345, DOI: 10.1186/10.1186/1687-1847-2013-345. · Zbl 1391.41008
[37] V.N. Mishra, Kejal Khatri and L.N. Mishra, On Simultaneous Approximation for Baskakov-Durrmeyer-Stancu type operators, Journal of Ultra Scientist of Physical Sciences, Vol. 24, No. (3)A, 2012, pp. 567-577. · Zbl 1339.41021
[38] V. Mihesan, Gamma approximating operators, Creat. Math. Inform., 17 (3) (2008), 466-472. · Zbl 1265.41055
[39] M.A. ¨Ozarslan, H. Aktu˘glu, Local approximation for certain King type operators, Filomat, 27:1 (2013), 173-181.
[40] R.S. Phillips, An inversion formula for Laplace transforms semi-groups of linear operators, Ann. Math., 59 (1954), 325-356. · Zbl 0059.10704
[41] P. Patel, V.N. Mishra, Approximation properties of certain summation integral type operators, Demonstratio Mathematica, Vol. XLVIII no. 1, 2015. · Zbl 1312.41024
[42] D.D. Stancu, Approximation of functions by a new class of linear polynomial operators, Rev. Roum. Math. Pures Appl., 13 (8) (1968), 1173-1194. · Zbl 0167.05001
[43] O. Sz´asz, Generalization of S. Bernstein’s polynomials to the infinite interval, J. Res. Nat. Bur. Stand., 45 (1950), 239-245.
[44] D.K. Verma, V. Gupta, P.N. Agrawal, Some approximation properties of BaskakovDurrmeyer-Stancu operators, Appl. Math. Comput., 218 (11) (2012), 6549-6556. · Zbl 1244.45005
[45] I. Y¨uksel, N. Ispir, Weighted approximation by a certain family of summation integral type operators, Comput. Math. Appl., 52 (2006), 1463171470. · Zbl 1134.45008
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.