PDF EndNote BibTex Cite

Year 2019, Volume 9, Issue 4, 936 - 948, 01.12.2019

Abstract

References

  • [1] Acar, T., Mishra, L.N. and Mishra V.N., Simultaneous Approximation for Generalized SrivastavaGupta Operators, Journal of Function Spaces Volume 2015, Article ID 936308, 11 pages.
  • [2] DeVore, R.A. and Lorentz, G.G., (1993), Constructive Approximation, Springer, Berlin.
  • [3] Gadjiev, A.D., (1976), Theorems of the type of P.P. korovkin’s theorems, Matematicheskie Zametki, 20 (5), pp. 781-786.
  • [4] Gadjiev, A.D., (1974), 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).
  • [5] Gairola, A.R., Deepmala and Mishra, L.N., (2017), On the q-derivatives of a certain linear positive operators, Iranian Journal of Science and Technology, Transactions A: Science, DOI 10.1007/s40995- 017-0227-8.
  • [6] Gairola, A.R., Deepmala and Mishra, L.N., (2016), 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. doi: 10.1007/s40010-016-0267-z
  • [7] Gandhi, R.B., Deepmala and Mishra, V.N., (2017), Local and global results for modified SzaszMirakjan operators, Math. Method. Appl. Sci., DOI: 10.1002/mma.4171.
  • [8] Goyal, M. and Agrawal, P.N., (2017), Bezier Variant of the Jakimovski-Leviatan-Paltanea operators based on Appell polynomials, ANNALI DELL UNIVERSITA DI FERRARA, 40 (7), pp. 2491-2504.
  • [9] Jakimovski, A. and Leviatan, D., (1969), Generalized Szasz operators for the approximation in the infinite interval, Mathematica (Cluj) 11, pp. 97-103.
  • [10] Karaisa, A., (2015), Approximation by Durrmeyer type Jakimovski-Leviatan operators, Math. Methods Appl. Sci., DOI: 10.1002/mma.3650.
  • [11] Kumar, A., (2017), Approximation by Stancu type generalized Srivastava-Gupta operators based on certain parameter, Khayyam J. Math., 3 , no. 2, pp. 147-159. DOI: 10.22034/kjm.2017.49477
  • [12] Kumar, A. and Vandana, (2018), Some approximation properties of generalized integral type operators, Tbilisi Mathematical Journal, 11 (1), pp. 99-116. DOI 10.2478/tmj-2018-0007
  • [13] Kumar, A. and Vandana, (2018), Approximation by genuine Lupas-Beta-Stancu operators, J. Appl. Math. and Informatics, 36 (1-2), pp. 15-28. https://doi.org/10.14317/jami.2018.015
  • [14] Kumar, A. and Vandana, (2020), Approximation properties of modified Srivastava-Gupta operators based on certain parameter, Bol. Soc. Paran. Mat., v. 38 (1), pp. 41-53. doi:10.5269/bspm.v38i1.36907.
  • [15] Kumar, A. and Mishra, L.N., (2017), Approximation by modified Jain-Baskakov-Stancu operators, Tbilisi Mathematical Journal, 10(2), pp. 185-199.
  • [16] Kumar, A., Mishra, V.N. and Tapiawala, D., (2017), Stancu type generalization of modified SrivastavaGupta operators, Eur. J. Pure Appl. Math, Vol. 10, No. 4, pp. 890-907.
  • [17] Kumar, A., Tapiawala, D. and Mishra, L.N., (2018), Direct estimates for certain integral type Operators, Eur. J. Pure Appl. Math, Vol. 11, No. 4, pp. 958-975.
  • [18] King, J.P., (2003), Positive linear operators which preserve x 2 , Acta Math. Hungar., 99 (3), pp. 203-208.
  • [19] Lenze, B., (1988), On Lipschitz type maximal functions and their smoothness spaces, Nederl. Akad. Indag. Math., 50, pp. 53-63.
  • [20] May, C.P., (1977), On Phillips operators, J. Approx. Theory, 20, pp. 315-332.
  • [21] Mursaleen, M. and Khan, T., (2017), On Approximation by Stancu type Jakimovski-LeviatanDurrmeyer Operators, Azerbaijan Journal of Mathematics, V. 7, No 1, pp. 16-26.
  • [22] Mishra, V.N. and Sharma, P., On approximation properties of Baskakov-Schurer-Szasz operators, arXiv:1508.05292v1 [math.FA] 21 Aug 2015.
  • [23] Mishra, V.N., Khatri, K. and Mishra, L.N., Some approximation properties of q-Baskakov-Beta-Stancu type operators, Journal of Calculus of Variations, Volume 2013, Article ID 814824, 8 pages.
  • [24] Mishra, V.N., Khatri, K. and Mishra, L.N., (2012), On Simultaneous Approximation for BaskakovDurrmeyer-Stancu type operators, Journal of Ultra Scientist of Physical Sciences, Vol. 24, No. (3) A, pp. 567-577.
  • [25] Mishra, V.N., Sharma, P. and Mishra, L.N., (2016), On statistical approximation properties of qBaskakov-Szasz-Stancu operators, Journal of Egyptian Mathematical Society, Vol. 24, Issue 3, pp. 396-401. DOI: 10.1016/j.joems.2015.07.005.
  • [26] Mishra, V.N., Khatri, K., Mishra, L.N. and 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.
  • [27] Mishra, V.N., Gandhi, R.B. and Mohapatraa, R.N., (2016), Summation-Integral type modification of Szasz-Mirakjan-Stancu operators, J. Numer. Anal. Approx. Theory, vol. 45, no.1, pp. 27-36.
  • [28] O¨zarslan, M.A. and Aktu˘glu, H., (2013), Local approximation for certain King type operators, Filomat, 27:1, pp. 173-181.
  • [29] Pˇaltˇanea, R., (2008), Modified Szasz-Mirakjan operators of integral form, Carpathian J. Math., 24 (3), pp. 378-385.
  • [30] Phillips, R.S., (1954), An inversion formula for Laplace transforms semi-groups of linear operators, Ann. Math., 59, pp. 325-356.
  • [31] Patel, P. and Mishra, V.N., (2015), Approximation properties of certain summation integral type operators, Demonstratio Mathematica, Vol. XLVIII no. 1.
  • [32] Stancu, D.D., (1968), Approximation of functions by a new class of linear polynomial operators, Rev. Roum. Math. Pures Appl., 13 (8), pp. 1173-1194.
  • [33] Sz´asz, O., (1950), Generalization of S. Bernstein’s polynomials to the infinite interval, J. Res. Nat. Bur. Stand., 45, pp. 239-245.
  • [34] Verma, D.K. and Gupta, V., (2015), Approximation for Jakimovski-Leviatan-Paltanea operators, Ann Univ Ferrara, 61, pp. 367-380.
  • [35] Verma, D.K., Gupta, V. and Agrawal, P.N., (2012), Some approximation properties of BaskakovDurrmeyer-Stancu operators, Appl. Math. Comput., 218 (11), pp. 6549-6556

APPROXIMATION BY STANCU TYPE JAKIMOVSKI-LEVIATAN-PǍLTǍNEA OPERATORS

Year 2019, Volume 9, Issue 4, 936 - 948, 01.12.2019

Abstract

The present article deals with the general family of summation-integral type operators. Here, we introduce the Stancu type generalization of the Jakimovski-Leviatan- Paltanea operators and study Voronovskaja-type asymptotic theorem, local approximation, weighted approximation, rate of convergence and pointwise estimates using the Lipschitz type maximal function. Also, we propose a king type modi cation of these operators to obtain better estimates.

References

  • [1] Acar, T., Mishra, L.N. and Mishra V.N., Simultaneous Approximation for Generalized SrivastavaGupta Operators, Journal of Function Spaces Volume 2015, Article ID 936308, 11 pages.
  • [2] DeVore, R.A. and Lorentz, G.G., (1993), Constructive Approximation, Springer, Berlin.
  • [3] Gadjiev, A.D., (1976), Theorems of the type of P.P. korovkin’s theorems, Matematicheskie Zametki, 20 (5), pp. 781-786.
  • [4] Gadjiev, A.D., (1974), 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).
  • [5] Gairola, A.R., Deepmala and Mishra, L.N., (2017), On the q-derivatives of a certain linear positive operators, Iranian Journal of Science and Technology, Transactions A: Science, DOI 10.1007/s40995- 017-0227-8.
  • [6] Gairola, A.R., Deepmala and Mishra, L.N., (2016), 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. doi: 10.1007/s40010-016-0267-z
  • [7] Gandhi, R.B., Deepmala and Mishra, V.N., (2017), Local and global results for modified SzaszMirakjan operators, Math. Method. Appl. Sci., DOI: 10.1002/mma.4171.
  • [8] Goyal, M. and Agrawal, P.N., (2017), Bezier Variant of the Jakimovski-Leviatan-Paltanea operators based on Appell polynomials, ANNALI DELL UNIVERSITA DI FERRARA, 40 (7), pp. 2491-2504.
  • [9] Jakimovski, A. and Leviatan, D., (1969), Generalized Szasz operators for the approximation in the infinite interval, Mathematica (Cluj) 11, pp. 97-103.
  • [10] Karaisa, A., (2015), Approximation by Durrmeyer type Jakimovski-Leviatan operators, Math. Methods Appl. Sci., DOI: 10.1002/mma.3650.
  • [11] Kumar, A., (2017), Approximation by Stancu type generalized Srivastava-Gupta operators based on certain parameter, Khayyam J. Math., 3 , no. 2, pp. 147-159. DOI: 10.22034/kjm.2017.49477
  • [12] Kumar, A. and Vandana, (2018), Some approximation properties of generalized integral type operators, Tbilisi Mathematical Journal, 11 (1), pp. 99-116. DOI 10.2478/tmj-2018-0007
  • [13] Kumar, A. and Vandana, (2018), Approximation by genuine Lupas-Beta-Stancu operators, J. Appl. Math. and Informatics, 36 (1-2), pp. 15-28. https://doi.org/10.14317/jami.2018.015
  • [14] Kumar, A. and Vandana, (2020), Approximation properties of modified Srivastava-Gupta operators based on certain parameter, Bol. Soc. Paran. Mat., v. 38 (1), pp. 41-53. doi:10.5269/bspm.v38i1.36907.
  • [15] Kumar, A. and Mishra, L.N., (2017), Approximation by modified Jain-Baskakov-Stancu operators, Tbilisi Mathematical Journal, 10(2), pp. 185-199.
  • [16] Kumar, A., Mishra, V.N. and Tapiawala, D., (2017), Stancu type generalization of modified SrivastavaGupta operators, Eur. J. Pure Appl. Math, Vol. 10, No. 4, pp. 890-907.
  • [17] Kumar, A., Tapiawala, D. and Mishra, L.N., (2018), Direct estimates for certain integral type Operators, Eur. J. Pure Appl. Math, Vol. 11, No. 4, pp. 958-975.
  • [18] King, J.P., (2003), Positive linear operators which preserve x 2 , Acta Math. Hungar., 99 (3), pp. 203-208.
  • [19] Lenze, B., (1988), On Lipschitz type maximal functions and their smoothness spaces, Nederl. Akad. Indag. Math., 50, pp. 53-63.
  • [20] May, C.P., (1977), On Phillips operators, J. Approx. Theory, 20, pp. 315-332.
  • [21] Mursaleen, M. and Khan, T., (2017), On Approximation by Stancu type Jakimovski-LeviatanDurrmeyer Operators, Azerbaijan Journal of Mathematics, V. 7, No 1, pp. 16-26.
  • [22] Mishra, V.N. and Sharma, P., On approximation properties of Baskakov-Schurer-Szasz operators, arXiv:1508.05292v1 [math.FA] 21 Aug 2015.
  • [23] Mishra, V.N., Khatri, K. and Mishra, L.N., Some approximation properties of q-Baskakov-Beta-Stancu type operators, Journal of Calculus of Variations, Volume 2013, Article ID 814824, 8 pages.
  • [24] Mishra, V.N., Khatri, K. and Mishra, L.N., (2012), On Simultaneous Approximation for BaskakovDurrmeyer-Stancu type operators, Journal of Ultra Scientist of Physical Sciences, Vol. 24, No. (3) A, pp. 567-577.
  • [25] Mishra, V.N., Sharma, P. and Mishra, L.N., (2016), On statistical approximation properties of qBaskakov-Szasz-Stancu operators, Journal of Egyptian Mathematical Society, Vol. 24, Issue 3, pp. 396-401. DOI: 10.1016/j.joems.2015.07.005.
  • [26] Mishra, V.N., Khatri, K., Mishra, L.N. and 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.
  • [27] Mishra, V.N., Gandhi, R.B. and Mohapatraa, R.N., (2016), Summation-Integral type modification of Szasz-Mirakjan-Stancu operators, J. Numer. Anal. Approx. Theory, vol. 45, no.1, pp. 27-36.
  • [28] O¨zarslan, M.A. and Aktu˘glu, H., (2013), Local approximation for certain King type operators, Filomat, 27:1, pp. 173-181.
  • [29] Pˇaltˇanea, R., (2008), Modified Szasz-Mirakjan operators of integral form, Carpathian J. Math., 24 (3), pp. 378-385.
  • [30] Phillips, R.S., (1954), An inversion formula for Laplace transforms semi-groups of linear operators, Ann. Math., 59, pp. 325-356.
  • [31] Patel, P. and Mishra, V.N., (2015), Approximation properties of certain summation integral type operators, Demonstratio Mathematica, Vol. XLVIII no. 1.
  • [32] Stancu, D.D., (1968), Approximation of functions by a new class of linear polynomial operators, Rev. Roum. Math. Pures Appl., 13 (8), pp. 1173-1194.
  • [33] Sz´asz, O., (1950), Generalization of S. Bernstein’s polynomials to the infinite interval, J. Res. Nat. Bur. Stand., 45, pp. 239-245.
  • [34] Verma, D.K. and Gupta, V., (2015), Approximation for Jakimovski-Leviatan-Paltanea operators, Ann Univ Ferrara, 61, pp. 367-380.
  • [35] Verma, D.K., Gupta, V. and Agrawal, P.N., (2012), Some approximation properties of BaskakovDurrmeyer-Stancu operators, Appl. Math. Comput., 218 (11), pp. 6549-6556

Details

Primary Language English
Journal Section Research Article
Authors

A. KUMAR This is me
Department of Com. Science, Dev Sanskriti Vishwavidyalaya, Haridwar-249 411, Uttarakhand, India


- VANDANA This is me
Department of Management Studies, Indian Institute of Technology, Madras, Tamil Nadu-600 036.

Publication Date December 1, 2019
Published in Issue Year 2019, Volume 9, Issue 4

Cite

Bibtex @ { twmsjaem760968, journal = {TWMS Journal of Applied and Engineering Mathematics}, issn = {2146-1147}, eissn = {2587-1013}, address = {Işık University ŞİLE KAMPÜSÜ Meşrutiyet Mahallesi, Üniversite Sokak No:2 Şile / İstanbul}, publisher = {Turkic World Mathematical Society}, year = {2019}, volume = {9}, number = {4}, pages = {936 - 948}, title = {APPROXIMATION BY STANCU TYPE JAKIMOVSKI-LEVIATAN-PǍLTǍNEA OPERATORS}, key = {cite}, author = {Kumar, A. and Vandana, -} }