{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,15]],"date-time":"2026-04-15T19:14:26Z","timestamp":1776280466983,"version":"3.50.1"},"reference-count":29,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2019,6,14]],"date-time":"2019-06-14T00:00:00Z","timestamp":1560470400000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2019,6,14]],"date-time":"2019-06-14T00:00:00Z","timestamp":1560470400000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Numer Algor"],"published-print":{"date-parts":[[2020,5]]},"DOI":"10.1007\/s11075-019-00752-4","type":"journal-article","created":{"date-parts":[[2019,6,14]],"date-time":"2019-06-14T05:11:12Z","timestamp":1560489072000},"page":"207-227","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":44,"title":["Approximation properties and error estimation of q-Bernstein shifted operators"],"prefix":"10.1007","volume":"84","author":[{"given":"Mohammad","family":"Mursaleen","sequence":"first","affiliation":[]},{"given":"Khursheed J.","family":"Ansari","sequence":"additional","affiliation":[]},{"given":"Asif","family":"Khan","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2019,6,14]]},"reference":[{"key":"752_CR1","doi-asserted-by":"publisher","first-page":"98","DOI":"10.1186\/s13660-016-1045-9","volume":"2016","author":"T Acar","year":"2016","unstructured":"Acar, T., Aral, A., Mohiuddine, S.A.: On Kantorovich modification of (p, q)-Baskakov operators. Journal of Inequalities and Applications 2016, 98 (2016)","journal-title":"Journal of Inequalities and Applications"},{"key":"752_CR2","doi-asserted-by":"publisher","first-page":"655","DOI":"10.1007\/s40995-016-0045-4","volume":"42","author":"T Acar","year":"2018","unstructured":"Acar, T, Aral, A., Mohiuddine, S.: Approximation by bivariate (p,q)-Bernstein Kantorovich operators. Iran. J. Sci. Technol. Trans. Sci. 42, 655\u2013662 (2018)","journal-title":"Iran. J. Sci. Technol. Trans. Sci."},{"key":"752_CR3","doi-asserted-by":"publisher","first-page":"2685","DOI":"10.1002\/mma.3721","volume":"39","author":"T Acar","year":"2016","unstructured":"Acar, T.: (P,q)-generalization of Szasz-Mirakyan operators. Math. Methods Appl. Sci. 39, 2685\u20132695 (2016)","journal-title":"Math. Methods Appl. Sci."},{"key":"752_CR4","doi-asserted-by":"publisher","DOI":"10.1515\/9783110884586","volume-title":"Korovkin-Type Approximation Theory and Its Applications, de Gruyter Studies in Mathematics, vol. 17","author":"F Altomare","year":"1994","unstructured":"Altomare, F., Campiti, M.: Korovkin-Type Approximation Theory and Its Applications, de Gruyter Studies in Mathematics, vol. 17. Walter de Gruyter and Co., Berlin (1994)"},{"key":"752_CR5","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4614-6946-9","volume-title":"Applications of Q-calculus in Operator Theory","author":"A Aral","year":"2013","unstructured":"Aral, A., Gupta, V., Agarwal, R.P.: Applications of Q-calculus in Operator Theory. Springer, New York (2013)"},{"key":"752_CR6","unstructured":"Bernstein, S.N.: D\u00e9monstation du th\u00e9or\u00e8me de Weierstrass fond\u00e9e sur le calcul de probabilit\u00e9s. Commun. Soc. Math. Kharkow 13, 1\u20132 (1912\u20131913)"},{"key":"752_CR7","first-page":"12","volume":"276","author":"Q-B Cai","year":"2016","unstructured":"Cai, Q.-B., Zhou, G.: On (p,q)-analogue of Kantorovich type Bernstein-Stancu-Schurer operators. Appl. Math. Comput. 276, 12\u201320 (2016)","journal-title":"Appl. Math. Comput."},{"key":"752_CR8","first-page":"269","volume":"76","author":"MM Derriennic","year":"2005","unstructured":"Derriennic, M.M.: Modified Bernstein polynomials and Jacobi polynomials in q-calculus. Rend. Circ. Mat Palermo Serie II 76, 269\u2013290 (2005)","journal-title":"Rend. Circ. Mat Palermo Serie II"},{"key":"752_CR9","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-662-02888-9","volume-title":"Constructive Approximation","author":"RA DeVore","year":"1993","unstructured":"DeVore, R.A., Lorentz, G.G.: Constructive Approximation. Springer, Berlin (1993)"},{"key":"752_CR10","doi-asserted-by":"publisher","first-page":"1610","DOI":"10.1016\/j.mcm.2011.10.059","volume":"55","author":"O Dogru","year":"2012","unstructured":"Dogru, O., Kanat, K.: On statistical approximation properties of the Kantorovich type Lupas operators. Math. Comput. Modell. 55, 1610\u20131620 (2012)","journal-title":"Math. Comput. Modell."},{"key":"752_CR11","first-page":"890","volume":"216","author":"AD Gadjiev","year":"2010","unstructured":"Gadjiev, A.D., Ghorbanalizadeh, A.M.: Approximation properties of a new type Bernstein-Stancu polynomials of one and two variables. Appl. Math. Comput. 216, 890\u2013901 (2010)","journal-title":"Appl. Math. Comput."},{"issue":"2","key":"752_CR12","doi-asserted-by":"publisher","first-page":"229","DOI":"10.1007\/s40010-016-0267-z","volume":"86","author":"AR Gairola","year":"2016","unstructured":"Gairola, A.R., Deepmala, Mishra, L.N.: Rate of approximation by finite iterates of q-Durrmeyer operators. Proc. Natl. Acad. Sci., India, Sect. A Phys. Sci. 86(2), 229\u2013234 (2016)","journal-title":"Proc. Natl. Acad. Sci., India, Sect. A Phys. Sci."},{"key":"752_CR13","doi-asserted-by":"publisher","first-page":"1382","DOI":"10.1016\/j.aml.2010.07.004","volume":"23","author":"OHH Edely","year":"2010","unstructured":"Edely, O.H.H., Mohiuddine, S.A., Noman, A.K.: Korovkin type approximation theorems obtained through generalized statistical convergence. Appl. Math. Lett. 23, 1382\u20131387 (2010)","journal-title":"Appl. Math. Lett."},{"key":"752_CR14","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4613-0071-7","volume-title":"Quantum Calculus","author":"V Kac","year":"2002","unstructured":"Kac, V., Cheung, P.: Quantum Calculus. Springer, New York (2002)"},{"key":"752_CR15","doi-asserted-by":"publisher","first-page":"752","DOI":"10.1016\/j.jmaa.2016.05.062","volume":"443","author":"U Kadak","year":"2016","unstructured":"Kadak, U.: On weighted statistical convergence based on (p,q)-integers and related approximation theorems for functions of two variables. Jour. Math. Anal. Appl. 443, 752\u2013764 (2016)","journal-title":"Jour. Math. Anal. Appl."},{"key":"752_CR16","doi-asserted-by":"publisher","first-page":"1633","DOI":"10.1016\/j.jmaa.2016.11.084","volume":"448","author":"U Kadak","year":"2017","unstructured":"Kadak, U.: Weighted statistical convergence based on generalized difference operator involving (p,q)-Gamma function and its applications to approximation theorems. Jour. Math. Anal. Appl. 448, 1633\u20131650 (2017)","journal-title":"Jour. Math. Anal. Appl."},{"issue":"4","key":"752_CR17","doi-asserted-by":"publisher","first-page":"1443","DOI":"10.1007\/s13398-017-0439-y","volume":"112","author":"U Kadak","year":"2018","unstructured":"Kadak, U., Mishra, V.N., Pandey, S.: Chlodowsky type generalization of (p,q)-Szasz operators involving Brenke type polynomials. RACSAM 112(4), 1443\u20131462 (2018)","journal-title":"RACSAM"},{"key":"752_CR18","doi-asserted-by":"publisher","first-page":"458","DOI":"10.1016\/j.cam.2016.12.016","volume":"317","author":"K Khan","year":"2017","unstructured":"Khan, K., Lobiyal, D.K.: B\u00e9zier curves based on Lupas (p,q)-analogue of Bernstein functions in CAGD. Jour. Comput. Appl. Math. 317, 458\u2013477 (2017)","journal-title":"Jour. Comput. Appl. Math."},{"key":"752_CR19","first-page":"961","volume":"90","author":"PP Korovkin","year":"1953","unstructured":"Korovkin, P.P.: On convergence of linear operators in the space of continuous functions (Russian). Dokl. Akad. Nauk SSSR (N.S.) 90, 961\u2013964 (1953)","journal-title":"Dokl. Akad. Nauk SSSR (N.S.)"},{"key":"752_CR20","volume-title":"Bernstein Polynomials","author":"GG Lorentz","year":"1953","unstructured":"Lorentz, G.G.: Bernstein Polynomials. University of Toronto Press, Toronto (1953)"},{"key":"752_CR21","first-page":"85","volume":"9","author":"A Lupa\u015f","year":"1987","unstructured":"Lupa\u015f, A.: A q-analogue of the Bernstein operator, Seminar on Numerical and Statistical Calculus. University of Cluj-Napoca 9, 85\u201392 (1987)","journal-title":"University of Cluj-Napoca"},{"key":"752_CR22","doi-asserted-by":"publisher","first-page":"345","DOI":"10.1186\/1687-1847-2013-345","volume":"2013","author":"VN Mishra","year":"2013","unstructured":"Mishra, V.N., Khatri, K., Mishra, L.N.: Statistical approximation by Kantorovich type discrete q-Beta operators. Adv. Diff. Equ. 2013, 345 (2013)","journal-title":"Adv. Diff. Equ."},{"issue":"12","key":"752_CR23","doi-asserted-by":"publisher","first-page":"1265","DOI":"10.1080\/01630563.2018.1477796","volume":"39","author":"VN Mishra","year":"2018","unstructured":"Mishra, V.N., Patel, P., Mishra, L.N.: The integral type modification of jain operators and its approximation properties. Numer. Funct. Anal. Optim. 39(12), 1265\u20131277 (2018)","journal-title":"Numer. Funct. Anal. Optim."},{"key":"752_CR24","first-page":"874","volume":"266","author":"M Mursaleen","year":"2015","unstructured":"Mursaleen, M., Ansari, K.J., Khan, A.: On (p,q) -analogue of Bernstein operators. Appl. Math. Comput. 266, 874\u2013882 (2015). [Erratum: Appl. Math. Comput., 278 (2016) 70-71]","journal-title":"Appl. Math. Comput."},{"key":"752_CR25","first-page":"683","volume":"36","author":"M Mursaleen","year":"2013","unstructured":"Mursaleen, M., Khan, A.: Statistical approximation properties of modified q-Stancu-Beta operators. Bull. Malaysian Math. Sci. Soc.(2) 36, 683\u2013690 (2013)","journal-title":"Bull. Malaysian Math. Sci. Soc.(2)"},{"key":"752_CR26","first-page":"548","volume":"232","author":"M Mursaleen","year":"2014","unstructured":"Mursaleen, M., Khan, F., Khan, A.: Statistical approximation for new positive linear operators of Lagrange type. Appl. Math Comput. 232, 548\u2013558 (2014)","journal-title":"Appl. Math Comput."},{"key":"752_CR27","first-page":"511","volume":"4","author":"GM Phillips","year":"1997","unstructured":"Phillips, G.M.: Bernstein polynomials based on the q -integers. Ann. Numer. Math. 4, 511\u2013518 (1997)","journal-title":"Ann. Numer. Math."},{"key":"752_CR28","first-page":"1173","volume":"13","author":"DD Stancu","year":"1968","unstructured":"Stancu, D.D.: Approximation of functions by a new class of linear polynomial operators. Rev. Roumaine Math. Pure Appl. 13, 1173\u20131194 (1968)","journal-title":"Rev. Roumaine Math. Pure Appl."},{"key":"752_CR29","doi-asserted-by":"publisher","first-page":"369","DOI":"10.2298\/FIL1802369R","volume":"32","author":"N Rao","year":"2018","unstructured":"Rao, N., Wafi, A.: (P,q)-bivariate-Bernstein-Chlodowsky operators. Filomat 32, 369\u2013378 (2018)","journal-title":"Filomat"}],"container-title":["Numerical Algorithms"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s11075-019-00752-4.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s11075-019-00752-4\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s11075-019-00752-4.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,6,12]],"date-time":"2020-06-12T23:06:25Z","timestamp":1592003185000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s11075-019-00752-4"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,6,14]]},"references-count":29,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2020,5]]}},"alternative-id":["752"],"URL":"https:\/\/doi.org\/10.1007\/s11075-019-00752-4","relation":{},"ISSN":["1017-1398","1572-9265"],"issn-type":[{"value":"1017-1398","type":"print"},{"value":"1572-9265","type":"electronic"}],"subject":[],"published":{"date-parts":[[2019,6,14]]},"assertion":[{"value":"28 May 2018","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"5 June 2019","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"14 June 2019","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}