{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,8]],"date-time":"2026-03-08T03:41:17Z","timestamp":1772941277801,"version":"3.50.1"},"reference-count":15,"publisher":"Springer Science and Business Media LLC","issue":"2","license":[{"start":{"date-parts":[[2020,3,26]],"date-time":"2020-03-26T00:00:00Z","timestamp":1585180800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2020,3,26]],"date-time":"2020-03-26T00:00:00Z","timestamp":1585180800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"funder":[{"name":"Technische Hochschule Mittelhessen"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Period Math Hung"],"published-print":{"date-parts":[[2020,6]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>In this paper we consider a link <jats:inline-formula><jats:alternatives><jats:tex-math>$$B_{n,\\rho }$$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:msub><mml:mi>B<\/mml:mi><mml:mrow><mml:mi>n<\/mml:mi><mml:mo>,<\/mml:mo><mml:mi>\u03c1<\/mml:mi><\/mml:mrow><\/mml:msub><\/mml:math><\/jats:alternatives><\/jats:inline-formula> between Baskakov type operators <jats:inline-formula><jats:alternatives><jats:tex-math>$$B_{n,\\infty }$$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:msub><mml:mi>B<\/mml:mi><mml:mrow><mml:mi>n<\/mml:mi><mml:mo>,<\/mml:mo><mml:mi>\u221e<\/mml:mi><\/mml:mrow><\/mml:msub><\/mml:math><\/jats:alternatives><\/jats:inline-formula> and genuine Baskakov\u2013Durrmeyer type operators <jats:inline-formula><jats:alternatives><jats:tex-math>$$ B_{n,1}$$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:msub><mml:mi>B<\/mml:mi><mml:mrow><mml:mi>n<\/mml:mi><mml:mo>,<\/mml:mo><mml:mn>1<\/mml:mn><\/mml:mrow><\/mml:msub><\/mml:math><\/jats:alternatives><\/jats:inline-formula> depending on a positive real parameter <jats:inline-formula><jats:alternatives><jats:tex-math>$$\\rho $$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:mi>\u03c1<\/mml:mi><\/mml:math><\/jats:alternatives><\/jats:inline-formula>. The topic of the present paper is the pointwise limit relation <jats:inline-formula><jats:alternatives><jats:tex-math>$$\\left( B_{n,\\rho }f\\right) \\left( x\\right) \\rightarrow \\left( B_{n,\\infty }f\\right) \\left( x\\right) $$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:mrow><mml:mfenced><mml:msub><mml:mi>B<\/mml:mi><mml:mrow><mml:mi>n<\/mml:mi><mml:mo>,<\/mml:mo><mml:mi>\u03c1<\/mml:mi><\/mml:mrow><\/mml:msub><mml:mi>f<\/mml:mi><\/mml:mfenced><mml:mfenced><mml:mi>x<\/mml:mi><\/mml:mfenced><mml:mo>\u2192<\/mml:mo><mml:mfenced><mml:msub><mml:mi>B<\/mml:mi><mml:mrow><mml:mi>n<\/mml:mi><mml:mo>,<\/mml:mo><mml:mi>\u221e<\/mml:mi><\/mml:mrow><\/mml:msub><mml:mi>f<\/mml:mi><\/mml:mfenced><mml:mfenced><mml:mi>x<\/mml:mi><\/mml:mfenced><\/mml:mrow><\/mml:math><\/jats:alternatives><\/jats:inline-formula> as <jats:inline-formula><jats:alternatives><jats:tex-math>$$\\rho \\rightarrow \\infty $$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:mrow><mml:mi>\u03c1<\/mml:mi><mml:mo>\u2192<\/mml:mo><mml:mi>\u221e<\/mml:mi><\/mml:mrow><\/mml:math><\/jats:alternatives><\/jats:inline-formula> for <jats:inline-formula><jats:alternatives><jats:tex-math>$$x\\ge 0.$$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:mrow><mml:mi>x<\/mml:mi><mml:mo>\u2265<\/mml:mo><mml:mn>0<\/mml:mn><mml:mo>.<\/mml:mo><\/mml:mrow><\/mml:math><\/jats:alternatives><\/jats:inline-formula> As a main result we derive uniform convergence on each compact subinterval of the positive real axis for all continuous functions <jats:italic>f<\/jats:italic> of polynomial growth.\n<\/jats:p>","DOI":"10.1007\/s10998-020-00337-y","type":"journal-article","created":{"date-parts":[[2020,3,26]],"date-time":"2020-03-26T10:02:31Z","timestamp":1585216951000},"page":"280-288","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["Convergence of linking Baskakov-type operators"],"prefix":"10.1007","volume":"80","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-1889-4850","authenticated-orcid":false,"given":"Ulrich","family":"Abel","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1283-7444","authenticated-orcid":false,"given":"Margareta","family":"Heilmann","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Vitaliy","family":"Kushnirevych","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2020,3,26]]},"reference":[{"issue":"2","key":"337_CR1","first-page":"249","volume":"113","author":"VA Baskakov","year":"1957","unstructured":"V.A. Baskakov, An instance of a sequence of positive linear operators in the space of continuous functions. Dokl. Akad. Nauk SSSR 113(2), 249\u2013251 (1957)","journal-title":"Dokl. Akad. Nauk SSSR"},{"issue":"3","key":"337_CR2","doi-asserted-by":"publisher","first-page":"297","DOI":"10.1007\/s00025-015-0511-x","volume":"69","author":"K Baumann","year":"2016","unstructured":"K. Baumann, M. Heilmann, I. Ra\u015fa, Further results for $$k$$th order Kantorovich modification of linking Baskakov type operators. Results Math. 69(3), 297\u2013315 (2016). https:\/\/doi.org\/10.1007\/s00025-015-0511-x","journal-title":"Results Math."},{"key":"337_CR3","unstructured":"J.L.Durrmeyer, Une formule d\u2019inversion de la transform \u00e9e de Laplace: applications \u00e0 la th\u00e9orie des moments,Th\u00e8se de 3e cycle, Facult\u00e9 des Sciences de l\u2019Universit\u00e9 de Paris (1967)"},{"issue":"135","key":"337_CR4","doi-asserted-by":"publisher","first-page":"783","DOI":"10.1007\/s10587-010-0049-8","volume":"60","author":"H Gonska","year":"2010","unstructured":"H. Gonska, R. P\u0103lt\u0103nea, Simultaneous approximation by a class of Bernstein\u2013Durrmeyer operators preserving linear functions. Czechoslovak Math. J. 60(135), 783\u2013799 (2010). https:\/\/doi.org\/10.1007\/s10587-010-0049-8","journal-title":"Czechoslovak Math. J."},{"issue":"7","key":"337_CR5","doi-asserted-by":"publisher","first-page":"1061","DOI":"10.1007\/s11253-010-0413-8","volume":"62","author":"H Gonska","year":"2010","unstructured":"H. Gonska, R. P\u0103lt\u0103nea, Quantitative convergence theorems for a class of Bernstein\u2013Durrmeyer operators preserving linear functions. Ukrainian Math. J. 62(7), 1061\u20131072 (2010). https:\/\/doi.org\/10.1007\/s11253-010-0413-8","journal-title":"Ukrainian Math. J."},{"issue":"1","key":"337_CR6","doi-asserted-by":"publisher","first-page":"105","DOI":"10.1007\/BF02836120","volume":"5","author":"M Heilmann","year":"1989","unstructured":"M. Heilmann, Direct and converse results for operators of Baskakov\u2013Durrmeyer operators. Approx. Theory Appl. 5(1), 105\u2013127 (1989). https:\/\/doi.org\/10.1007\/BF02836120","journal-title":"Approx. Theory Appl."},{"key":"337_CR7","unstructured":"M. Heilmann, I. Ra\u015fa, $$k$$-th order Kantorovich modification of linking Baskakov type operators, in P.N. Agrawal et al. (ed.) Recent Trends in Mathematical Analysis and its Applications, Proceedings of the Conference ICRTMAA 2014, Roorkee, India, December 2014, Proceedings in Mathematics & Statistics, 143, 229\u2013242 (2015)"},{"key":"337_CR8","volume-title":"Die Folge der Betaoperatoren, Dissertation","author":"A Lupa\u015f","year":"1972","unstructured":"A. Lupa\u015f, Die Folge der Betaoperatoren, Dissertation (Universit\u00e4t Stuttgart, Stuttgart, 1972)"},{"key":"337_CR9","first-page":"257","volume":"49","author":"SM Mazhar","year":"1985","unstructured":"S.M. Mazhar, V. Totik, Approximation by modified Sz\u00e1sz operators. Acta Sci. Math. 49, 257\u2013269 (1985)","journal-title":"Acta Sci. Math."},{"key":"337_CR10","first-page":"109","volume":"5","author":"R P\u0103lt\u0103nea","year":"2007","unstructured":"R. P\u0103lt\u0103nea, A class of Durrmeyer type operators preserving linear functions. Ann. Tiberiu Popoviciu Semin. Funct. Equ. Approx. Convexity (Cluj-Napoca) 5, 109\u2013117 (2007)","journal-title":"Ann. Tiberiu Popoviciu Semin. Funct. Equ. Approx. Convexity (Cluj-Napoca)"},{"issue":"3","key":"337_CR11","first-page":"378","volume":"24","author":"R P\u0103lt\u0103nea","year":"2008","unstructured":"R. P\u0103lt\u0103nea, Modified Sz\u00e1sz-Mirakjan operators of integral form. Carpathian J. Math. 24(3), 378\u2013385 (2008)","journal-title":"Carpathian J. Math."},{"issue":"3\u20134","key":"337_CR12","first-page":"356","volume":"9","author":"R P\u0103lt\u0103nea","year":"2014","unstructured":"R. P\u0103lt\u0103nea, Simultaneous approximation by a class of Sz\u00e1sz\u2013Mirakjan operators. J. Appl. Funct. Anal. 9(3\u20134), 356\u2013368 (2014)","journal-title":"J. Appl. Funct. Anal."},{"key":"337_CR13","doi-asserted-by":"publisher","first-page":"325","DOI":"10.2307\/1969697","volume":"59","author":"RS Phillips","year":"1954","unstructured":"R.S. Phillips, An inversion formula for Laplace transforms and semi-groups of linear operators. Ann. Math. (Second Ser.) 59, 325\u2013356 (1954). https:\/\/doi.org\/10.2307\/1969697","journal-title":"Ann. Math. (Second Ser.)"},{"key":"337_CR14","doi-asserted-by":"publisher","first-page":"122","DOI":"10.1016\/0021-9045(85)90039-5","volume":"45","author":"A Sahai","year":"1985","unstructured":"A. Sahai, G. Prasad, On simultaneous approximation by modified Lupas operators. J. Approx. Theory 45, 122\u2013128 (1985). https:\/\/doi.org\/10.1016\/0021-9045(85)90039-5","journal-title":"J. Approx. Theory"},{"key":"337_CR15","unstructured":"M.\u00a0Wagner, Quasi-Interpolanten zu genuinen Baskakov\u2013Durrmeyer-Typ Operatoren, Dissertation Universit\u00e4t Wuppertal (2013)"}],"container-title":["Periodica Mathematica Hungarica"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10998-020-00337-y.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s10998-020-00337-y\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10998-020-00337-y.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,3,26]],"date-time":"2021-03-26T01:13:02Z","timestamp":1616721182000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s10998-020-00337-y"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,3,26]]},"references-count":15,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2020,6]]}},"alternative-id":["337"],"URL":"https:\/\/doi.org\/10.1007\/s10998-020-00337-y","relation":{},"ISSN":["0031-5303","1588-2829"],"issn-type":[{"value":"0031-5303","type":"print"},{"value":"1588-2829","type":"electronic"}],"subject":[],"published":{"date-parts":[[2020,3,26]]},"assertion":[{"value":"26 March 2020","order":1,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}