Mohammad Ayman-Mursaleen, Nadeem Rao, Mamta Rani, Adem Kilicman, Ahmed Ahmed Hussin Ali Al-Abied, Pradeep Malik
{"title":"关于具有形状参数 α 的混合型伯恩斯坦-舒勒-康托洛维奇算子近似的说明","authors":"Mohammad Ayman-Mursaleen, Nadeem Rao, Mamta Rani, Adem Kilicman, Ahmed Ahmed Hussin Ali Al-Abied, Pradeep Malik","doi":"10.1155/2023/5245806","DOIUrl":null,"url":null,"abstract":"The objective of this paper is to construct univariate and bivariate blending type <span><svg height=\"6.1673pt\" style=\"vertical-align:-0.2063904pt\" version=\"1.1\" viewbox=\"-0.0498162 -5.96091 7.51131 6.1673\" width=\"7.51131pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\"><g transform=\"matrix(.013,0,0,-0.013,0,0)\"></path></g></svg>-</span>Schurer–Kantorovich operators depending on two parameters <span><svg height=\"11.439pt\" style=\"vertical-align:-2.15067pt\" version=\"1.1\" viewbox=\"-0.0498162 -9.28833 17.881 11.439\" width=\"17.881pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\"><g transform=\"matrix(.013,0,0,-0.013,0,0)\"><use xlink:href=\"#g113-223\"></use></g><g transform=\"matrix(.013,0,0,-0.013,11.017,0)\"></path></g></svg><span></span><svg height=\"11.439pt\" style=\"vertical-align:-2.15067pt\" version=\"1.1\" viewbox=\"21.463183800000003 -9.28833 26.836 11.439\" width=\"26.836pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\"><g transform=\"matrix(.013,0,0,-0.013,21.513,0)\"></path></g><g transform=\"matrix(.013,0,0,-0.013,25.998,0)\"></path></g><g transform=\"matrix(.013,0,0,-0.013,32.238,0)\"></path></g><g transform=\"matrix(.013,0,0,-0.013,37.381,0)\"></path></g><g transform=\"matrix(.013,0,0,-0.013,43.621,0)\"></path></g></svg></span> and <span><svg height=\"11.7782pt\" style=\"vertical-align:-3.42938pt\" version=\"1.1\" viewbox=\"-0.0498162 -8.34882 18.273 11.7782\" width=\"18.273pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\"><g transform=\"matrix(.013,0,0,-0.013,0,0)\"></path></g><g transform=\"matrix(.013,0,0,-0.013,10.642,0)\"></path></g></svg><span></span><svg height=\"11.7782pt\" style=\"vertical-align:-3.42938pt\" version=\"1.1\" viewbox=\"21.855183800000002 -8.34882 6.415 11.7782\" width=\"6.415pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\"><g transform=\"matrix(.013,0,0,-0.013,21.905,0)\"><use xlink:href=\"#g113-49\"></use></g></svg></span> to approximate a class of measurable functions on <span><svg height=\"12.7178pt\" style=\"vertical-align:-3.42947pt\" version=\"1.1\" viewbox=\"-0.0498162 -9.28833 32.645 12.7178\" width=\"32.645pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\"><g transform=\"matrix(.013,0,0,-0.013,0,0)\"><use xlink:href=\"#g113-92\"></use></g><g transform=\"matrix(.013,0,0,-0.013,4.485,0)\"><use xlink:href=\"#g113-49\"></use></g><g transform=\"matrix(.013,0,0,-0.013,10.725,0)\"><use xlink:href=\"#g113-45\"></use></g><g transform=\"matrix(.013,0,0,-0.013,15.868,0)\"><use xlink:href=\"#g113-50\"></use></g><g transform=\"matrix(.013,0,0,-0.013,25.014,0)\"></path></g></svg><span></span><svg height=\"12.7178pt\" style=\"vertical-align:-3.42947pt\" version=\"1.1\" viewbox=\"35.500183799999995 -9.28833 13.832 12.7178\" width=\"13.832pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\"><g transform=\"matrix(.013,0,0,-0.013,35.55,0)\"></path></g><g transform=\"matrix(.013,0,0,-0.013,41.933,0)\"><use xlink:href=\"#g113-94\"></use></g><g transform=\"matrix(.013,0,0,-0.013,46.418,0)\"><use xlink:href=\"#g113-45\"></use></g></svg><span></span><svg height=\"12.7178pt\" style=\"vertical-align:-3.42947pt\" version=\"1.1\" viewbox=\"51.512183799999995 -9.28833 17.646 12.7178\" width=\"17.646pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\"><g transform=\"matrix(.013,0,0,-0.013,51.562,0)\"><use xlink:href=\"#g113-114\"></use></g><g transform=\"matrix(.013,0,0,-0.013,61.577,0)\"><use xlink:href=\"#g117-92\"></use></g></svg><span></span><span><svg height=\"12.7178pt\" style=\"vertical-align:-3.42947pt\" version=\"1.1\" viewbox=\"72.7891838 -9.28833 6.571 12.7178\" width=\"6.571pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\"><g transform=\"matrix(.013,0,0,-0.013,72.839,0)\"><use xlink:href=\"#g113-49\"></use></g></svg>.</span></span> We present some auxiliary results and obtain the rate of convergence of these operators. Next, we study the global and local approximation properties in terms of first- and second-order modulus of smoothness, weight functions, and by Peetre’s <span><svg height=\"8.68572pt\" style=\"vertical-align:-0.0498209pt\" version=\"1.1\" viewbox=\"-0.0498162 -8.6359 9.95144 8.68572\" width=\"9.95144pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\"><g transform=\"matrix(.013,0,0,-0.013,0,0)\"></path></g></svg>-</span>functional in different function spaces. Moreover, we present some study on numerical and graphical analysis for our operators.","PeriodicalId":54214,"journal":{"name":"Journal of Mathematics","volume":"17 1","pages":""},"PeriodicalIF":1.3000,"publicationDate":"2023-12-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"A Note on Approximation of Blending Type Bernstein–Schurer–Kantorovich Operators with Shape Parameter α\",\"authors\":\"Mohammad Ayman-Mursaleen, Nadeem Rao, Mamta Rani, Adem Kilicman, Ahmed Ahmed Hussin Ali Al-Abied, Pradeep Malik\",\"doi\":\"10.1155/2023/5245806\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"The objective of this paper is to construct univariate and bivariate blending type <span><svg height=\\\"6.1673pt\\\" style=\\\"vertical-align:-0.2063904pt\\\" version=\\\"1.1\\\" viewbox=\\\"-0.0498162 -5.96091 7.51131 6.1673\\\" width=\\\"7.51131pt\\\" xmlns=\\\"http://www.w3.org/2000/svg\\\" xmlns:xlink=\\\"http://www.w3.org/1999/xlink\\\"><g transform=\\\"matrix(.013,0,0,-0.013,0,0)\\\"></path></g></svg>-</span>Schurer–Kantorovich operators depending on two parameters <span><svg height=\\\"11.439pt\\\" style=\\\"vertical-align:-2.15067pt\\\" version=\\\"1.1\\\" viewbox=\\\"-0.0498162 -9.28833 17.881 11.439\\\" width=\\\"17.881pt\\\" xmlns=\\\"http://www.w3.org/2000/svg\\\" xmlns:xlink=\\\"http://www.w3.org/1999/xlink\\\"><g transform=\\\"matrix(.013,0,0,-0.013,0,0)\\\"><use xlink:href=\\\"#g113-223\\\"></use></g><g transform=\\\"matrix(.013,0,0,-0.013,11.017,0)\\\"></path></g></svg><span></span><svg height=\\\"11.439pt\\\" style=\\\"vertical-align:-2.15067pt\\\" version=\\\"1.1\\\" viewbox=\\\"21.463183800000003 -9.28833 26.836 11.439\\\" width=\\\"26.836pt\\\" xmlns=\\\"http://www.w3.org/2000/svg\\\" xmlns:xlink=\\\"http://www.w3.org/1999/xlink\\\"><g transform=\\\"matrix(.013,0,0,-0.013,21.513,0)\\\"></path></g><g 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xlink:href=\\\"#g113-49\\\"></use></g></svg></span> to approximate a class of measurable functions on <span><svg height=\\\"12.7178pt\\\" style=\\\"vertical-align:-3.42947pt\\\" version=\\\"1.1\\\" viewbox=\\\"-0.0498162 -9.28833 32.645 12.7178\\\" width=\\\"32.645pt\\\" xmlns=\\\"http://www.w3.org/2000/svg\\\" xmlns:xlink=\\\"http://www.w3.org/1999/xlink\\\"><g transform=\\\"matrix(.013,0,0,-0.013,0,0)\\\"><use xlink:href=\\\"#g113-92\\\"></use></g><g transform=\\\"matrix(.013,0,0,-0.013,4.485,0)\\\"><use xlink:href=\\\"#g113-49\\\"></use></g><g transform=\\\"matrix(.013,0,0,-0.013,10.725,0)\\\"><use xlink:href=\\\"#g113-45\\\"></use></g><g transform=\\\"matrix(.013,0,0,-0.013,15.868,0)\\\"><use xlink:href=\\\"#g113-50\\\"></use></g><g transform=\\\"matrix(.013,0,0,-0.013,25.014,0)\\\"></path></g></svg><span></span><svg height=\\\"12.7178pt\\\" style=\\\"vertical-align:-3.42947pt\\\" version=\\\"1.1\\\" viewbox=\\\"35.500183799999995 -9.28833 13.832 12.7178\\\" width=\\\"13.832pt\\\" 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A Note on Approximation of Blending Type Bernstein–Schurer–Kantorovich Operators with Shape Parameter α
The objective of this paper is to construct univariate and bivariate blending type -Schurer–Kantorovich operators depending on two parameters and to approximate a class of measurable functions on . We present some auxiliary results and obtain the rate of convergence of these operators. Next, we study the global and local approximation properties in terms of first- and second-order modulus of smoothness, weight functions, and by Peetre’s -functional in different function spaces. Moreover, we present some study on numerical and graphical analysis for our operators.
期刊介绍：
Journal of Mathematics is a broad scope journal that publishes original research articles as well as review articles on all aspects of both pure and applied mathematics. As well as original research, Journal of Mathematics also publishes focused review articles that assess the state of the art, and identify upcoming challenges and promising solutions for the community.
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