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Construction of a new family of Bernstein‐Kantorovich operators |
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| Authors: | S A Mohiuddine Tuncer Acar Abdullah Alotaibi |
| Affiliation: | 1. Operator Theory and Applications Research Group, Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah 21589, Saudi Arabia;2. Faculty of Science and Arts, Department of Mathematics, Kirikkale University, Yahsihan, 71450 Kirikkale, Turkey |
| Abstract: | In the present paper, we construct a new sequence of Bernstein‐Kantorovich operators depending on a parameter α. The uniform convergence of the operators and rate of convergence in local and global sense in terms of first‐ and second‐order modulus of continuity are studied. Some graphs and numerical results presenting the advantages of our construction are obtained. The last section is devoted to bivariate generalization of Bernstein‐Kantorovich operators and their approximation behaviors. |
| Keywords: | Bernstein‐Kantorovich operators bivariate Bernstein‐Kantorovich operators modulus of continuity rate of convergence |
