Affiliation:
1. School of Mathematics and Statistics, Xiamen University of Technology, Xiamen 361024, Fujian, China
2. School of Mathematics and Computer Science, Quanzhou Normal University, Quanzhou 362000, Fujian, China
Abstract
<abstract><p>This paper introduced a novel class of bivariate $ \lambda $-Bernstein operators defined on triangular domain, denoted as $ B_{m}^{\lambda_1, \lambda_2}(f; x, y) $. These operators leverage a new class of bivariate Bézier basis functions defined on triangular domain with shape parameters $ \lambda_1 $ and $ \lambda_2 $. A Korovkin-type approximation theorem for $ B_{m}^{\lambda_1, \lambda_2}(f; x, y) $ was established, with the convergence rate being characterized by both the complete and partial moduli of continuity. Additionally, a local approximation theorem and a Voronovskaja-type asymptotic formula were derived for $ B_{m}^{\lambda_1, \lambda_2}(f; x, y) $. Finally, the convergence of $ B_{m}^{\lambda_1, \lambda_2}(f; x, y) $ to $ f(x, y) $ was illustrated through graphical representations and numerical examples, highlighting instances where they surpass the performance of standard bivariate Bernstein operators defined on triangular domain, $ B_{m}(f; x, y) $.</p></abstract>
Publisher
American Institute of Mathematical Sciences (AIMS)
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