Stability of some positive linear operators on compact disk

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• 作者：M. MURSALEEN ^{mursaleenm@gmail.com" class="auth_mail" title="E-mail the corresponding author} ; Khursheed J. ANSARI ^{ansari.jkhursheed@gmail.com" class="auth_mail" title="E-mail the corresponding author} ; Asif KHAN ^{asifjnu07@gmail.com" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Hyers-Ulam stability ; Bernstein-Schurer operators ; Kantrovich-Schurer operators ; Lorentz operators ; stability constants
• 刊名：Acta Mathematica Scientia
• 出版年：2015
• 出版时间：November 2015
• 年：2015
• 卷：35
• 期：6
• 页码：1492-1500
• 全文大小：344 K

文摘

Recently, Popa and Rasa [27, 28] have shown the (in)stability of some classical operators defined on [0, 1] and found best constant when the positive linear operators are stable in the sense of Hyers-Ulam. In this paper we show Hyers-Ulam (in)stability of complex Bernstein-Schurer operators, complex Kantrovich-Schurer operators and Lorentz operators on compact disk. In the case when the operator is stable in the sense of Hyers and Ulam, we find the infimum of Hyers-Ulam stability constants for respective operators.