
doi: 10.18514/mmn.2004.71
Summary: Let \(p,q\) be two non-negative given integers. The sequence \((\tilde{K}_{m,n,p,q})_{m,n\in N}\), \(\tilde{K}_{m,n,p,q}:L_1([0,1]\times [0,1])\to C([0,1]\times[0,1])\), \[ \left(\tilde{K}_{m,n,p,q} f\right)(x,y) \] \[ = (m+p+1)(n+p+1)\times \sum\nolimits^{m+p}_{k=0}\sum\nolimits^{n+q}_{j=0} \tilde{p}_{m,k}(x)\tilde{p}_{n j}(y)\int\nolimits^{\frac{k+1}{m+p+1}}_{\frac{k}{m+p+1}} \int^{\frac{j+1}{n+q+1}}_{\frac{j}{n+q+1}}f(s,t) ds\,dt \] of bivariate Kantorovich-Schurer operators is constructed and some approximation properties of the sequence \(\left\{\tilde{K}_{m,n,p,q} f\right\}_{m,n\in N}\) are studied.
Sisha-Mond theorem, Bernstein operator, QA Mathematics / matematika, Schurer operator, first order modulus of smoothness, bivariate operator, Approximation by positive operators, Multidimensional problems, linear positive operator, Kantorovich operator, Korovkin theorem
Sisha-Mond theorem, Bernstein operator, QA Mathematics / matematika, Schurer operator, first order modulus of smoothness, bivariate operator, Approximation by positive operators, Multidimensional problems, linear positive operator, Kantorovich operator, Korovkin theorem
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