The main aim of this article is to introduce a new type of
q
-Chlodowsky and
q
-Szasz-Durrmeyer hybrid operators on weighted spaces. To this end, we give approximation properties of the modified new
q
-Hybrid operators. Moreover, in the weighted spaces, we examine the rate of convergence of the modified new
q
-Hybrid operators by means of moduli of continuity. In addition, we derive Voronovskaja’s type asymptotic formula for the related operators.
We define GBS operators of Durrmeyer operators for bivariate functions on simplex and we give their approximations and rate of their approximations for B-continuous and B-differentiable functions. We show that the GBS type the operators of new Durrmeyer have better approximation than the new operators.
Bu çalışmada başlangıç değerlere bağlı kesirli mertebeden (Fractional order) Pseudo-Hiperbolik kısmi diferansiyel denkleminin homotopi pertürbasyon metoduyla çözümü incelenecektir. Kesirli mertebeden Pseoudo-Hiperbolik kısmi diferansiyel denkleminin farklı yöntemlerle çözümü mevcut olmasına rağmen homotopi pertürbasyon yöntemiyle çözümü daha kısa ve hata payı daha az olduğundan çözüm bu yöntemle yapılmıştır. Ayrıca Matlab programı yardımıyla tam çözüm grafik ile görselleştirilmiştir.
In this paper, the approximation properties and the rate of convergence of modified bivariate Bernstein-Durrmeyer Operators on a triangular region are examined. Furthermore, definitions and some properties of modulus of continuity for functions of two variables are given. Voronovskaya and Gr\"{u}ss Voronovskaja type theorems are used to determine the order of approximation. The GBS (Generalized Boolean Sum) operator of Bivariate Bernstein-Durrmeyer type on a triangular region is studied. Lastly, some numerical examples are given and related graphs are plotted for comparison.
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