Browsing by Author "Kajla, Arun"
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Item Approximation by Stancu-Durrmeyer Type Operators Based on P´olya-Eggenberger Distribution(Filomat, 2018) Kajla, ArunItem Approximation by α-Baskakov−Jain Type Operators(Filomat, 2022) Kajla, ArunItem Bézier-summation-integral-type operators that include Pólya–Eggenberger distribution(Mathematics, 2022) Mohiuddine, Sayed Abdul; Kajla, Arun; Alotaibi, AbdullahWe define the summation-integral-type operators involving the ideas of Pólya–Eggenberger distribution and Bézier basis functions, and study some of their basic approximation properties. In addition, by means of the Ditzian–Totik modulus of smoothness, we study a direct theorem as well as a quantitative Voronovskaja-type theorem for our newly constructed operators. Moreover, we investigate the approximation of functions with derivatives of bounded variation (DBV) of the aforesaid operators.Item Blending type approximation by Stancu-Kantorovich operators based on Pólya-Eggenberger distribution(Open Physics, 2017) Kajla, ArunItem Durrmeyer-Type Generalization of -Bernstein Operators(Mathematics, 2022) Kajla, Arun; Mohiuddine, S,A; Alotaibi, AbdullahIn the present manuscript, we consider -Bernstein-Durrmeyer operators involving a strictly positive continuous function. Firstly, we prove a Voronovskaja type, quantitative Voronovskaja type and Gr¨ uss-Voronovskaja type asymptotic formula, the rate of convergence by means of the modulus of continuity and for functions in a Lipschitz type space. Finally, we show that the numerical examples which describe the validity of the theoretical example and the effectiveness of the defined operators.Item Durrmeyer-Type Generalization of Parametric Bernstein Operators(Symmetry, 2020) Kajla, ArunItem Generalized Bernstein–Durrmeyer operators of blending type(Afrika Matematika, 2019) Kajla, ArunIn this note, we derive some approximation properties of the generalized Bernstein-Kantorovich-type operators based on two nonnegative parameters consid- ered by A. Kajla [Appl. Math. Comput. 2018]. We establish a Voronovskaja-type asymptotic theorem for these operators. The rate of convergence for differential func- tions whose derivatives are of bounded variation is also derived. Finally, we show the convergence of the operators to certain functions by illustrative graphics using Mathe- matica software.Item A Kantorovich variant of a generalized Bernstein operators(Journal of Mathematics and Series, 2019) Kajla, ArunItem On the bézier variant of the srivastava-gupta operators(Constructive Mathematical Analysis, 2018) Kajla, ArunIn the present paper, we introduce the Bézier variant of the Srivastava-Gupta operators, which preserve constant as well as linear functions. Our study focuses on a direct approximation theorem in terms of the Ditzian-Totik modulus of smoothness, respectively the rate of convergence for differentiable functions whose derivatives are of bounded variation.Item Some Smoothness Properties of the Lupas Kantorovich Type Operators Based on Polaya Distribution(Filomat, 2018) Kajla, Arun