Generalized q-Baskakov operators

By Ali Aral, Vijay Gupta. 2011

125 citations recorded by the source corpus.

In the present paper we propose a generalization of the Baskakov operators, based on q integers. We also estimate the rate of convergence in the weighted norm. In the last section, we study some shape preserving properties and the property of monotonicity of q-Baskakov operators.

Subfields: Applied Mathematics, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/4e6302eb93c6c8fdcebd6f08c57455ffcd71baaa

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In Applied Mathematics

1. Mohamed Kamal Aouf
2. Tamer M. Seoudy
3. Tuncer Acar
4. Muhammad Arif
5. Maslina Darus
6. Gülsüm Ulusoy
7. Jin-Lin Liu
8. H. Aldweby

In Statistics and Probability

1. Gülsüm Ulusoy
2. Tuncer Acar
3. Muhammad Arif
4. Vishnu Narayan Mishra
5. Maslina Darus
6. Kejal Khatri
7. Mohamed Kamal Aouf
8. Lakshmi Narayan Mishra

Citations in the corpus

• Some Approximation Properties of -Baskakov-Beta-Stancu Type Operators (2013, background): “Also, Aral and Gupta [4] defined 𝑞-generalization of the Baskakov operators and investigated some approximation properties of these operators.”
• q‐Voronovskaya type theorems for q‐Baskakov operators (2016, methodology): “We recall the q-Baskakov operators defined in [24].”
• Some Subordination Results on -Analogue of Ruscheweyh Differential Operator (2014, background): “In ([3–5]) the q-analogue of Baskakov Durrmeyer operator has been proposed, which is based on q-analogue of beta function.”
• Coefficient estimates of new classes of q-starlike and q-convex functions of complex order (2016, background): “Aral and Gupta [8, 9, 10] defined and studied the q -analogue of Baskakov Durrmeyer operator which is based on q -analogue of beta function.”
• Convolution Properties for Certain Classes of Analytic Functions Defined by -Derivative Operator (2014, background): “Aral and Gupta [3–5] defined and studied the q-analogue of Baskakov Durrmeyer operator which is based on q-analogue of beta function.”
• A Subfamily of Univalent Functions Associated with -Analogue of Noor Integral Operator (2018, methodology): “Later on, Aral and Gupta [3, 4] defined the 𝑞-Baskakov-Durrmeyer operator by using𝑞-beta function while in papers [5, 6] the authors discussed the 𝑞-generalization of complex operators known as 𝑞-Picard and 𝑞-Gauss-Weierstrass singular integral operators.”