Some Estimates in Approximation Theory Using Differences of Linear Positive Operators | Chapter 7 | Current Overview on Science and Technology Research Vol. 3

 In this chapter, we examine the distinctions between linear positive operators' approximation properties. In this article, we have talked about quantitative estimates for the differences between Baskakov operators and several Baskakov variants, such as Baskakov with Baskakov-Szasz and Baskakov-Durrmeyer operators. Additionally, the distinctive qualities of the Baskakov-Szasz and Baskakov-Durrmeyer operators have been given. In the end, we define the weighted modulus of smoothness as the quantitative estimate for these operators.

Author(s) Details:

Prerna Sharma,
Department of Basic Science, Sardar Vallabh Bhai Patel University of Agriculture and Technology, Meerut (UP), India.

Diwaker Sharma,
Modern Academy Group of Institutions, Modinagar, (U.P.), India.

Please see the link here: https://stm.bookpi.org/COSTR-V3/article/view/8166

Approximation Properties of Linear Positive Operators for Stancu Type of Generalization | Chapter 14 | Novel Research Aspects in Mathematical and Computer Science Vol. 1

 Gupta and Srivastava [1] proposed an integral variation of the Baskakov operator with weights of Szasz basis functions to approach the Lebesgue integral function on the interval [0,] in 1993. In simultaneous approximation, they got some direct results. The topic of Lp-approximation is extended in this chapter, and the Baskakov-Szasz-Stancu operators are introduced. For linear combinations of Baskakov-Szasz Stancu type operators, we derive a straightforward theorem. We employ the Steklov mean methodology to prove our main theorem, which is a linear approximation method.

Author(S) Details

Prerna Sharma
Department of Basic Science, Sardar Vallabh Bhai Patel University of Agriculture and Technology, Meerut (U.P), India.

View Book:- https://stm.bookpi.org/NRAMCS-V1/article/view/6700

Emphasizing on Simultaneous Approximation of Unbounded Functions | Chapter 13 | Current Topics on Mathematics and Computer Science Vol. 4

 The term "approximation" comes from the Latin word "approximatus." In our environment, the phrase can be given to a variety of attributes (e.g., value, amount, image, description) that are nearly, but not exactly correct or similar, but not identical. Approximation is commonly used to approximate numbers, but it is also used to approximate mathematical functions, forms, and physical laws [1,2]. When the right model is difficult to utilise, approximation can refer to using a simplified technique or model. To make calculations easier, an approximation model is utilised. If exact representations are not possible due to insufficient information, approximations may be utilised. We offer a comprehensive overview of approximation using linear positive operators in this chapter [2], a useful tool for increasing the order of approximation. The features of operators are not confined to finite variation functions, but also include unbounded variation functions [3]. Many writers have investigated and employed rate of convergence, moduli of smoothness, and other methods to obtain diverse results for a variety of operators. To approximate an unbounded function, we employ summation-integral type linear positive operators. Dual Beta type operators are the term for these operators. For this, we use simultaneous approximation and the Voronovskaya type asymptotic formula to obtain moments and other types of findings.

Author (S) Details

Sangeeta Garg
Department of Mathematics, Roorkee College of Engineering, Roorkee (UK), India.

View Book :-  https://stm.bookpi.org/CTMCS-V4/article/view/2288