By Vijay Gupta, Ravi P. Agarwal

The research of linear confident operators is a space of mathematical experiences with major relevance to stories of computer-aided geometric layout, numerical research, and differential equations. This publication makes a speciality of the convergence of linear optimistic operators in genuine and intricate domain names. The theoretical features of those operators were an lively quarter of analysis over the last few many years. during this quantity, authors Gupta and Agarwal discover new and extra effective tools of utilising this examine to stories in Optimization and research. The textual content can be of curiosity to upper-level scholars looking an creation to the sector and to researchers constructing leading edge approaches.

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24. 26. 27. 28. Let 0 < ˛ < 1 and 1 < p < 1. For an f 2 Lp Œ0; 1/, the following are equivalent: (i) jjSn f f jjLp Œ0;1/ Ä Kn ˛ ; n D 1; 2; : : :. x/: Abel and Gupta j Dk [4] estimated the rate of convergence for the operators Vn;˛ , which is discussed here in Chap. 7. 1Cx/q k q and the statistical convergence of these operators are discussed. For details on q-operators, we refer the reader to the 2013 book by Aral, Gupta, and Agrawal [31]. 3 Durrmeyer-Type Operators In 1967, J. L. 1 k x/n k : Derriennic [58] first studied these operators in detail, and she obtained some direct results in ordinary and simultaneous approximation.

0; 1/. 24. 26. 27. 28. Let 0 < ˛ < 1 and 1 < p < 1. For an f 2 Lp Œ0; 1/, the following are equivalent: (i) jjSn f f jjLp Œ0;1/ Ä Kn ˛ ; n D 1; 2; : : :. x/: Abel and Gupta j Dk [4] estimated the rate of convergence for the operators Vn;˛ , which is discussed here in Chap. 7. 1Cx/q k q and the statistical convergence of these operators are discussed. For details on q-operators, we refer the reader to the 2013 book by Aral, Gupta, and Agrawal [31]. 3 Durrmeyer-Type Operators In 1967, J. L. 1 k x/n k : Derriennic [58] first studied these operators in detail, and she obtained some direct results in ordinary and simultaneous approximation.

15 ([230]). 1/; n ! 1/; ı ! 1/; as h ! 16 ([230]). Let 0 < ˛ Ä 1. 1 C x/ b ; 0 < a < 1; b:0; 0 < ˛ < 1, and CB Œ0; 1/ is the set of bounded continuous functions on Œ0; 1/: In 2011, Feng [70] introduced a new norm and a new K-functional. Using the K-functional, he established direct and inverse theorems for the Baskakov operators with the Jacobi-type weight. 17 ([70]). 18 ([70]). Suppose f 2 Ca;b; ; 0 < ˛ < 1. t ˛ /; 0 < t < 1: ˛ /; n 2. 8). 19 ([230]). For a bounded and continuous function f W Œ0; 1/ !