Some approximation properties by a class of bivariate operators. (4th February 2019)

• Record Type: Journal Article
• Authors: Acu, Ana Maria; Acar, Tuncer; Muraru, Carmen‐Violeta; Radu, Voichiţa Adriana
• Other Names: Yıldırım Kenan guestEditor.; Rasa Ioan guestEditor.; Acar Tuncer guestEditor.; Abazari Reza guestEditor.
• Is Part Of: Mathematical methods in the applied sciences. Volume 42:Number 16(2019)
• Page Start: 5551
• Page End: 5565
• Publication Date: 2019-02-04
• Subjects: Bernstein operators -- GBS‐type operators -- modulus of continuity; Mathematics -- Periodicals; Technology -- Mathematics -- Periodicals; 519
• DOI: 10.1002/mma.5515
• Languages: English
• ISSNs: 0170-4214

Abstract

Abstract : Starting with the well‐ known Bernstein operators, in the present paper, we give a new generalization of the bivariate type. The approximation properties of this new class of bivariate operators are studied. Also, the extension of the proposed operators, namely, the generalized Boolean sum (GBS) in the Bögel space of continuous functions is given. In order to underline the fact that in this particular case, GBS operator has better order of convergence than the original ones, some numerical examples are provided with the aid of Maple soft. Also, the error of approximation for the modified Bernstein operators and its GBS‐type operator are compared.