Generalized Bernstein Polynomials
Generalized Bernstein Polynomials
ABSTRACT: This thesis consisting of three chapters is concerned with Bernstein polynomials. In the first chapter, an introduction to Bernstein polynomials is given. Then, basic properties of Bernstein polynomials are studied in the second chapter. Last chapter studies the generalized Bernstein polynomials and since it is known that generalized Bernstein polynomials are related to q-integers, we gave basic properties of q-integers. In this chapter, convergence properties of Bernstein polynomials are also given. In addition, we introduced some probabilistic considerations of generalized Bernstein polynomials. Keywords: Bernstein polynomials; generalized Bernstein polynomials; q-integers; Convergence. ………………………………………………………………………………………………………………………… ÖZ: Bu çalısma üç bölümden olusmaktadır. Bu tezde Bernstein polinomları çalısılmıstır. Ilk olarak Bernstein polinomlarının tanımı yapılmıs ve baslıca özellikleri incelenmistir. Ikinci bölümde genellestirilmis Bernstein polinomlari incelenmis ve bu polinomlar q-tamsayılarıyla ilgili oldugundan q-tamsayılarının baslıca özellikleri de verilmistir. Sonrasında Bernstein polinomlarının yakınsaklık özellikleri çalısılmıstır. Buna ek olarak Bernstein polinomlarının bazı olasılık metodlarıyla yakınsaklık özellikleri ele alınmıstır. Anahtar kelimeler: Bernstein polinomları; genellestirilmis Bernstein polinomları; qtamsayıları; yakınsaklık.
Bernstein Polynomials, Bernstein Polynomials, Generalized Bernstein Polynomials, Q-Integers, Convergence, Approximation theory, Convergence, Generalized Bernstein Polynomials, Q-Integers, Mathematics
Bernstein Polynomials, Bernstein Polynomials, Generalized Bernstein Polynomials, Q-Integers, Convergence, Approximation theory, Convergence, Generalized Bernstein Polynomials, Q-Integers, Mathematics
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