On a class of modied new Bernstein operators

다국어 초록 (Multilingual Abstract)

In this paper, by giving a slight modification of the class of new Bernstein type operators introduved in [3], we introduce a class of modified new Bernstein type operators and claim that the midified new Bernstein type operators is more close to classcial Bernstein polynomial in comparison to operators defined in [3]. We prove Voronovskaja type theorem for these operators. We also present a q-analogue of these operators which is an interesting generalizaiton of Bernstein polynomials based on the q-integers, introduved by G M Phillips in [10].

참고문헌 (Reference)

1 T. R. Prabhakar, 19 : 7-, 1971

2 M. Garg, "q-Analogues of Saigos fractional calculus operators" 3 (3): 169-179, 2011

3 G. Bangerzako, "Variational calculus on q-nonuniform lattices" 306 : 161-179, 2005

4 Adders Wiman, "Uber die Nullsteliun der fuctionen E (x)" 29 : 217-234, 1905

5 G. M. Mittag-Le er, "Sur la representation analytique deune branche uniforme une function monogene" 29 : 101-181, 1905

6 G.M. Mittag-Le er, "Sur la nuovelle function E (x). C. R" 137 (137): 554-558, 1903

7 S.D. Purohit, "Summation formulae for basic hypergeometric functions via fractional q-calculus" 64 (64): 67-75, 2009

8 E.D. Rainville, "Special functions" Chelsea Publishing Company 1960

9 Jian-Ping Fang, "SOME APPLICATIONS OF q-DIFFERENTIAL OPERATOR" 대한수학회 47 (47): 223-233, 2010

10 S.D.Purohit, "On generalized fractional q-integral operators involving the q-Gauss hypergeometric function" 2 (2): 35-44, 2010

11 Z.S.I. Mansour, "Linear sequential q-di erence equations of fractional order" 12 (12): 159-178, 2009

12 M.H.Abu-Risha, "Linear q-di erence equations" 26 : 481-494, 2007

13 P.M. Rajkovic, "Fractional integrals and deriva-tives in q-calculus" 1 : 1-13, 2007

14 G. Gasper, "Basic hypergeometric series" Cambridge University Press 1990

15 K. Sharma, "Application of fractional calculus operators to related areas" 33-40, 2011

16 M. Saigo, "A remark on integral operators involving the Gauss hypergeometric functions" 11 : 135-143, 1978

17 M. Sharma, "A note on a generalized M-series as a special function of fractional calculus" 12 (12): 2009

18 T. Ernst, "A method for q-calculus" 10 (10): 487-525, 003