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New Improved Approximation by Linear Combination in Lp Spaces

Received: 23 August 2015     Accepted: 7 September 2015     Published: 16 October 2015
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Abstract

In this paper we extend our studies for Modified Lupas operators introduced by Sahai and Prasad. We introduce and develop some direct results for Stancu type generalization of above operators using linear approximation method. Fubini’s theorem is used extensively to prove our main theorem. The anticipated improvement is made through technique of linear combination is well corroborated by the results in the paper. Here, modification of operators through Stancu generalization plays an important role to obtain better approximation results.

Published in American Journal of Applied Mathematics (Volume 3, Issue 6)
DOI 10.11648/j.ajam.20150306.11
Page(s) 243-249
Creative Commons

This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.

Copyright

Copyright © The Author(s), 2015. Published by Science Publishing Group

Keywords

Stancu Type Generalization, Linear Combination, Order of Approximation

References
[1] A. Sahai and G. Prasad. On simultaneous approximation by modified Lupas operators, J. Approx. Theory, 45(1985), 122-128.
[2] C. P May, Saturation and inverse theorems for combinations of a class of exponential operators, Can. J. Math., XXVIII, 6 (1976), 1224-1250.
[3] D. D. Stancu, Approximation of function by a new class of polynomial operators, Rev. Roum. Math. Pures et Appl., 13(8) (1968), 1173-1194.
[4] Z. Ditzian and V. Totik. “Moduli of smoothness”, Springer Seriesin computational Mathematics 9, Springer-Verlag, Berlin, Heidelberg, New York, 1987.
[5] R. K. S. Rathore, Linear Combination of Linear Positive Operators and Generating Relations in Special Functions, Ph. D. Thesis, I. I. T. Delhi (India) (1973).
[6] E. Hewitt and K. Stormberg, Real and Abstract Analysis, McGraw-Hill, New York (1956).
[7] S. Goldberg and A. Meir, Minimum moduli of ordinary differential operators, Proc. London Math. Soc., 23(3) (1971), 1-15.
[8] B. Wood, L_p-approximation by linear combination of integral Bernstein type operators, Anal. Nume’r. Theor. Approx., 13(1) (1984), 65-72.
[9] A. Zygmund, Trignometrical Series, Dover Publications, Inc., N. Y. (1985).
[10] V. Gupta, A note on modified Baskakov operators, Approx. theory and its Appl. 10(3) (1994), 74-78s.
[11] Gupta Vijay and Ravi P. Agarwal, convergence estimate in approximation theory, New York, Springer, 2014.
[12] Gupta Vijay and Neha Malik “Approximation for genuine summation-integral type link operators”, Applied Mathematics and computation, 260 (2015), 321-330.
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    Srivastava Anshul. (2015). New Improved Approximation by Linear Combination in Lp Spaces. American Journal of Applied Mathematics, 3(6), 243-249. https://doi.org/10.11648/j.ajam.20150306.11

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    ACS Style

    Srivastava Anshul. New Improved Approximation by Linear Combination in Lp Spaces. Am. J. Appl. Math. 2015, 3(6), 243-249. doi: 10.11648/j.ajam.20150306.11

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    AMA Style

    Srivastava Anshul. New Improved Approximation by Linear Combination in Lp Spaces. Am J Appl Math. 2015;3(6):243-249. doi: 10.11648/j.ajam.20150306.11

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  • @article{10.11648/j.ajam.20150306.11,
      author = {Srivastava Anshul},
      title = {New Improved Approximation by Linear Combination in Lp Spaces},
      journal = {American Journal of Applied Mathematics},
      volume = {3},
      number = {6},
      pages = {243-249},
      doi = {10.11648/j.ajam.20150306.11},
      url = {https://doi.org/10.11648/j.ajam.20150306.11},
      eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajam.20150306.11},
      abstract = {In this paper we extend our studies for Modified Lupas operators introduced by Sahai and Prasad. We introduce and develop some direct results for Stancu type generalization of above operators using linear approximation method. Fubini’s theorem is used extensively to prove our main theorem. The anticipated improvement is made through technique of linear combination is well corroborated by the results in the paper. Here, modification of operators through Stancu generalization plays an important role to obtain better approximation results.},
     year = {2015}
    }
    

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    T2  - American Journal of Applied Mathematics
    JF  - American Journal of Applied Mathematics
    JO  - American Journal of Applied Mathematics
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    AB  - In this paper we extend our studies for Modified Lupas operators introduced by Sahai and Prasad. We introduce and develop some direct results for Stancu type generalization of above operators using linear approximation method. Fubini’s theorem is used extensively to prove our main theorem. The anticipated improvement is made through technique of linear combination is well corroborated by the results in the paper. Here, modification of operators through Stancu generalization plays an important role to obtain better approximation results.
    VL  - 3
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Author Information
  • Mathematics, Department of Applied Sciences, Northern India Engineering College, Indraprastha University, New Delhi, India

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