Degree of Approximation of Conjugate Series of a Fourier Series by Hausdroff and Norlund Product Summability

  • Sunita Sarangi
  • S. K. Paikray
  • M. Dash
  • M. Misra
  • U. K. Misra
Conference paper
Part of the Smart Innovation, Systems and Technologies book series (SIST, volume 33)

Abstract

Lipchitz class of function had been introduced by McFadden. Recently dealing with degree of approximation of conjugate series of a Fourier series of a function of Lipchitz class Misra et al. and Paikray et al. have established certain theorems. Extending their results, in this paper a theorem on degree of approximation of a function f belongs to a class of \( Lip\left( {\alpha ,r} \right)\) by using product summability \( \left( {E,q} \right)\left( {N,p_{n} } \right) \) has been established.

Keywords

Degree of approximation \( Lip\left( {\alpha ,r} \right)\) class of function \( \left( {E,q} \right) \)-mean \( \left( {N,p_{n} } \right) \)-mean \( \left( {E,q} \right)\left( {N,p_{n} } \right)\)-mean Fourier series Conjugate series Lebesgue integral 

References

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  2. 2.
    Misra, U.K., Misra, M., Padhy, B.P., Buxi, S.K.: On degree of approximation by product means of conjugate series of Fourier series. Int. J. Math. Sci. Eng. Appl. 6(122), 363–370 (2012)Google Scholar
  3. 3.
    Paikray, S.K., Misra, U.K., Jati, R.K., Sahoo, N.C.: On degree of approximation of Fourier series by product means. Bull. Soc. Math. Serv. Stand. 1(4), 12–20 (2012)Google Scholar
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    Titchmarch, E.C.: The Theory of Functions, pp. 402–403. Oxford University Press, Oxford (1939)Google Scholar
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    Zygmund, A.: Trigonometric Series, vol. I, 2nd edn, Cambridge University press, Cambridge (1959)Google Scholar

Copyright information

© Springer India 2015

Authors and Affiliations

  • Sunita Sarangi
    • 1
  • S. K. Paikray
    • 2
  • M. Dash
    • 1
  • M. Misra
    • 3
  • U. K. Misra
    • 4
  1. 1.Department of MathematicsRavenshaw UniversityCuttackIndia
  2. 2.Department of MathematicsVSSUTBurlaIndia
  3. 3.Department of MathematicsB.A. CollegeBerhampurIndia
  4. 4.Department of MathematicsNISTBerhampurIndia

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