Trigonometric Fourier Approximation of the Conjugate Series of a Function of Generalized Lipchitz Class by Product Summability

  • B. P. PadhyEmail author
  • P. K. Das
  • M. Misra
  • P. Samanta
  • U. K. Misra
Conference paper
Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 410)


Trigonometric Fourier approximation and Lipchitz class of function had been introduced by Zygmund and McFadden respectively. Dealing with degree of approximation of conjugate series of a Fourier series of a function of Lipchitz class Misra et al. have established certain theorems. Extending their results, in this paper a theorem on trigonometric approximation of conjugate series of Fourier series of a function \( f \in \,Lip\,\left( {\alpha ,r} \right) \) by product summability (E, s) (N, p n , q n ) has been established.


Fourier approximation \( Lip\,\left( {\alpha ,r} \right) \) class of function (E, q) mean (N, pn, qn) mean (E, s) (N, pn, qn) product mean Conjugate fourier series Lebesgue integral 

2010-Mathematics Subject Classification:

42B05 42B08 


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Copyright information

© Springer India 2016

Authors and Affiliations

  • B. P. Padhy
    • 1
    Email author
  • P. K. Das
    • 2
  • M. Misra
    • 3
  • P. Samanta
    • 4
  • U. K. Misra
    • 5
  1. 1.Department of Mathematics, School of Applied SciencesKIIT UniversityBhubaneswarIndia
  2. 2.Biswasray Science CollegeGanjamIndia
  3. 3.Department of MathematicsB.A. CollegeBerhampurIndia
  4. 4.Department of MathematicsBerhampur UniversityBerhampurIndia
  5. 5.National Institute of Scince and TechnologyGanjamIndia

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