On degree of approximation of conjugate series of a Fourier series by product summability

Mahendra Misraa, B. P. Padhyb, Dattaram Bisoyic, and U. K. Misrad,*

On degree of approximation of conjugate series of a Fourier series by product summability

Authors :

Mahendra Misra^a, B. P. Padhy^b, Dattaram Bisoyi^c, and U. K. Misra^d,*

Author Address :

^aP. G. Department of Mathematics, N. C. College(Autonomous), Jajpur, Odisha, India.
^bDepartment of Mathematics, Roland Institute of Technology, Golanthara-761008, Odisha, India.
^cDepartment of Mathematics, L. N. Mahavidyalaya, Kodala, Ganjam, Odisha, India.
^dDepartment of Mathematics, National Institute of Science and Technology, Palur Hills, Golanthara-761008, Odisha, India.

*Corresponding author.

Abstract :

In this paper a theorem on degree of approximation of a function $f \in Lip (\alpha,r)$ by product summability $(E,q)(\bar{N},p_{n})$ of conjugate series of Fourier series associated with $f$ has been proved.

Keywords :

Degree of Approximation, $Lip (\alpha, r)$ class of function, $(E,q)$ mean, $(\bar{N}, p_{n})$ mean, $(E,q)(\bar{N},p_{n})$ product mean, Fourier series, conjugate of t

DOI :

Article Info :

Received : November 11, 2012; Accepted : March 20, 2013.