A CLASS OF FUNCTIONS AND THEIR DEGREE OF APPROXIMATION BY ALMOST $(N, p, \alpha)$ METHOD

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RAJIV SINHA
HEMANT KUMAR

Abstract




Qureshi [6] proved a theorem for the degree of approximation of a periodic function $\bar f$, conjugate to a $2\pi$-periodic function $f$ and belonging to the class Lip $\theta$, by almost matrix mean of its conjugate series. The above theorem was further generalized by Qureshi and Nema [8] for a function belonging to the class $W(L^p, \Psi_1(t))$ by almost matrix mean. In the present paper we have discussed degree of approximation of above class of functions by almost $(N , p, \alpha)$ method.




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How to Cite
SINHA, R., & KUMAR, H. (1997). A CLASS OF FUNCTIONS AND THEIR DEGREE OF APPROXIMATION BY ALMOST $(N, p, \alpha)$ METHOD. Tamkang Journal of Mathematics, 28(2), 79–85. https://doi.org/10.5556/j.tkjm.28.1997.4245
Section
Papers

References

G. G. Lorentz, "A contribution to the theory of divergent series," Acta Match., 80 (1948), 167-190.

L. Mc Fadden, "Absolute Norlund summability," Duke Math. J., 9(1942), 163-207

K. Qureshi, "On the degree of approximation of functions belonging to the class Lip(a , q), Tamkang Jour. Math., 15(1)(1984), 5-11.

K. Qureshi, "On the degree of approximation of function belonging to weighted $W(L^p, Psi_1(t))$", Indian J. Pure Appl. Math., 13(4)(1982), 471-475

K. Qureshi, "On the degree of approximation of a periodic function f by almost Norlund means," Tamkang J. Math., 12(1)(1961), 35-36.

K. Qureshi, "On the degree of approximation of a class of functions by means of a conjugate series," R. U.M .J ., 15(1984), 63-68.

A. Zygrnund, Trigonometric series, Vol. 1, 2nd Ed. Cambridge University Press, Cambridge, 1959.

K. Qureshi and H. K. Nema, "A class of functions and their degree of approxmation", The Mathematics Stndcnt, 52(1-4)(1984), 33-10.