Estimation of degree of approximation of functions belonging to Lipschitz class by Nörlund Cesaro product summability means
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A number of researchers (See [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14]) have determined the degree of approximation of functions belonging to Lipschitz classes, using Cesaro, Euler and generalized Nörlund and various product summability means. Recently Krasniqi [15] has determined the degree of approximation of conjugate of functions using (E,q)(C, α, β) means. Mishra and Khatri [7] also determined the degree of approximation by using (Np.E1) product means in the Hölder metric. In this paper, we have determined the degree of approximation of functions belonging to Lipschitz class and weighted class by using (N, p)(C, θ, β) means of Fourier series and conjugate series of Fourier series which in particular becomes (E, q)(C, θ, β).
Abstract
A number of researchers (See [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14]) have determined the degree of approximation of functions belonging to Lipschitz classes, using Cesaro, Euler and generalized Nörlund and various product summability means. Recently Krasniqi [15] has determined the degree of approximation of conjugate of functions using (E,q)(C, α, β) means. Mishra and Khatri [7] also determined the degree of approximation by using (Np.E1) product means in the Hölder metric. In this paper, we have determined the degree of approximation of functions belonging to Lipschitz class and weighted class by using (N, p)(C, θ, β) means of Fourier series and conjugate series of Fourier series which in particular becomes (E, q)(C, θ, β).
참고문헌 (18)
- P. Chandra, "Trigonometric approximation of function in Lp-norm", J. Math. Anal. Appl, 275, pp.13~26 (2002)
- XHEVAT ZAHIR KRASNIQI, "ON THE POWER INTEGRABILITY WITH WEIGHT OF DOUBLE TRIGONOMETRIC SERIES", Advanced Studies in Contemporary Mathematics, 31(2), pp.221~242 (2021), 장전수학회
- XHEVAT ZAHIR KRASNIQI, "ON APPROXIMATION OF CONTINUOUS BIVARIATE PERIODIC FUNCTIONS BY DEFERRED GENERALIZED DE LA VALLÉE POUSSIN MEANS OF THEIR FOURIER SERIES", Advanced Studies in Contemporary Mathematics, 32(3), pp.387~402 (2022), 장전수학회
- H. H. Khan, "On the degree of approximation of functions belonging to the class Lip(α, p)", Indian J. pure Appl. Math, 5, pp.132~136 (1974)
- S. Lal, "On Kλ summability of conjugate series of Fourier series", Bull. Calcutta Math. Soc, 89, pp.97~104 (1997)
- Lakshmi Narayan Mishra, "Tauberian theorems for weighted means of double sequences in intuitionistic fuzzy normed spaces", Yugoslav Journal of Operations Research, 32(3), pp.377~388 (2022), National Library of Serbia[DOI]
- V. N. Mishra, "Degree of approximation on f ∈ Hw class by the (Np.E1) means in the H¨older Metric", Int. J. Math. and Math. Sci, pp.1~9 (2014)
- L. N. Mishra, "On the trigonometric approximation of signals belonging to generalized weighted Lipschitz W(Lr, ξ(t))(r ≥ 1)) class by matrix C1.Np operator of conjugate series of its Fourier series", Applied Mathematics and Computation, 237, pp.252~263 (2014)
- V. N. Mishra, "Trigonometric approximation of signals (functions) in Lp −norm", International Journal of Contemporary Mathematical Sciences, 7, pp.909~918 (2012)
- Vishnu Narayan Mishra, "Trigonometric approximation of periodic Signals belonging to generalized weighted Lipschitz W'(L_r,ξ(t)),(r≥1) -- class by Nörlund-Euler (N,p_n) (E,q) operator of conjugate series of its Fourier series", Journal of Classical Analysis, (2), pp.91~105 (2014), Element d.o.o.[DOI]
- V. N. Mishra, "Using linear operators to approximate signals of Lip(α, p), (p ≥ 1)-class", Filomat, 27, pp.353~363 (2013)
- V. N. Mishra, "Some problems on approximations of functions in Banach spaces", Ph. D., pp.2007
- H. K. Nigam, "A study on approximation of conjugate of functions belonging to Lipschitz class and generalized Lipschitz class by product means of conjugate series of Fourier series", Thai J. math, 10, pp.275~287 (2012)
- H. K. Nigam, "Approximation of conjugate functions belonging to Lip(α, r)class and to weighted W(Lr, ξ(t)) class by product means of conjugate Fourier series", Eur. J. Pure Appl. Math, 3, pp.276~286 (2011)
- X. Z. Krasniqi, "On the degree of approximation of functions belonging to the Lipschitz class by (E, q)(C, α, β) means", Khayyam Journal of Mathematics, 1, pp.243~252 (2015)
- Deepmala, "Trigonometric approximation of signals (functions)belonging to the W(Lr, ξ(t)), (r ≥ 1)− class by (E, q)(q ≥ 0)-means of the conjugate series of its Fourier series, GJMS Special Issue for Recent Advances in Mathematical Sciences and Applications-13", Global Journal of Mathematical Sciences, 2, pp.61~69 (2014)
- X. Z. Krasniqi, "On the degree of approximation of functions of the Lipschitz class by (E, q)(C, α, β) means", J. Numer. Math. stoch, 4, pp.40~47 (2012)
- A. Zygmund, "Trigonometric Series, Vol.1" (1959), Cambridge Univ. Press