Trigonometric approximation of signals (functions) belonging to certain Lipschitz spaces using C ^δ.C operator

References

[1] A. A. Das, S. K. Paikray, T. Pradhan and H. Dutta, Approximation of signals in the weighted Zygmund class via Euler–Hausdorff product summability mean of Fourier series, J. Indian Math. Soc. (N. S.) 87 (2020), no. 1–2, 22–36. 10.18311/jims/2020/22506Search in Google Scholar

[2] U. Deg̃er, On approximation to functions in the W ⁢ ( L p , ξ ⁢ ( t ) ) class by a new matrix mean, Novi Sad J. Math. 46 (2016), no. 1, 1–14. 10.30755/NSJOM.2013.020Search in Google Scholar

[3] Deepmala and L.-I. Piscoran, Approximation of signals (functions) belonging to certain Lipschitz classes by almost Riesz means of its Fourier series, J. Inequal. Appl.2016 (2016), Paper No. 163. 10.1186/s13660-016-1101-5Search in Google Scholar

[4] S. Devaiya and S. K. Srivastava, Approximation of functions and conjugate of functions using product mean ( E , q ) ⁢ ( E , q ) ⁢ ( E , q ) , Palest. J. Math. 11 (2022), 29–37. Search in Google Scholar

[5] S. Z. Jafarov, On approximation of a weighted Lipschitz class functions by means t n ⁢ ( h ; x ) , N n β ⁢ ( h ; x ) and R n β ⁢ ( h ; x ) of Fourier series, Trans. Natl. Acad. Sci. Azerb. Ser. Phys.-Tech. Math. Sci. Math. 40 (2020), 118–129. 10.29228/proc.50Search in Google Scholar

[6] H. H. Khan and G. Ram, On the degree of approximation, Facta Univ. Ser. Math. Inform. 18 (2003), 47–57. Search in Google Scholar

[7] X. Z. Krasniqi and Deepmala, On approximation of functions belonging to some classes of functions by ( N , p n , q n ) ⁢ ( E , θ ) means of conjugate series of its Fourier series, Khayyam J. Math. 6 (2020), no. 1, 73–86. Search in Google Scholar

[8] J. K. Kushwaha, L. Rathour, V. N. Mishra and K. Kumar, Estimation of degree of approximation of functions belonging to Lipschitz class by Nörlund Cesãro product summability means, Ann. Fuzzy Math. Inform. 24 (2022), no. 3, 239–252. Search in Google Scholar

[9] H. K. Nigam and M. Hadish, On approximation of function in generalized Zygmund class using C η ⁢ T operator, J. Math. Inequal. 14 (2020), no. 1, 273–289. 10.7153/jmi-2020-14-18Search in Google Scholar

[10] T. Pradhan, S. K. Paikray and U. Misra, Approximation of signals belonging to generalized Lipschitz class using ( N ¯ , p n , q n ) ⁢ ( E , s ) -summability mean of Fourier series, Cogent Math. 3 (2016), Article ID 1250343. 10.1080/23311835.2016.1250343Search in Google Scholar

[11] E. Z. Psarakis and G. V. Moustakides, An L 2 -based method for the design of 1-D zero phase FIR digital filters, IEEE Trans. Circuits Syst. I Fund. Theory Appl. 44 (1997), no. 7, 591–601. 10.1109/81.596940Search in Google Scholar

[12] A. Rathore and U. Singh, On the degree of approximation of functions in a weighted Lipschitz class by almost matrix summability method, J. Anal. 28 (2020), no. 1, 21–33. 10.1007/s41478-017-0030-0Search in Google Scholar

[13] U. Singh, On the trigonometric approximation of functions in a weighted Lipschitz class, J. Anal. 29 (2021), no. 1, 325–335. 10.1007/s41478-020-00267-5Search in Google Scholar

[14] U. Singh and A. Rathore, A note on the degree of approximation of functions belonging to certain Lipschitz class by almost Riesz means, Stud. Univ. Babeş-Bolyai Math. 63 (2018), no. 3, 371–379. 10.24193/subbmath.2018.3.08Search in Google Scholar

[15] U. Singh and S. K. Srivastava, Approximation of conjugate of functions belonging to weighted Lipschitz class W ⁢ ( L p , ξ ⁢ ( t ) ) by Hausdorff means of conjugate Fourier series, J. Comput. Appl. Math. 259 (2014), 633–640. 10.1016/j.cam.2013.02.026Search in Google Scholar

[16] U. Singh and S. K. Srivastava, Trigonometric approximation of functions belonging to certain Lipschitz classes by C 1 ⋅ T operator, Asian-Eur. J. Math. 7 (2014), no. 4, Article ID 1450064. 10.1142/S1793557114500648Search in Google Scholar

[17] S. Sonker and P. Sangwan, Approximation of Fourier and its conjugate series by triple Euler product summability, J. Phys. Conf. Ser. 1770 (2021), Article ID 012003. 10.1088/1742-6596/1770/1/012003Search in Google Scholar

[18] S. K. Srivastava and S. Devaiya, Error estimation of signals (functions) belonging to class W ⁢ ( L p , Ψ ⁢ ( t ) , β ) for hump matrices, AIP Conf. Proc. 2435 (2022), Article ID 020043. 10.1063/5.0083602Search in Google Scholar

[19] S. K. Srivastava and U. Singh, Trigonometric approximation of periodic functions belonging to Lip ⁢ ( ω ⁢ ( t ) , p ) -class, J. Comput. Appl. Math. 270 (2014), 223–230. 10.1016/j.cam.2014.01.020Search in Google Scholar

[20] S. K. Srivastava and U. Singh, Trigonometric approximation of periodic functions belonging to weighted Lipschitz class W ⁢ ( L p , Ψ ⁢ ( t ) , β ) , Function Spaces in Analysis, Contemp. Math. 645, American Mathematical Society, Providence (2015), 283–291. 10.1090/conm/645/12937Search in Google Scholar