A study on convergence of non-convolution type double singular integral operators

Öz

Anahtar Kelimeler

• μ-generalized Lebesgue points,pointwise convergence

Kaynakça

1. C. Bardaro and G. Vinti, On Approximation Properties of Certain Non-convolution Integral Operators, Journal of Approximation Theory 62(1990), 358-371.
2. P. L. Butzer and R. J. Nessel, Fourier Analysis and Approximation, vol. I. Academic Press, New York, London, (1971).
3. A.D. Gadjiev, On the order of convergence of singular integrals which depend on two parameters, Special Problems of Functional Analysis and their Appl. to the Theory of Diff. Eq. and the Theory of Func., Izdat. Akad. Nauk Azerba13 ̆053'fdažan. SSR. (1968), 40–44.
4. S.R. Ghorpade, B.V. Limaye, A Course in Multivariable Calculus and Analysis, Springer, New York, (2010).
5. R. G. Mamedov, On the order of convergence of m-singular integrals at generalized Lebesgue points and in the space Lp(-∞, ∞), Izv. Akad. Nauk SSSR Ser. Mat 27(1963), no.2, 287-304.
6. W. Rudin, Real and Complex Analysis, Mac Graw Hill Book Company, London, (1987).
7. B. Rydzewska, Approximation des fonctions par des intégrales singulières ordinaires, Fasc. Math. (7) (1973), 71–81.
8. B. Rydzewska, Approximation des fonctions de deux variables par des intégrales singulières doubles, Fasc. Math. (8) (1974), 35–45.

9. S. Siudut, On the convergence of double singular integrals, Comment. Math. Prace Mat. 28 (1) (1988), 143-146.
10. S. Siudut, A theorem of Romanovski type for double singular integrals, Comment. Math. Prace Mat. 29 (1989), 277-289.
11. R. Taberski, Singular integrals depending on two parameters, Rocznicki Polskiego towarzystwa matematycznego, Seria I. Prace matematyczne, VII, (1962), 173-179.
12. R. Taberski, On double integrals and Fourier Series, Ann. Polon. Math. 15 (1964), 97–115
13. H. Karsli, On Approximation Properties of Non-Convolution Type Nonlinear Integral Operator, Anal. Theory Appl., Vol. 26, No. 2 (2010), 140-152
14. G. Uysal, M. M. Yilmaz, E. Ibikli, A study on pointwise approximation by double singular integral operators, J. Inequal. Appl., 2015:94, 2015.
15. G. Uysal and M. M. Yilmaz, Some theorems on the approximation of non-integrable functions via singular integral operators, Proc. Jangjeon Math. Soc., 18(2015), no. 2, 241-251.
16. G. Uysal and E. Ibikli, Further Results On Approximation By Double Singular Integral Operators with Radial Kernels, Journal of Pure and Applied Mathematics: Advances and App.,Volume 14, Number 2, 2015, Pages 151-166.
17. G. Uysal , M. Menekse Yilmaz and E. Ibikli, Approximation by Radial Type Multidimensional Singular Integral Operators,Palestine Journal of Mathematics, 2016, no:5(2), 61-70.
18. G. Uysal, E. Ibikli, Weighted approximation by double singular integral operators with radially defined kernels, Math. Sci. (Springer) 10 (2016), 1-9.
19. M. M. Yilmaz, G. Uysal, and E. Ibikli, A note on rate of convergence of double singular integral operators, Adv. Difference Equ., 2014:287, 2014.
20. Wolfram, S., The Mathematica Book, Fifth Edition (2003), Wolfram Media, Inc., 1488 pp.
21. L. N. Mishra, V. N. Mishra, K. Khatri, Deepmala, On The Trigonometric approximation of signals belonging to generalized weighted Lipschitz W(L'^r,ξ(t))(r≥1) class by matrix (C^1.N_p ) operator of conjugate series of its Fourier series, Applied Mathematics and Computation, vol.237 (2014), 252-263.
22. V. N. Mishra, K. Khatri, L.N. Mishra, Deepmala, Trigonometric approximation of periodic signals belonging to generalized weighted Lipschitz W^( ^' ) (L^r,ξ(t))(r≥1) class by Norlund-Euler (N ,p_n) belonging to operator of conjugate series of its Fourier series, Journal of Classical Analysis, Vol.5, Number 2(2014), 91-95. doi:10.7153/jca-05-08.
23. V. N. Mishra, Some Problems on Approximations of Functions in Banach Spaces, Ph.D. Thesis (2007), Indian Institute of Technology, Roorkee 247 667, Uttarakhand, India.
24. V. N. Mishra, L.N. Mishra, Trigonometric Approximation of Signals (Functions) in L _p (p≥1) norm, International Journal of Contemporary Mathematical Sciences, Vol. 7, no. 19, (2012), pp. 909 - 918.