A THEOREM ON WEIGHTED APPROXIMATION BY SINGULAR INTEGRAL OPERATORS

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  • Alexits, G., Konvergenzprobleme der Orthogonalreihen, Verlag der Ungarischen Akademie der Wissenschaften, Budapest, (1960), 307.
  • Atakut, Ç., On derivatives of Bernstein type rational functions of two variables, Ap- plied Mathematics and Computation, Vol. 218, 3, (2011), 673–677.
  • Bardaro, C. and Gori Cocchieri, C., On the degree of approximation for a class of singular integrals, (Italian) Rend. Mat. (7) 4, 4 (1984), 481–490.
  • Bardaro, C., On approximation properties for some classes of linear operators of convolution type, Atti Sem. Mat. Fis. Univ. Modena 33, 2 (1984), 329–356.
  • Bardaro, C. and Mantellini, I., Pointwise convergence theorems for nonlinear Mellin convolution operators, Int. J. Pure Appl. Math., 27, 4 (2006), 431–447.
  • Bardaro, C., Karsli, H. and Vinti, G., On pointwise convergence of linear Integral operators with homogeneous kernel, Integral Transforms and Special Functions, Vol. , 6(2008), 429-439.
  • Butzer, P. L. and Nessel, R. J., Fourier Analysis and Approximation, Vol. I. Academic Press, New York, London, 1971.
  • Büyükyazıcı, I. and Ibikli, E., The approximation properties of generalized Bernstein polynomials of two variables, Applied Mathematics and Computation, 156 (2), (2004), 380.
  • Faddeev, D. K., On the representation of summable functions by means of singular integrals at Lebesgue points. Mat. Sbornik, Vol 1 (43), 3, (1936), 351-368.
  • Gadjiev, A. D., The order of convergence of singular integrals which depend on two parameters, in: Special Problems of Functional Analysis and their Appl. to the Theory of Diğ . Eq. and the Theory of Func., Izdat. Akad. Nauk Azerba¼ıdaµzan. SSR., (1968), 44.
  • ·Izgi, A., Approximation by a Class of New Type Bernstein Polynomials of one and two Variables, Global Journal of Pure and Applied Mathematics, Vol. 9, 1, (2013), p55.
  • Karsli, H, and Ibikli, E., On convergence of convolution type singular integral opera- tors depending on two parameters, Fasc. Math., 38(2007), 25-39.
  • Mamedov, R. G., On the order of convergence ofm-singular integrals at generalized Lebesgue points and in the spaceLP( 1; 1), Izv. Akad. Nauk. SSSR Ser. Mat. 27 (2) (1963), 287-304.
  • Mishra V. N, Some problems on approximations of functions in Banach spaces, Ph. D. Thesis, Indian Institute of Technology, Roorkee 247 667, Uttarakhand, India. Mishra V. N., Mishra L.N.,Trigonometric Approximation of Signals (Functions) in Lp(p )-norm, International Journal of Contemporary Mathematical Sciences (IJCMS), Vol.7, no.19, 2012, pp. 909-918.
  • Rydzewska, B., Approximation des fonctions par des intégrales singulières ordinaires, Fasc. Math., 7(1973), 71–81.
  • Natanson, I. P., Theory of functions of a real variable, (1964).
  • Siudut, S., On the convergence of double singular integral, Comment. Math. Prace Mat. 28 (1) (1988), 277-289.
  • Siudut, S., A theorem of Romanovski type for double singular integral, Comment. Math. Prace Mat. 29, (1989), 143-146.
  • Siudut, S., Some Remarks on Theorems of Romanovski and Faddeev type, Comment. Math. Prace Mat., 29, 2 (1990), 287-296.
  • Taberski, R., Singular integrals depending on two parameters, Rocznicki Polskiego towarzystwa matematycznego, Taberski, R., On double integrals and Fourier Series, Ann. Polon. Math. 15(1964), –115.
  • Taberski, R., On double singular integrals, Rocznicki Polskiego towarzystwa matem- atycznego, Seria I. Prace Matematyczne XIX (1976), 155-160.
  • Uysal, G., Yılmaz, M. M. and Ibikli, E., A study on pointwise approximation by double singular integral operators, J. Inequal. Appl. 2015 (2015), 94
  • Uysal, G., and Ibikli, E., Further results on approximation by double singular integral operators with radial kernels, J. Pure and Appl. Math.: Adv. and Appl., 14, 2, (2015), 166.
  • Uysal, G., Yılmaz, M. M. and Ibikli, E., Approximation by radial type multidimen- sional singular integral operators, Palestine J. of Math., Vol. 5, 2, (2016), 61-70.
  • Uysal, G., and Ibıklı, E., Weighted approximation by double singular integral opera- tors with radially de…ned kernels, Mathematical Sciences 10(4), (2016), 149-157.
  • Current address, O.Guller:Ankara University, Faculty of Science, Department of Mathemat- ics, Ankara, Turkey. E-mail address : ozgeguller2604@gmail.com ORCID Address:
  • Current address, E.Ibikli: Ankara University, Faculty of Science, Department of Mathematics, Ankara, Turkey. E-mail address : Ertan.Ibikli@ankara.edu.tr ORCID Address: http://orcid.org/0000-0002-4743-6229