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Derivatives of a polynomial of best approximation and modulus of smoothness in generalized Lebesgue spaces with variable exponent

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Języki publikacji
EN
Abstrakty
EN
The relation between derivatives of a polynomial of best approximation and the best approximation of the function is investigated in generalized Lebesgue spaces with variable exponent. In addition, the relationship between the fractional modulus of smoothness of the function and its de la Vallée-Poussin sums is studied.
Wydawca
Rocznik
Strony
245--251
Opis fizyczny
Bibliogr. 40 poz.
Twórcy
  • Department of Mathematics and Science Education, Faculty of Education, Muş Alparslan University, 49250, Muş, Turkey
  • Institute of Mathematics and Mechanics, National Academy of Sciences of Azerbaijan, 9 B. Vahabzadeh str., AZ 1141, Baku, Azerbaijan
Bibliografia
  • [1] Diening L., Höstö P., Nekvinda A., Open problems in variable exponent Lebesgue and Sobolev spaces, In: Function Spaces, Differential Operators and Nonlinear Analysis, Proc. Conf. held in Milovy, Bohemian-Moravian Uplands, May 29-June 2, 2004, Math. Inst. Acad. Sci. Czech. Republic. Praha, 2005, 38-58
  • [2] Kokilashvili V., On a progress in the theory of integral operators in weighted Banach spaces, In: Function spaces, Differential Operators and Nonlinear Analysis, Proc. Conf. held in Milovy, Bohemian-Moravian Uplands, May 29-June 2, 2004, Math. Inst. Acad. Sci. Czech Republic, Praha, 2005, 152-174
  • [3] Kováčik O., Rákosnik J., On spaces Lp(x) and Wk,p(x), Czechoslovak Math. J., 1991, 41(116), 592-618
  • [4] Samko S. G., Diferentiation and integration of variable order an the spaces Lp(x), Operator theory for complex and hyper-complex analysis (Mexico City, 1994), 203-219, Contemp,. Math., 212, Amer. Math. Soc., Providence, RI, 1998
  • [5] Samko S. G., On a progres in the theory of Lebesgue spaces with variable exponent: maximal and singular operators, Integral Transforms Spec. Funct., 2005, 16(5-6), 461-482
  • [6] Sharapudinov I. I., The topology of the space Lp(t)([0, 1]), Matem. Zametki, 1979, 26(4), 613-632 (in Russian); English transl.: Math. Notes., 1979, 26(3-4), 796-806
  • [7] Sharapudinov I. I., Uniform boundedness in Lp(p = p(x)) of some families of convolution operators, Math. Notes., 1996, 59(1-2), 205-212
  • [8] Samko S. G., Kilbas A. A., Marichev O. I., Fractional integrals and derivatives, Theory and applications, Gordon and Breach Sci. Publ., 1993
  • [9] Akgün R., Kokilashvili V., On converse theorems of trigonometric approximation in weighted variable exponent Lebesgue spaces, Banach J. Math. Anal., 2011, 5(1), 70-82
  • [10] Akgün R., Trigonometric approximation of functions in generalized Lebesgue spaces with variable exponent, Ukrainian Math. J., 2011, 63(1), 1-26
  • [11] Akgün R., Improved converse theorems and fractional moduli of smoothness in Orlicz spaces, Bull. Malays. Math. Sci. Soc., 2013, 36(1), 49-62
  • [12] Akgün R., Isralov D. M., Approximation in weighted Orlicz spaces, Math. Slovaca, 2011, 61(4), 601-618
  • [13] DeVore R. A., Lorentz G. G., Constructive approximation, Springer, New York, 1993
  • [14] Guven A., Trigonometric approximation of functions in weighted Lp spaces, Sarajevo J. Math., 2009, 5(17), 99-108
  • [15] Guven A., Isralov D. M., Approximation by means of Fourier trigonometric series in weighted Orlicz spaces, Adv. Stud. Contemp. Math. (Kyundshang), 2009, 19(2), 283-295
  • [16] Guven A., Isralov D. M., Trigonometric approximation in generalized Lebesgue spaces Lp(x), J. Mat. Inequal. 2010, 4(2), 285-299
  • [17] Ibragimov I. I., Mamedkhanov D. I., A constructive characterization of a certain class of functions, Dokl. Akad. Nauk. SSSR, 1975, 223(1), 35-37 (in Russian)
  • [18] Israfilov D. M., Approximation by p-Faber polynomials in the weighted Smirnov class Ep(G, w) and the Bieberbach polynomials, Constr. Approx., 2001, 17, 335-351
  • [19] Israfilov D. M., Akgün R., Approximation in weighted Smirnov-Orlicz classes, J. Math. Kyoto Univ., 2006, 46, 755-770
  • [20] Israfilov D. M., Guven A., Approximation by trigonometric polynomials in weighted Orlicz spaces, Studia Math., 2006, 174(2), 147-168
  • [21] Israfilov D. M., Kokilashvili V., Samko S. G., Approximation in weighted Lebesgue spaces and Smirnov spaces with variable exponent, Proc. A. Ramadze Math. Inst., 2007, 143, 25-35
  • [22] Jafarov S. Z., Approximation by rational functions in Smirnov-Orlicz classes, J. Math. Anal. Appl., 2011, 379, 870-877
  • [23] Jafarov S. Z., Approximation by trigonometric polynomials in rearrangement invariant quasi Banach function spaces, Mediterr. J. Math., 2015, 12, 37-50
  • [24] Jafarov S. Z., The inverse theorem of approximation of the function in Smirnov-Orlicz classes, Math.Inequal. Appl., 2012, 12(4), 835-844
  • [25] Jafarov S. Z., Approximation by Fejér sums of Fourier trigonometric series in weighted Orlicz spaces, Hacet, J. Math. Stat., 2013, 42(3), 259-268
  • [26] Jafarov S. Z., Mamedkhanov J. I., On approximation by trigonometric polynomials in Orlicz spaces, Georgian Math. J., 2012, 19(4), 687-695
  • [27] Jafarov S. Z., Approximation of conjugate functions by trigonometric polynomials in weighted Orlicz spaces, J. Math. Inequal., 2013, 7(2), 271-281
  • [28] Kokilashvili V., Samko S. G., Operators of harmonic analysis in weighted spaces with non-standard growth, J. Math. Anal. Appl., 2009, 352, 15-34
  • [29] Kokilashvili V., Samko S. G., A refined inverse inequality of approximation in weighted variable exponent Lebesgue spaces, Proc. A. Razmadze Math. Inst., 2009, 151, 134-138
  • [30] Kokilashvili V., Tsanava T., On the normestimate of deviation by linear summability means and an extension of the Bernstein inequality, Proc. A. Razmadze Math Inst., 2010, 154, 144-146
  • [31] Mamedkhanov D. M., Approximation in complex plane and singular operators with a Cauchy kernel, Dissertation doct. Phys-math. nauk. the University of Tbilisi, 1984 (in Russian)
  • [32] Sunouchı V., Derivatives of a polynomial of best approximation, Jahresbericht d. DMV, 1968, 70, 165-166
  • [33] Stechkin S. B., The approximation of periodic functions by Fejér sums, Trudy Math. Inst. Steklov, G2, 1961, 522-523 (in Russian)
  • [34] Sharapudinov I. I., Approximation of functions in the metric of the space Lp(t)([a, b]) and quadrature (in Russian), Constructive function theory 81 (Varna, 1981), 189-193, Publ. House Bulgar. Acad. Sci., Soa, 1983
  • [35] Simonov B. V., Tikhonov S. Yu., Embedding theorems in the constructive theory of approximations, Mat. Sb. 2008, 199 (9), 107-148 (in Russian); translation in Sb. Math. 2008, 199(9-10), 1367-1407
  • [36] Timan A. F., Theory of approximation of functions of a real variable, Pergamon Press and MacMillan, 1963; Russian orginal published by Fizmatgiz, Moscow, 1960
  • [37] Trigub R. M., Belinsky E. S., Fourier analysis and approximation of functions, Kluwer, Dordrecht, 2004
  • [38] Yildirir Y. E., Isralov D. M., Simultaneous and converse approximation theorems in weighted Lebesgue spaces, Math. Inequal. Appl., 2011, 14(2), 359-371
  • [39] Yildirir Y. E., Isralov D. M., Approximation theorems in weighted Lorentz spaces, Carpathian J. Math., 2010, 26(1), 108-119
  • [40] Zygmund A., Trigonometric series, vol. I and II, Cambridge, 1959
Uwagi
PL
Opracowanie ze środków MNiSW w ramach umowy 812/P-DUN/2016 na działalność upowszechniającą naukę (zadania 2017).
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-8651c513-d44d-49d5-b1db-b7c354fe8232
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