Abstract:
One-sided Steklov means are used to introduce moduli of continuity of natural order in variable $L^{p(\cdot)}_{2\pi}$-spaces. A direct theorem of Jackson-Stechkin type and an inverse theorem of Salem-Stechkin type are given. Similar results are obtained for the conjugate functions.
Bibliography: 24 titles.
Keywords:
variable Lebesgue space, variable Sobolev space, $K$-functional, generalized modulus of continuity, direct and inverse approximation theorems, conjugate function.
\Bibitem{Vol17}
\by S.~S.~Volosivets
\paper Approximation of functions and their conjugates in variable Lebesgue spaces
\jour Sb. Math.
\yr 2017
\vol 208
\issue 1
\pages 44--59
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Linking options:
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This publication is cited in the following 21 articles:
S. Jafarov, “Approximation by Nörlund type means in the grand Lebesgue spaces with variable exponent”, Vestn. Udmurtsk. un-ta. Matem. Mekh. Kompyut. nauki, 34:1 (2024), 19–32
Ahmet Testici, Daniyal M. Israfilov, “Approximation by trigonometric polynomials in weighted Morrey spaces”, Mosc. Math. J., 24:1 (2024), 91–105
S. S. Volosivets, “Riesz–Zygmund Means and Approximation in Variable Exponent Grand Spaces”, Results Math, 79:5 (2024)
S. Volosivets, “Approximation in Variable Exponent Spaces and Growth of Norms of Trigonometric Polynomials”, Anal Math, 49:1 (2023), 307
Sadulla Jafarov, “On approximation properties of functions by means of Fourier and Faber series in weighted Lebesgue spaces with variable exponent”, Mathematica Moravica, 27:1 (2023), 97
O. L. Vinogradov, “Direct and inverse theorems of approximation theory in Banach function spaces”, St. Petersburg Math. J., 35:6 (2024), 907–928
S. S. Volosivets, “Approximation by linear means of Fourier series and realization functionals in weighted Orlicz spaces”, Probl. anal. Issues Anal., 11(29):2 (2022), 106–118
D. M. Israfilzade, E. Gursel, “Convolutions and approximations in the variable exponent spaces”, BAUN Fen. Bil. Enst. Dergisi., 24:2 (2022), 636–644
R. Akgun, “Approximation properties of Bernstein singular integrals in variable exponent Lebesgue spaces on the real axis”, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., 71:4 (2022), 1058–1079
R. Akgun, “Exponential approximation in variable exponent Lebesgue spaces on the real line”, Constructive Mathematical Analysis, 5:4 (2022), 214–237
S. S. Volosivets, “Realization functionals and description of a modulus of smoothness in variable exponent Lebesgue spaces”, Russian Math. (Iz. VUZ), 66:6 (2022), 8–19
D. M. Israfilov, E. Gursel, “Approximation by $p(\cdot)$-Faber polynomials in the variable Smirnov classes”, Math. Meth. Appl. Sci., 44:9 (2021), 7479–7490
A. Testici, D. M. Israfilov, “Approximation by matrix transforms in generalized grand Lebesgue spaces with variable exponent”, Appl. Anal., 100:4 (2021), 819–834
S. S. Volosivets, “Modified modulus of smoothness and approximation in weighted Lorentz spaces by Borel and Euler means”, Probl. anal. Issues Anal., 10(28):1 (2021), 87–100
A. Testici, D. M. Israfilov, “Linear methods of approximation in weighted Lebesgue spaces with variable exponent”, Hacet. J. Math. Stat., 50:3 (2021), 744–753
A. Testici, “Approximation theorems in weighted Lebesgue spaces with variable exponent”, Filomat, 35:2 (2021), 561–577
D. M. Israfilov, E. Gursel, “Direct and inverse theorems in variable exponent Smirnov classes”, Proc. Inst. Math. Mech., 47:1 (2021), 55–66
R. Akgun, “Direct theorems of trigonometric approximation for variable exponent Lebesgue spaces”, Rev. Un. Mat. Argentina, 60:1 (2019), 121–135
Sadulla Jafarov, “Approximation by Zygmund means in variable exponent Lebesque spaces”, Mathematica Moravica, 23:1 (2019), 27
D. M. Israfilov, A. Testici, “Simultaneous approximation in Lebesgue space with variable exponent”, Proc. Inst. Math. Mech. Natl. Acad. Sci. Azerb., 44:1 (2018), 3–18
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