Approximation by polynomials,
Inequalities in approximation (Bernstein,
Jackson,
Nikolʹskiĭ-type inequalities),
Rate of convergence,
Inverse theorems,
Simultaneous approximation,
Best constants,
Spaces of measurable functions ($L_p$-spaces,
Orlicz spaces,
Lorentz spaces,
rearrangement invariant spaces,
etc.).
Subject:
Approximations and Expansions
Harmonic analysis on Euclidean spaces
Main publications:
Ramazan Akgun, “Improved converse theorems and fractional moduli of smoothness in Orlicz spaces”, Bull. Malays. Math. Sci. Soc. (2), 36:1 (2013), 49-62
Ramazan Akgun, “Approximating polynomials for functions of weighted Smirnov-Orlicz spaces”, J. Funct. Spaces Appl., 2012 (2012), 1–41
Ramazan Akgun and Vakhtang Kokilashvili, “The refined estimates of trigonometric approximation for functions with generalized derivatives in weighted variable exponent Lebesgue spaces”, Georgian Math. J., 19:4 (2012), 611–626
Ramazan Akgun, “Trigonometric approximation of functions in generalized Lebesgue spaces with variable exponent”, Ukrainian Math. J., 63:1 (2011), 1–26
Ramazan Akgun, “Inequalities for one sided approximation in Orlicz spaces”, Hacettepe journal of mathematics and statistics, 40:2 (2011), 231–240
R. Akgün, “Jackson type inequalities for differentiable functions in weighted Orlicz spaces”, Algebra i Analiz, 34:1 (2022), 1–34; St. Petersburg Math. J., 34:1 (2023), 1–24
R. Akgün, “Realization and characterization of modulus of smoothness in weighted Lebesgue spaces”, Algebra i Analiz, 26:5 (2014), 64–87; St. Petersburg Math. J., 26:5 (2015), 741–756
Approximation by polynomials in Bergman spaces R. Akgun International conference on Function Spaces and Approximation Theory dedicated to the 110th anniversary of S. M. Nikol'skii May 27, 2015 14:30
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