TAILIEUCHUNG - Convolution and Jackson inequalities in Musielak–Orlicz spaces

In the present work we prove some direct and inverse theorems for approximation by trigonometric polynomials in Musielak–Orlicz spaces. Furthermore, we get a constructive characterization of the Lipschitz classes in these spaces. | Turk J Math (2018) 42: 2166 – 2185 © TÜBİTAK doi: Turkish Journal of Mathematics Research Article Convolution and Jackson inequalities in Musielak–Orlicz spaces 1 Ramazan AKGÜN1 ,,Yunus Emre YILDIRIR2,∗, Department of Mathematics, Faculty of Arts and Science, Balıkesir University, Balıkesir, Turkey 2 Department of Mathematics, Faculty of Education, Balıkesir University, Balıkesir, Turkey Received: • Accepted/Published Online: • Final Version: Abstract: In the present work we prove some direct and inverse theorems for approximation by trigonometric polynomials in Musielak–Orlicz spaces. Furthermore, we get a constructive characterization of the Lipschitz classes in these spaces. Key words: Musielak–Orlicz space, direct and inverse theorem, Lipschitz class, trigonometric approximation 1. Introduction Musielak–Orlicz spaces are similar to Orlicz spaces but are defined by a more general function with two variables φ (x, t) . In these spaces, the norm is given by virtue of the integral ∫ φ (x,

• Toán học
• Musielak–Orlicz space
• Direct and inverse theorem
• Lipschitz class
• Trigonometric approximation
• Polynomial approximation problems
• Computational complexity
• Approximation algorithms
• Heuristic computation
• Heuristic methods
• NP hard problems
• Journal of Computer Science and Cybernetics
• Alternating current electrical systems
• Integer quadratic programming
• Non linear knapsack problems arising
• Polynomial time approximation schemes