Ramazan AKGÜN, Arash GHORBANALIZADEH

6784

Approximation by integral functions of finite degree in variable exponent Lebesgue spaces on the real axis

We obtain several inequalities of approximation by integral functions of finite degree in generalized Lebesgue spaces with variable exponent defined on the real axis. Among them are direct, inverse, and simultaneous estimates of approximation by integral functions of finite degree in $L^{p\left( \cdot \right)}.$ An equivalence of modulus of continuity with Peetre's $K$ -functional is established. A constructive characterization of Lipschitz class is also obtained.
Keywords:

Direct theorem, inverse theorem, modulus of continuity simultaneous approximation, Lipschitz class,

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Turkish Journal of Mathematics-Cover
  • ISSN: 1300-0098
  • Yayın Aralığı: 6
  • Yayıncı: TÜBİTAK
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