مجلة جامعة تشرين للبحوث والدراسات العلمية، سلسلة العلوم الأساسية (Nov 2018)

Approximation of complex functions from Lebesgue space with variable exponent L^p(.) (Γ) on Dini smooth curves

  • Mohammad Ali,
  • Hasan Baddour,
  • Nour Dahman

Journal volume & issue
Vol. 40, no. 5

Abstract

Read online

. In this research, we have studied some of the new properties of the fractional modulus of smoothness defined by the researcher Akgun in 2011. Then we have investigated the direct problem of approximation theory of complex functions from Lebesgue spaces with variable exponent on Dini smooth curves by rational functions related to Faber polynomials using fractional modulus of smoothness. We have obtained approximation of analytic functions from Smirnov class with variable exponent on a simply connected domain bounded by Dini smooth curve using fractional modulus of smoothness. It should be noted that in 2016, both researchers Israfilov and Testici studied approximation of functions from on Dini smooth curves using modulus of smoothness identifier with the following relation: .