A Sharp Double Inequality Involving Trigonometric Functions and Its Applications

نویسندگان

  • ZHEN-HANG YANG
  • YU-MING CHU
  • S.-H. WU
  • M. L. GLASSER
  • D. H. BAILEY
  • J. M. BORWEIN
  • A. MATTINGLY
چکیده

We present the best possible parameters p,q ∈ (0,1] such that the double inequality 1 3p2 cos(px)+ 1− 1 3p2 < sin(x) x < 1 3q2 cos(qx)+ 1− 1 3q2 holds for all x ∈ (0,π/2) . As applications, some new inequalities for the sine integral, Catalan constant and Schwab-Borchardt mean are found. Mathematics subject classification (2010): 26D05, 26E60.

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تاریخ انتشار 2016