Sharp bounds for cosh(x)x,sinh(x)x, and sin(x)x were obtained, as well as one new bound for ex+arctan(x)x. A new situation to note about the obtained boundaries is the symmetry in the upper and lower boundary, where the upper boundary differs by a constant from the lower boundary. New consequences of the inequalities were obtained in terms of the Riemann–Liovuille fractional integral and in terms of the standard integral.
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