On the third logarithmic coefficient in some subclasses of close-to-convex functions

For analytic functions f in the unit disk $${\mathbb {D}}$$D normalized by $$f(0)=0$$f(0)=0 and $$f'(0)=1$$f′(0)=1 satisfying in $${\mathbb {D}}$$D respectively the conditions $${{\,\mathrm{Re}\,}}\{ (1-z)f'(z) \}> 0,\ {{\,\mathrm{Re}\,}}\{ (1-z^2)f'(z) \}> 0,\ {{\,\mathrm{Re}\,}}\{ (1-z+z^2)f'(z) \}> 0,\ {{\,\mathrm{Re}\,}}\{ (1-z)^2f'(z) \} > 0,$$Re{(1-z)f′(z)}>0,Re{(1-z2)f′(z)}>0,Re{(1-z+z2)f′(z)}>0,Re{(1-z)2f′(z)}>0, the sharp upper bound of the third logarithmic coefficient in case when $$f''(0)$$f′′(0) is real was computed.