  We deal with an isoperimetric problem on the Finsler hyperbolic plane. The
space is defined as the Lie group of proper affine transformations of the line
with a left-invariant Finsler structure. To state the problem, we use the
left-invariant volume form. The optimal isoperimetric loops are found in terms
of convex trigonometry functions. We also propose a generalization of the
isoperimetric inequality in parametric form.
