Bounds for the Chebyshev Functional Defined on the q-Circles with Application

In this paper, we move beyond the classical setting by redefining the Chebyshev functional in the context of q-circles situated within Minkowski space, rather than the standard Euclidean circles in R2. This approach introduces a new theoretical framework suitable for non-Euclidean geometries. We derive sharp estimates for the functional when applied to functions on q-circles that adhere to Hölder-type continuity conditions.