On <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" id="d1e1235" altimg="si7.svg"><mml:mrow><mml:mo>(</mml:mo><mml:mi>β</mml:mi><mml:mo>,</mml:mo><mml:mi>γ</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math>-Chebyshev functions and points of the interval

In this paper, we introduce the class of $(\beta,\gamma)$-Chebyshev functions and corresponding points, which can be seen as a family {\it generalized} Chebyshev polynomials points. For functions, prove that they are orthogonal in certain subintervals $[-1,1]$ with respect to weighted arc-cosine measure. particular investigate cases where become polynomials, deriving new results concerning classical first kind. Besides, show subsets Chebyshev-Lobatto points instances We also study behavior Lebesgue constants polynomial interpolant at these on varying parameters $\beta$ $\gamma$.