Shape-Preserving Properties of Max-Product Type Nonlinear $q-$Bernstein–Chlodowsky Operators

In [29], a new class of nonlinear Bernstein--Chlodowsky operators of max-product type based on $q$-integers was introduced, and corresponding error estimations were established. The present work is devoted to a further investigation of these operators with particular emphasis on their shape-preserving properties. Specifically, we examine the preservation of structural features such as monotonicity, convexity under the action of the proposed operators. These properties are essential in various applications of approximation theory. The results presented here extend the foundational work in [29] and contribute to a deeper understanding of the qualitative behavior of $q$-based max-product type operators within the framework of nonlinear approximation.