Shape Preserving Properties of Parametric Szász Type Operators on Unbounded Intervals

Abstract

The Be´zier-type operator has become a powerful tool in operator theory, neural networks, curve and surface design and representation because of its good shape-preserving properties. Motivated by the improvements of the operator in computational disciplines, we investigate some elementary properties of two kinds of modified Sza´sz type basis functions, depending on non-negative parameters. Using the derivative, the symmetry of variables, the modulus of continuity and the concave continuous modulus, we study some shape preserving properties of these operators concerning monotonicity, convexity, starshapedness, semi-additivity and the preservation of smoothness. Moreover, some illustrative examples are provided to demonstrate the approximation behavior of the proposed operators and the classical ones.