A new sequence of approximation operators involving modified Bessel functions of first kind

The present article deals with an approximation operator, which is based on the modified Bessel function of the first kind. Such operators are linear positive operators and preserve only the constant functions among the power test functions. We construct these operators by a partial differential equation (PDE). Also, a more general form based on two parameters is captured from the PDE. We establish some direct approximation results and, in addition, consider the composition of these operators with Szász–Mirakyan operators, which provide us with another new operator, which is based on generalized Laguerre polynomials. We also estimate the approximation process for the new composite operator.