Order of Approximation for Exponential Sampling Type Neural Network Operators

In the present article, we derive certain direct approximation results for the family of exponential sampling type neural network operators. The Voronovskaja type theorem of convergence for these operators is proved. Further, the Jackson-type inequalities concerning the order of approximation for these family of operators are established by utilizing the notion of logarithmic modulus of continuity for the involved functions and their higher derivatives. In order to improve the order of convergence, we provide a constructive mechanism by considering the linear combination of these operators. At the end, we also discuss a few numerical examples based on the presented theory.