Approximation by family of max–min sampling operators in function spaces
摘要
This note aims to introduce a family of max–min sampling operators and investigates their approximation properties in some significant function spaces. We introduce and study the approximation capabilities of a novel family of sampling operators, namely generalized max–min sampling operators and Kantorovich type max–min sampling operators. This study has been carried out in the space of continuous functions, classical Lebesgue spaces and Orlicz spaces. The Orlicz spaces are generalizations of Lebesgue spaces consisting of some more significant function spaces like Logarithmic space and Exponential space. Following the theoretical groundwork, we illustrate the practical performance of our operators in function reconstruction through numerical examples, graphical representations and error estimates, and in signal denoising. Our findings establish that these operators perform better than certain existing families of sampling operators in the approximation process.