On a novel probabilistic Sampling Kantorovich operators and their application (2506.12053v1)

Abstract: This article starts with the fundamental theory of stochastic type convergence and the significance of uniform integrability in the context of expectation value. A novel probabilistic sampling kantorovich (PSK-operators) is established with the help of classical sampling operators (SK-operators). We establish the proof of the fundamental theorem of approximation and a lemma corresponding to the PSK- operators. Moreover, some examples are illustrated not only in numerical form but also in a detailed study of some important features of an image at different samples. Eventually, a comparative analysis is made on the basis of some parameters like peak signal noise ratio (PSNR), structural similarity index (SSIM) etc. between the classical and probabilistic sense in tabulated form, which connects the whole dots of the theory present in the article.