Approximation by Kantorovich-type max-min operators and its applications

In this study, we construct max-product and max-min kind pseudo-linear discrete operators. First, we obtain some approximation results for bounded and uniformly continuous functions. Then, the rate of convergence for these approximations using a suitable Lipschitz class of continuous functions is also discussed. Some applications for verifying our results are also given. Furthermore, we approximate fuzzy numbers using our operators. Finally, we apply our approximation in image processing.

show abstract

Nonlinear approximation by $N$-dimensional sampling type discrete operators with applications

Aslan

2024

Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat.

View full text Add to dashboard Cite

In this paper, we explore $N$-dimensional nonlinear discrete operators, closely related to generalized sampling series. We investigate their approximation properties by using the supremum norm and employ a summability method to generalize the discrete operators. The order of convergence is studied by using suitable Lipschitz classes of uniformly continuous functions. We exemplify kernel functions that meet the necessary conditions. Additionally, in the final section of the paper, we propose an operator-based method for digital image zooming.

show abstract

Approximation by Kantorovich-type max-min operators and its applications

Cited by 3 publications

References 33 publications

P2P Strategy for Energy Cost Reduction in Multi-Energy Hubs Considering Uncertainty and Flexibility

P2P Strategy for Energy Cost Reduction in Multi-Energy Hubs Considering Uncertainty and Flexibility

Approximation by n-dimensional max-product and max-min kind discrete operators with applications

Nonlinear approximation by $N$-dimensional sampling type discrete operators with applications

Contact Info

Product

Resources

About