Abstract
Direct and converse approximation theorems for the Shepard operator (1) are given in uniform metric. The main result is Theorem 3 which completes the characterization of Lipschitz classes by the order of approximation by the Shepard operator for λ>2.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Criscuolo, G. and Mastroianni, G., Estimates of the Shepard Interpolatory Procedure, Acta Math. Hung. (to appear).
Vecchia, B. Della and Mastroianni, G., Pointwise Simultaneous Approximation by Rational Operators (to appear in J. Approx. Theory).
Vecchia, B. Della, Mastroianni, G. and Totik, V., Saturation of the Shepard Operators, Appr. Theory and its Appl. 6:4(1990), 76–84.
Somorjai, G., On a Saturation Problem, Acta Math. Acad. Sci. Hungar., 32(1978), 377–381.
Author information
Authors and Affiliations
Additional information
Research supported by National Science Foundation of the Hungarian Academy of Sciences, Grant No. 1801
Rights and permissions
About this article
Cite this article
Szabados, J. Direct and converse approximation theorems for the Shepard operator. Approx. Theory & its Appl. 7, 63–76 (1991). https://doi.org/10.1007/BF02836457
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF02836457