Approximations of Set-Valued Functions by Metric Linear Operators
نویسندگان
چکیده
In this work, we introduce new approximation operators for univariate setvalued functions with general compact images. We adapt linear approximation methods for real-valued functions by replacing linear combinations of numbers with new metric linear combinations of finite sequences of compact sets, thus obtaining ”metric analogues” operators for set-valued functions. The new metric linear combination extends the binary metric average of Artstein. Approximation estimates for the metric analogue operators are derived. As examples we study metric Bernstein operators, metric Shoenberg operators and metric polynomial interpolants.
منابع مشابه
Weighted composition operators between Lipschitz algebras of complex-valued bounded functions
In this paper, we study weighted composition operators between Lipschitz algebras of complex-valued bounded functions on metric spaces, not necessarily compact. We give necessary and sufficient conditions for the injectivity and the surjectivity of these operators. We also obtain sufficient and necessary conditions for a weighted composition operator between these spaces to be compact.
متن کاملCompact composition operators on real Banach spaces of complex-valued bounded Lipschitz functions
We characterize compact composition operators on real Banach spaces of complex-valued bounded Lipschitz functions on metric spaces, not necessarily compact, with Lipschitz involutions and determine their spectra.
متن کاملSome local fixed point results under $C$-class functions with applications to coupled elliptic systems
The main objective of the paper is to state newly fixed point theorems for set-valued mappings in the framework of 0-complete partial metric spaces which speak about a location of a fixed point with respect to an initial value of the set-valued mapping by using some $C$-class functions. The results proved herein generalize, modify and unify some recent results of the existing literature. As an ...
متن کاملApproximations of Set-Valued Functions Based on the Metric Average
This paper investigates the approximation of set-valued functions with compact images (not necessarily convex), by adaptations of the Schoenberg spline operators and the Bernstein polynomial operators. When replacing the sum between numbers in these operators, by the Minkowski sum between sets, the resulting operators approximate only set valued functions with compact-convex images [10]. To obt...
متن کاملApproximation of Set-valued Functions with Compact Images—an Overview
Continuous set-valued functions with convex images can be approximated by known positive operators of approximation, such as the Bernstein polynomial operators and the Schoenberg spline operators, with the usual sum between numbers replaced by the Minkowski sum of sets. Yet these operators fail to approximate set-valued functions with general sets as images. The Bernstein operators with growing...
متن کامل