Quantitative approximation by shift invariant multivariate sublinear-Choquet operators
Abstract
A very general multivariate positive sublinear Choquet integral type operator is given through a convolution-like iteration of another multivariate general positive sublinear operator with a multivariate scaling type function. For it, sufficient conditions are given for shift invariance, preservation of global smoothness, convergence to the unit with rates. Furthermore, two examples of very general multivariate specialized operators are presented fulfilling all the above properties; the higher order of multivariate approximation of these operators is also studied.
A Appendix
Let
We observe (for any
Therefore, it holds the multivariate global smoothness preservation property
References
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© 2018 Walter de Gruyter GmbH, Berlin/Boston
Articles in the same Issue
- Frontmatter
- Quantitative approximation by shift invariant multivariate sublinear-Choquet operators
- Periodic solutions for periodic second-order differential equations with variable potentials
- Oscillatory behavior of higher order nonlinear homogeneous neutral delay dynamic equations with positive and negative coefficients
- Non-Archimedean hyperstability of Cauchy–Jensen functional equations on a restricted domain
- Koebe domains for the class of typically real functions that are convex in two directions
- Some variational principles associated with ODEs of maximal symmetry. Part 2: The general case
- Composite relaxed resolvent operator and Yosida approximation operator for solving a system of Yosida inclusions
- Multiple values and unicity problem of meromorphic mappings sharing different families of moving hyperplanes
- Generalization of different type integral inequalities for generalized (𝑠, 𝑚)-preinvex Godunova–Levin functions
- On the multiobjective control problem
- Fuzzy 𝛿-𝐼-continuity in mixed fuzzy ideal topological spaces
Articles in the same Issue
- Frontmatter
- Quantitative approximation by shift invariant multivariate sublinear-Choquet operators
- Periodic solutions for periodic second-order differential equations with variable potentials
- Oscillatory behavior of higher order nonlinear homogeneous neutral delay dynamic equations with positive and negative coefficients
- Non-Archimedean hyperstability of Cauchy–Jensen functional equations on a restricted domain
- Koebe domains for the class of typically real functions that are convex in two directions
- Some variational principles associated with ODEs of maximal symmetry. Part 2: The general case
- Composite relaxed resolvent operator and Yosida approximation operator for solving a system of Yosida inclusions
- Multiple values and unicity problem of meromorphic mappings sharing different families of moving hyperplanes
- Generalization of different type integral inequalities for generalized (𝑠, 𝑚)-preinvex Godunova–Levin functions
- On the multiobjective control problem
- Fuzzy 𝛿-𝐼-continuity in mixed fuzzy ideal topological spaces
