Series representations in spaces of vector‐valued functions via Schauder decompositions
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DOI: 10.1002/mana.201900172
Abstract: It is a classical result that every C ‐valued holomorphic function has a local power series representation. This even remains true for holomorphic functions with values in a locally complete locally convex Hausdorff space E… read more here.
Keywords: locally convex; series; valued functions; schauder decompositions ... See more keywords
Weak limit of iterates of some random-valued functions and its application
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DOI: 10.1007/s00010-019-00650-z
Abstract: Given a probability space $$ (\Omega , {\mathcal {A}}, P) $$ ( Ω , A , P ) , a complete and separable metric space X with the $$ \sigma $$ σ -algebra $$ {\mathcal… read more here.
Keywords: random valued; valued functions; iterates random; limit iterates ... See more keywords
The abstract Dirichlet problem for continuous vector-valued functions
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DOI: 10.1007/s00013-016-1015-y
Abstract: Let X be a simplex with the set $${\text {ext}}\, X$$extX of extreme points being Lindelöf. We show that a continuous bounded mapping defined on $${\text {ext}}\, X$$extX with values in a Fréchet space F… read more here.
Keywords: dirichlet problem; continuous vector; vector valued; abstract dirichlet ... See more keywords
The Metric Integral of Set-Valued Functions
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DOI: 10.1007/s11228-017-0403-1
Abstract: This paper introduces a new integral of univariate set-valued functions of bounded variation with compact images in ℝd${\mathbb {R}}^d$. The new integral, termed the metric integral, is defined using metric linear combinations of sets and… read more here.
Keywords: integral set; metric integral; valued functions; set valued ... See more keywords
Interpolation sets in spaces of continuous metric-valued functions
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DOI: 10.1016/j.jmaa.2018.06.053
Abstract: Let $X$ and $M$ be a topological space and metric space, respectively. If $C(X,M)$ denotes the set of all continuous functions from X to M, we say that a subset $Y$ of $X$ is an… read more here.
Keywords: interpolation sets; continuous metric; metric valued; sets spaces ... See more keywords
Shift maps and their variants on inverse limits with set-valued functions
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DOI: 10.1016/j.topol.2018.02.015
Abstract: Abstract Inverse limit spaces of compacta with upper semi-continuous compact set-valued functions are studied via shift maps and their variants. We give a representation of such spaces as the limits of ordinary inverse sequences, which… read more here.
Keywords: shift maps; set valued; inverse limit; valued functions ... See more keywords
SINGULAR INTEGRALS SUPPORTED BY SUBVARIETIES FOR VECTOR-VALUED FUNCTIONS
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DOI: 10.1017/nmj.2017.13
Abstract: In this paper, we show that singular integrals supported by subvarieties are bounded on $L^{p}(\mathbb{R}^{n};\mathbf{X})$ for $1 read more here.
Keywords: integrals supported; singular integrals; subvarieties vector; vector valued ... See more keywords
Towards a Unified Framework of Matrix Derivatives
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DOI: 10.1109/access.2018.2867234
Abstract: The need of processing and analyzing massive statistics simultaneously requires the derivatives of matrix-to-scalar functions (scalar-valued functions of matrices) or matrix-to-matrix functions (matrix-valued functions of matrices). Although derivatives of a matrix-to-scalar function have already been… read more here.
Keywords: framework matrix; second approach; valued functions; approach ... See more keywords
Some Integral Inequalities for Log- $h$ -Convex Interval-Valued Functions
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DOI: 10.1109/access.2019.2925153
Abstract: We introduce the log- $h$ -convex concept for the interval-valued functions (IVFs) and establish some of the new Jensen’s, Hadamard’s, and Hadamard-Fejér’s inequalities for this kind of functions, which generalize some known results. Meanwhile, some… read more here.
Keywords: valued functions; inequalities log; interval valued; log convex ... See more keywords
Characterizing functions of n-uninorms with continuous underlying functions
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DOI: 10.1109/tfuzz.2021.3057231
Abstract: The characterizing set-valued functions were introduced for uninorms with continuous underlying functions and these set-valued functions were useful for the complete characterization of such uninorms. In this work we study the characterizing functions of n-uninorms… read more here.
Keywords: underlying functions; set valued; valued functions; continuous underlying ... See more keywords
Iq-Calculus and Iq-Hermite–Hadamard inequalities for interval-valued functions
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DOI: 10.1186/s13662-020-02902-8
Abstract: In this paper, we introduce the Iq-derivative and Iq-integral for interval-valued functions and give their basic properties. As a promotion of q-Hermite–Hadamard inequalities, we also give the Iq-Hermite-Hadamard inequalities for interval-valued functions. At the same time,… read more here.
Keywords: hermite hadamard; interval valued; valued functions; hadamard inequalities ... See more keywords