Results 231 to 240 of about 59,918 (272)

Operator Inequalities Involving Operator Monotone Functions

2021
In this chapter, we gather improvements of known operator inequalities involving positive linear maps, geometric means, operator monotone functions, and doubly concave functions. We note that these types of operator inequalities have essential applications in the theory of functional equations in non-euclidean geometry.
Mohammad Bagher Ghaemi, Nahid Gharakhanlu, Themistocles M. Rassias, Reza Saadati   +3 more
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Cyclical monotonicity of maximal monotone step operators

Boletim da Sociedade Brasileira de Matemática, 1982
Let X and Y be two locally convex Hausdorff topological vector spaces paired by a bilinear form \(\). A multimapping \(T: X\to 2^ y\) is said to be a locally step operator if each \(x\in X\) has a neighborhood U such that \(\{Ty\}_{y\in U}\) is a finite family of sets, that is, if locally T takes a finite number of set values.
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Homogenization of monotone operators

Nonlinear Analysis: Theory, Methods & Applications, 1990
The authors deal with the homogenization of a sequence of nonlinear monotone operators \({\mathcal A}_ a: H_ 0^{1,p}(\Omega)\to H^{- 1,q}(\Omega)\) of the form \({\mathcal A}_ nu=-div(a(x/\epsilon_ n,Du))\). We prove a representation formula for the homogenized operator under the assumptions that \(a=a(y,\xi)\) is periodic in y, maximal monotone in ...
V. Chaido Piat, Defranceschi, Anneliese
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Pictures of monotone operators

Set-Valued Analysis, 1996
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Monotonicity versus Non-Monotonicity in Random Operators

1999
The past two decades have brought widespread interest and a large number of publications in the mathematical theory of random operators. While this has lead to many deep results and considerable mathematical insights, there are still important open problems which are far from being solved.
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Operator Monotone and Operator Convex Functions

1997
In this chapter we study an important and useful class of functions called operator monotone functions. These are real functions whose extensions to Hermitian matrices preserve order. Such functions have several special properties, some of which are studied in this chapter. They are closely related to properties of operator convex functions.
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Sums of Monotone Operators

2011
The sum of two monotone operators is monotone. However, maximal monotonicity of the sum of two maximally monotone operators is not automatic and requires additional assumptions. In this chapter, we provide flexible sufficient conditions for maximality. Under additional assumptions, conclusions can be drawn about the range of the sum, which is important
Heinz H. Bauschke, Patrick L. Combettes
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Monotone Operators

2021
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Homogenization of Monotone Operators

2009
Although Eduardo ZARANTONELLO first introduced monotone operators for solving a problem in continuum mechanics,1 the theory of monotone operators quickly became taught as a part of functional analysis. In his course on nonlinear partial differential equations in the late 1960s, Jacques-Louis LIONS taught about a dichotomy, the compactness method, and ...
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Monotone and Accretive Operators

1985
So far we have mainly been concerned with existence of solutions to F x = y in some Banach space X, using compactness arguments. Now we also study uniqueness, using monotonicity arguments.
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