Fitzpatrick transform of monotone relations in Hadamard spaces

AbstractIn the present paper, monotone relations and maximal monotone relations from an Hadamard space to its linear dual space are investigated. Fitzpatrick transform of monotone relations in Hadamard spaces is introduced. It is shown that Fitzpatrick transform of a special class of monotone relations is proper, convex and lower semi-continuous. Finally, a representation result for monotone relations is given.

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Bregmanf-Projection Operator with Applications to Variational Inequalities in Banach Spaces

Abstract and Applied Analysis ◽

10.1155/2014/594285 ◽

2014 ◽

Vol 2014 ◽

pp. 1-10 ◽

Cited By ~ 1

Author(s):

Chin-Tzong Pang ◽

Eskandar Naraghirad ◽

Ching-Feng Wen

Keyword(s):

Banach Space ◽

Variational Inequalities ◽

Banach Spaces ◽

Projection Operator ◽

Dual Space ◽

Reflexive Banach Space ◽

Lower Semicontinuous ◽

Existence Of A Solution ◽

Bregman Functions ◽

Proper Convex

Using Bregman functions, we introduce the new concept of Bregman generalizedf-projection operatorProjCf, g:E*→C, whereEis a reflexive Banach space with dual spaceE*; f: E→ℝ∪+∞is a proper, convex, lower semicontinuous and bounded from below function;g: E→ℝis a strictly convex and Gâteaux differentiable function; andCis a nonempty, closed, and convex subset ofE. The existence of a solution for a class of variational inequalities in Banach spaces is presented.

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Nonlinear random equations with maximal monotone operators in Banach spaces

Mathematical Proceedings of the Cambridge Philosophical Society ◽

10.1017/s0305004100063726 ◽

1985 ◽

Vol 98 (3) ◽

pp. 529-532 ◽

Cited By ~ 1

Author(s):

Dimitrios Kravvaritis

Keyword(s):

Banach Space ◽

Dual Space ◽

Real Banach Space ◽

Maximal Monotone ◽

Maximal Monotone Operators ◽

Monotone Operators ◽

Measurable Space ◽

Random Operator ◽

Image Position ◽

Monotone Type

Let X be a real Banach space, X* its dual space and ω a measurable space. Let D be a subset of X, L: Ω × D → X* a random operator and η:Ω →X* a measurable mapping. The random equation corresponding to the double [L, η] asks for a measurable mapping ξ: Ω → D such thatRandom equations with operators of monotone type have been studied recentely by Kannan and Salehi [7], Itoh [6] and Kravvarits [8].

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Support Points of the Class of Close-to-Convex Functions

Canadian Mathematical Bulletin ◽

10.4153/cmb-1976-027-8 ◽

1976 ◽

Vol 19 (2) ◽

pp. 177-179 ◽

Cited By ~ 3

Author(s):

E. Grassmann ◽

W. Hengartner ◽

G. Schober

Keyword(s):

Linear Space ◽

Convex Functions ◽

Dual Space ◽

Convex Combination ◽

Holomorphic Functions ◽

Support Point ◽

The Other ◽

Support Points ◽

Proper Convex ◽

Compact Convergence

Let H(U) be the linear space of holomorphic functions on U = {z:|z|<1} endowed with the topology of compact convergence, and denote by H′(U) its topological dual space. Let be a compact subset of H(U) and ƒ∈F. We say ƒ is a support point of if there exists an L∈H'(U), non-constant on , such that On the other hand, ƒ is an extreme point of if ƒ is not a proper convex combination of two other points of .

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Monotone relations in Hadamard spaces

Filomat ◽

10.2298/fil1919347m ◽

2019 ◽

Vol 33 (19) ◽

pp. 6347-6358

Author(s):

Ali Moslemipour ◽

Mehdi Roohi ◽

Mohammad Mardanbeigi ◽

Mahdi Azhini

Keyword(s):

Dual Space ◽

Hadamard Space ◽

Characterization Result

In this paper, the notion of W-property for subsets of X x X? is introduced and investigated, where X is an Hadamard space and X? is its linear dual space. It is shown that an Hadamard space X is flat if and only if X x X? has W-property. Moreover, the notion of monotone relation from an Hadamard space to its linear dual space is introduced. A characterization result for monotone relations with W-property (and hence in flat Hadamard spaces) is given. Finally, a type of Debrunner-Flor Lemma concerning extension of monotone relations in Hadamard spaces is proved.

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A subdifferential characterisation of Banach spaces with the Radon–Nikodym property

Bulletin of the Australian Mathematical Society ◽

10.1017/s0004972700040156 ◽

2002 ◽

Vol 66 (2) ◽

pp. 313-316 ◽

Cited By ~ 7

Author(s):

J. R. Giles

Keyword(s):

Banach Space ◽

Banach Spaces ◽

Dual Space ◽

Natural Embedding ◽

Lower Semi ◽

Nikodym Property

A Banach space has the Radon–Nikodym Property if and only if every continuous weak* lower semi–continuous gauge on the dual space has a point of its domain where its subdifferential is contained in the natural embedding.

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