Maximal Monotone Inclusions and Fitzpatrick Functions

2015 ◽  
Vol 171 (3) ◽  
pp. 757-784 ◽  
Author(s):  
J. M. Borwein ◽  
J. Dutta
Symmetry ◽  
2020 ◽  
Vol 12 (9) ◽  
pp. 1456
Author(s):  
Aviv Gibali ◽  
Yekini Shehu

The forward–backward–forward (FBF) splitting method is a popular iterative procedure for finding zeros of the sum of maximal monotone and Lipschitz continuous monotone operators. In this paper, we introduce a forward–backward–forward splitting method with reflection steps (symmetric) in real Hilbert spaces. Weak and strong convergence analyses of the proposed method are established under suitable assumptions. Moreover, a linear convergence rate of an inertial modified forward–backward–forward splitting method is also presented.


2013 ◽  
Vol 43 (1) ◽  
pp. 119-130
Author(s):  
Declan William Kavanagh

This essay argues that the work of a lesser-known mid-eighteenth-century satirist Charles Churchill (1731–1764) provides a rich literary source for queer historical considerations of the conflation of xenophobia with effeminophobia in colonial imaginings of Ireland. This article analyzes Churchill's verse-satire The Rosciad (1761) through a queer lens in order to reengage the complex history of queer figurations of Ireland and the Irish within the British popular imagination. In the eighth edition of The Rosciad – a popular and controversial survey of London's contemporary players – Churchill portrays the Irish actor Thady Fitzpatrick as an effeminate fribble, before championing the manly acting abilities of the English actor David Garrick. The phobic attack on Fitzpatrick in The Rosciad is a direct response to Fitzpatrick's involvement in the ‘Fitzgiggo’ riots of January 1763 at the Drury Lane and Covent-Garden theatres. While Churchill's lampooning of the actor recalls Garrick's earlier satirizing of Fitzpatrick as a fribble in The Fribbleriad (1741) and Miss in her Teens (1747), The Rosciad is unique in its explicit conflation of androgyny with ethnicity through Irish classification. The portraiture of Fitzpatrick functions, alongside interrelated axes of ethnicity, class and gender, to prohibit access to a ‘normative’ middle-class English identity, figured through the ‘manly’ theatrical sensibility of the poem's hero, Garrick. Moreover, in celebrating a ‘Truly British Age’, the poem privileges English female players, in essentialist and curiously de-eroticized terms, as ‘natural’ though flawed performers. By analyzing Churchill's phobic juxtaposition of Garrick and the female players against the Irish fribble, this article evinces how mid-century discourses of effeminacy were also instrumental in enforcing racial taxonomies.


Mathematics ◽  
2020 ◽  
Vol 8 (9) ◽  
pp. 1395
Author(s):  
Charles Castaing ◽  
Christiane Godet-Thobie ◽  
Le Xuan Truong

This paper is devoted to the study of evolution problems involving fractional flow and time and state dependent maximal monotone operator which is absolutely continuous in variation with respect to the Vladimirov’s pseudo distance. In a first part, we solve a second order problem and give an application to sweeping process. In a second part, we study a class of fractional order problem driven by a time and state dependent maximal monotone operator with a Lipschitz perturbation in a separable Hilbert space. In the last part, we establish a Filippov theorem and a relaxation variant for fractional differential inclusion in a separable Banach space. In every part, some variants and applications are presented.


2019 ◽  
Vol 80 (3) ◽  
pp. 665-678 ◽  
Author(s):  
Ernö Robert Csetnek ◽  
Yura Malitsky ◽  
Matthew K. Tam
Keyword(s):  

2001 ◽  
Vol 25 (4) ◽  
pp. 273-287 ◽  
Author(s):  
A. Addou ◽  
B. Mermri

We are interested in constructing a topological degree for operators of the formF=L+A+S, whereLis a linear densely defined maximal monotone map,Ais a bounded maximal monotone operators, andSis a bounded demicontinuous map of class(S+)with respect to the domain ofL. By means of this topological degree we prove an existence result that will be applied to give a new formulation of a parabolic variational inequality problem.


2018 ◽  
Vol 2018 ◽  
pp. 1-10 ◽  
Author(s):  
Teffera M. Asfaw

LetXbe a real locally uniformly convex reflexive Banach space with locally uniformly convex dual spaceX⁎. LetT:X⊇D(T)→2X⁎be a maximal monotone operator andC:X⊇D(C)→X⁎be bounded and continuous withD(T)⊆D(C). The paper provides new existence theorems concerning solvability of inclusion problems involving operators of the typeT+Cprovided thatCis compact orTis of compact resolvents under weak boundary condition. The Nagumo degree mapping and homotopy invariance results are employed. The paper presents existence results under the weakest coercivity condition onT+C. The operatorCis neither required to be defined everywhere nor required to be pseudomonotone type. The results are applied to prove existence of solution for nonlinear variational inequality problems.


Sign in / Sign up

Export Citation Format

Share Document