We introduce new general iterative approximation methods for finding a common fixed point of a countable family of nonexpansive mappings. Strong convergence theorems are established in the framework of reflexive Banach spaces which admit a weakly continuous duality mapping. Finally, we apply our results to solve the the equilibrium problems and the problem of finding a zero of an accretive oper...

We have conclusively established the duality between noncommutative Maxwell-Chern-Simons theory and Self-Dual model, the latter in ordinary spacetime, to the first non-trivial order in the noncommutativity parameter θ , with θ = 0. This shows that the former theory is free for marginally noncommutative spacetimes. A θ-generalized covariant mapping between the variables of the two models in ques...

A class of mathematical dualities have played a central role in mapping states in gauge theory to states in the spacetime string theory dual. This includes the classical Schur-Weyl duality between symmetric groups and Unitary groups, as well as generalisations involving Brauer and Hecke algebras. The physical string dualities involved include examples from the AdS/CFT correspondence as well as ...

Abstract. In this paper we derive by means of the duality theory necessary and sufficient optimality conditions for convex optimization problems having as objective function the composition of a convex function and a linear continuous mapping defined on a separated locally convex space with values in an finitedimensional space. We use the general results for deriving optimality conditions for t...

We use the duality between compactly supported cohomology of the associative graph complex and the cohomology of the mapping class group to show that the duals of the Kontsevich cycles [Wλ] correspond to polynomials in the Miller-Morita-Mumford classes. We also compute the coefficients of the first two terms of this polynomial. This extends the results of [Igu], giving a more detailed answer to...

We have conclusively established the duality between noncommutative Maxwell-Chern-Simons theory and Self-Dual model, the latter in ordinary spacetime, to the first non-trivial order in the noncommutativity parameter, θ , with θ = 0. This shows that the former theory is free. A θ-generalized covariant mapping between the variables of the two models in question has been derived explicitly, that c...

The Swampland Program aims to address the question, "when does an effective field theory model of quantum gravity have ultraviolet complete embedding in string theory?", and can be regarded as a bottom-up approach investigations gravity. An alternative top-down aim explore imprints constraints imposed by dualities symmetries on representations most celebrated example this is mirror symmetry. Mi...

Convexity theory and duality theory are important issues in math- ematical programming. Within the framework of credibility theory, this paper rst introduces the concept of convex fuzzy variables and some basic criteria. Furthermore, a convexity theorem for fuzzy chance constrained programming is proved by adding some convexity conditions on the objective and constraint functions. Finally,...

A continuum version of the vortex-boson duality in (3+1) dimensions is formulated and its implications studied in the context of a pair Wigner crystal in underdoped cuprate super-conductors. The dual theory to a phase fluctuating superconductor (or superfluid) is shown to be a theory of bosonic strings interacting through a Kalb-Ramond rank-2 tensorial gauge field. String condensation produces ...

Symmetry-breaking phase transitions are an example of non-equilibrium processes that require real-time treatment, a major challenge in strongly coupled systems without long-lived quasiparticles. Holographic duality provides such an approach by mapping strongly coupled field theories in D dimensions into weakly coupled quantum gravity in D+1 anti-de Sitter spacetime. Here we use holographic dual...