In this paper, we first present an impulsive version of Filippov’s Theorem for first-order neutral functional differential inclusions of the form, d dt [y(t)− g(t, yt)] ∈ F (t, yt), a.e. t ∈ J\{t1, . . . , tm}, y(t+k )− y(tk ) = Ik(y(tk )), k = 1, . . . , m, y(t) = φ(t), t ∈ [−r, 0], where J = [0, b], F is a set-valued map and g is a single-valued function. The functions Ik characterize the jum...

Let X be a Banach space and K a nonempty subset of X. The set K is called proximinal if for each x ∈ X, there exists an element y ∈ K such that ‖x − y‖ d x,K , where d x,K inf{‖x − z‖ : z ∈ K}. Let CB K , C K , P K , F T denote the family of nonempty closed bounded subsets, nonempty compact subsets, nonempty proximinal bounded subsets of K, and the set of fixed points, respectively. A multivalu...

According to semigroup theories and Sadovskii fixed point theorem, this paper is mainly concerned with the existence of solutions for an impulsive neutral differential and integrodifferential systems with nonlocal conditions in Banach spaces. As an application of this main theorem, a practical consequence is derived for the sub-linear growth case. In the end, an example is also given to show th...

Abstract: In this paper a logic suitable for reasoning disquotationally about truth, TJK, is presented and shown to have a standard model. This work improves on Hartry Field’s recent results establishing consistency and ω-consistency of truth-theories with strong conditional logics. A novel method utilising the Banach fixed point theorem for contracting functions on complete metric spaces is in...

Halpern and Huang recently showed that there are relevant directions in the space of interactions at the Gaussian fixed point. I show that their result can be derived from Polchinski's form of the Wilson renormalization group. The derivation shows that the existence of these directions is independent of the cutoff function used.

In this paper we establish the proof-theoretic equivalence of (i) ATR and c

Using holographic renormalization, we study correlation functions throughout a renormalization group flow between two-dimensional superconformal field theories. The ultraviolet theory is an N = (4, 4) CFT which can be thought of as a symmetric product of U(2) super WZW models. It is perturbed by a relevant operator which preserves one-quarter supersymmetry and drives the theory to an infrared f...

We introduce a notion of graph homeomorphisms which uses the concept of dimension and homotopy for graphs. It preserves the dimension of a subbasis, cohomology and Euler characteristic. Connectivity and homotopy look as in classical topology. The Brouwer-Lefshetz fixed point leads to the following discretiszation of the Kakutani fixed point theorem: any graph homeomorphism T with nonzero Lefsch...

In this paper, we study existence of mild solutions for a second order impulsive neutral functional differential equations with state-dependent delay. By using a fixed point theorem for condensing maps combined with theories of a strongly continuous cosine family of bounded linear operators, we prove the main existence theorems. As applications of these obtained results, some practical conseque...

Article history: Received 10 March 2015 Received in revised form 6 June 2015 Accepted 10 July 2015 Available online 14 July 2015 Editor: J. Hisano We propose a novel RG method to specify the location of the IR fixed point in lattice gauge theories and apply it to the SU(3) gauge theories with N f fundamental fermions. It is based on the scaling behavior of the propagator through the RG analysis...