Existence of fixed point and best proximity point of p-cyclic orbital phi-contraction map

In this manuscript, p-cyclic orbital ϕ-contraction map over closed, nonempty, convex subsets of a uniformly convex Banach space X possesses a unique best proximity point if the auxiliary function ϕ is strictly increasing. The given result unifies and extend some existing results in the related literature. We provide an illustrative example to indicate the validity of the observed result.

Exponential Stability Analysis and Application of Parameters Switched Neural Networks Via Intermittent Observation and Feedback Control

This paper deals with a type of the exponential stability problem for the switched neural networks with timevarying delays driven by Brownian noise. As a prerequisite to main theorem, the existence and uniqueness of the solution to the main system are proved via contraction map theory. Based on intermittent observation control, the stability trajectory of the switched neural networks with time-varying delays is obtained. Employing stochastic analysis method, the exponential stability conditions are established via applying It^o formula and the matched pair technique. A numerical example for the main system with respect to intermittent observation control is provided to illustrate the effectiveness of results and potential of the proposed techniques. Meanwhile, the feasibility of stability control in multiagents system is verified by the method obtained.

On the existence problem for a fixed point of a generalized contracting multivalued mapping

We discuss the still unresolved question, posed in [S. Reich, Some Fixed Point Problems, Atti Accad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Natur., 57:8 (1974), 194–198], of existence in a complete metric space X of a fixed point for a generalized contracting multivalued map Φ: X⇉X having closed values Φ(x)⊂X for all x∈X. Generalized contraction is understood as a natural extension of the Browder–Krasnoselsky definition of this property to multivalued maps: ∀x,u∈X h(φ(x),φ(u))≤ η(ρ(x,u)), where the function η:R_+→R_+ is increasing, right continuous, and for all d>0, η(d)<d (h(•,•) denotes the Hausdorff distance between sets in the space X). We give an outline of the statements obtained in the literature that solve the S. Reich problem with additional requirements on the generalized contraction Φ. In the simplest case, when the multivalued generalized contraction map Φ acts in R, without any additional conditions, we prove the existence of a fixed point for this map.

Construction and Simulation of Composite Measures and Condensation Model for Designing Probabilistic Computational Applications

The probabilistic algorithms are widely applied in designing computational applications such as distributed systems and probabilistic databases, to determine distributed consensus in the presence of random failures of nodes or networks. In distributed computing, symmetry breaking is performed by employing probabilistic algorithms. In general, probabilistic symmetry breaking without any bias is preferred. Thus, the designing of randomized and probabilistic algorithms requires modeling of associated probability spaces to generate control-inputs. It is required that discrete measures in such spaces are computable and tractable in nature. This paper proposes the construction of composite discrete measures in real as well as complex metric spaces. The measures are constructed on different varieties of continuous smooth curves having distinctive non-linear profiles. The compositions of discrete measures consider arbitrary functions within metric spaces. The measures are constructed on 1-D interval and 2-D surfaces and, the corresponding probability metric product is defined. The associated sigma algebraic properties are formulated. The condensation measure of the uniform contraction map is constructed as axioms. The computational evaluations of the proposed composite set of measures are presented.

The Geometric Structure of Symplectic Contraction

We show that the symplectic contraction map of Hilgert–Manon–Martens [9], a symplectic version of Popov’s horospherical contraction, is simply the quotient of a Hamiltonian manifold $M$ by a “stratified null foliation” that is determined by the group action and moment map. We also show that the quotient differential structure on the symplectic contraction of $M$ supports a Poisson bracket. We end by proving a very general description of the topology of fibers of Gelfand–Zeitlin (also spelled Gelfand–Tsetlin or Gelfand–Cetlin) systems on multiplicity-free Hamiltonian $U(n)$ and $SO(n)$ manifolds.

Uniqueness of solution for higher-order fractional differential equations with conjugate type integral conditions

In this article, we prove the existence and uniqueness of solution for some higher-order fractional differential equations with conjugate type integral conditions. The interesting point lies in that the Lipschitz constant is closely associated with the first eigenvalues corresponding to the relevant linear operator. The discussion is based on the Banach contraction map principle and the theory of

Error estimates for approximating best proximity points for cyclic contractive maps

We find a priori and a posteriori error estimates of the best proximity point for the Picard iteration associated to a cyclic contraction map, which is defined on a uniformly convex Banach space with modulus of convexity of power type.

pg-Extensions and p-Extensions with applications to C(X)

Essential extensions and p-extensions have been studied for commutative rings with identity in various papers, such as [P. Bhattacharjee, M. L. Knox and W. Wm. McGovern, p-Extensions, Proceedings for the OSU-Denison Conference, AMS series Contemporary Mathematics Series (to appear); p-Embeddings, Topology Appl. 160(13) (2013) 1566–1576; R. M. Raphael, Algebraic Extensions of Commutative Regular Rings, Canad. J. Math. 22(6) (1970) 1133–1155]. The present paper applies these concepts to certain subrings of C(X). Moreover, the paper introduces a new ring extension, called a pg-extension, and determines its relation to both essential extension and p-extension. It turns out that the pg-extension R ↪ S induces a well-defined contraction map between principal ideals [Formula: see text] and [Formula: see text].

ON A CLASS OF ELLIPTIC SYSTEM OF SCHRÖDINGER–POISSON TYPE

In this paper we prove existence and qualitative properties of solutions for a nonlinear elliptic system arising from the coupling of the nonlinear Schrödinger equation with the Poisson equation. We use a contraction map approach together with estimates of the Bessel potential used to rewrite the system in an integral form.