*Correspondence: [email protected] 3Department of Mathematics, GDCW, Bosan Road, Multan, Pakistan Full list of author information is available at the end of the article Abstract In this paper, we first introduce a cyclic generalized contraction map in metric spaces and give an existence result for a best proximity point of such mappings in the setting of a uniformly convex Banach space. Then we...

We consider valued fields with a distinguished contractive map as valued modules over the Ore ring of difference operators. We prove quantifier elimination for separably closed valued fields with the Frobenius map, in the pure module language augmented with functions yielding components for a p-basis and a chain of subgroups indexed by the valuation group.

     Dx(t) + f(t, x(t), x(t)) = 0, t ∈ (0, 1), x(0) = ∫ 1 0 g0(s, x(s))ds, x(1) = ∫ 1 0 g1(s, x(s))ds, x(0) = 0, k = 2, 3, · · · , [α]− 1. By means of the Banach contraction mapping principle, some new results on the existence and uniqueness are obtained. It is interesting to note that the sufficient conditions for the existence and uniqueness of solutions are dependent on the order α.

I provide a new proof of uniqueness of equilibrium in a wide class of global games. I show that the joint best-response in these games is a contraction. The uniqueness result then follows as a corollary of the contraction property. Furthermore, the contraction mapping approach provides a revealing intuition for why uniqueness arises: Complementarities in games generate multiplicity of equilibri...

It is shown that if P is a weak∗-continuous contractive projection on a JBW∗-triple M , then P(M) is of type I or semifinite, respectively, if M is of the corresponding type. We also show that P(M) has no infinite spin part if M is a type I von Neumann algebra.  2002 Elsevier Science (USA). All rights reserved.

We show that the range of a contractive projection on a Lebesgue-Bochner space of Hilbert valued functions Lp(H) is isometric to a p-direct sum of Hilbertvalued Lp-spaces. We explicit the structure of contractive projections. As a consequence for every 1 < p < ∞ the class Cp of p-direct sums of Hilbertvalued Lp-spaces is axiomatizable (in the class of all Banach spaces).

We shall prove the existence and uniqueness theorem of a solution to the nonlocal fuzzy differential equation using the contraction mapping principle. Ams Mathematics Subject Classification : 94D05, 34C27

*Correspondence: [email protected] 3Department of Mathematics, Kano University of Science and Technology, P.M.B. 3042, Wudil, Kano, Nigeria Full list of author information is available at the end of the article Abstract In this paper, we introduce the notion of cyclic R-contraction mapping and then study the existence of fixed points for such mappings in the framework of metric spaces. Examples ...

Abstract We study difference equations which arise as discrete approximations to three-point boundary value problems for systems of first-order ordinary differential equations. We obtain new results of the existence of solutions to the discrete problem by employing Euler’s method. The existence of solutions are proven by the contraction mapping theorem and the Brouwer fixed point theorem in Euc...

Abstract—In this paper, a class of generalized bi-directional associative memory (BAM) neural networks with mixed delays is investigated. On the basis of Lyapunov stability theory and contraction mapping theorem, some new sufficient conditions are established for the existence and uniqueness and globally exponential stability of equilibrium, which generalize and improve the previously known res...