Let T be a periodic time scale. We use a fixed point theorem due to Krasnoselskii to show that the nonlinear neutral dynamic equation with infinite delay x(t) = −a(t)x(t) + (Q(t, x(t− g(t))))) + ∫ t −∞ D (t, u) f (x(u)) ∆u, t ∈ T, has a periodic solution. Under a slightly more stringent inequality we show that the periodic solution is unique using the contraction mapping principle. Also, by the...

Let T be a periodic time scale. We use a fixed point theorem due to Krasnosel’skĭı to show that the nonlinear neutral dynamic equation with delay x(t) = −a(t)x(t) + (Q(t, x(t), x(t− g(t))))) +G ` t, x(t), x(t− g(t)) ́ , t ∈ T, has a periodic solution. Under a slightly more stringent inequality we show that the periodic solution is unique using the contraction mapping principle. Also, by the aid ...

Abstract We show the theory of formal ultradifferentiable normalization. The tools utilized here are KAM methods and Contraction Mapping Principle in Banach space fixed with weighted norms.

In a fuzzy metric space (X;M; *), where * is a continuous t-norm,a locally fuzzy contraction mapping is de ned. It is proved that any locally fuzzy contraction mapping is a global fuzzy contractive. Also, if f satis es the locally fuzzy contractivity condition then it satis es the global fuzzy contrac-tivity condition.    

in this paper, we establish and prove the existence of best proximity points for multivalued cyclic $f$- contraction mappings in complete metric spaces. our results improve and extend various results in literature.

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

The aim of this paper is to propose a new generalization metric space which may open framework. As an application, we consider the analog Banach contraction mapping principle that works properly.

In this paper, we study some common fixed point results for weakly compatible mapping satisfying Generalized Contraction Principle in G-metric space by using a control function.

We discuss about the generalized $F$-contraction mappings in partially ordered metric spaces. For this, we first introduce the notion of ordered weakly $F$-contraction mapping. We also present some fixed point results about this type of mapping in partially ordered metric spaces. Next, we introduce the notion of $acute{mathrm{C}}$iri$acute{mathrm{c}}$ type generalized ordered weakly $F$-contrac...