The aim of the present paper is to establish a common fixed point theorem for sequence of self mappings under (φ, ψ)-weak contractions in fuzzy metric space employing the control function which generalizes and improves various well-known comparable results.

Let X be a topological space and let Φ ⊂ C(X). Then there exists a topological space Y containing X as a subspace and such that Φ = C(Y )|X, if and only if Φ is weakly composition closed, i.e., for any index set I, any fi ∈ Φ (i ∈ I) and any continuous map k : R → R we have k ◦ 〈fi〉 ∈ Φ, where 〈fi〉 : X → R is the map with i-th coordinate fi. The analogous statement is valid for functions to any...

Let A and B be Banach algebras with bounded approximate identities let Φ:A→B a surjective continuous linear map which preserves two-sided zero products (i.e., Φ(a)Φ(b)=Φ(b)Φ(a)=0 whenever ab=ba=0). We show that Φ is weighted Jordan homomorphism provided product determined weakly amenable. These conditions are in particular fulfilled when the group algebra L1(G) G any locally compact group. also...

In this paper, we prove fixed point theorem for φ − H contraction in fuzzy metric space in sense of George and Veeramani.

For any n-dimensional compact spin Riemannian manifold M with a given spin structure and a spinor bundle ΣM , and any compact Riemannian manifold N , we show an ǫ-regularity theorem for weakly Dirac-harmonic maps (φ, ψ) : M ⊗ΣM → N ⊗ φ∗TN . As a consequence, any weakly Dirac-harmonic map is proven to be smooth when n = 2. A weak convergence theorem for approximate Dirac-harmonic maps is establi...

We construct finite time blow-up solutions to the 2-dimensional harmonic map flow into the sphere S2, ut = ∆u+ |∇u|u in Ω× (0, T ) u = φ on ∂Ω× (0, T ) u(·, 0) = u0 in Ω, where Ω is a bounded, smooth domain in R2, u : Ω×(0, T ) → S2, u0 : Ω̄ → S2 is smooth, and φ = u0 ∣∣ ∂Ω . Given any points q1, . . . , qk in the domain, we find initial and boundary data so that the solution blows-up precisely ...

(ii) Denote this map by φ, which is induced by the compositions with εi : Xi ↪→ ⊔ j Xj , i ∈ I. If φ(fi) = φ(gj) for some fi ∈ Hom(Y,Xi) and gj ∈ Hom(Y,Xj), then we must have i = j because φ(fi) and φ(gj) have the same image. Since φ(fi) = εi ◦ fi, φ(gi) = εi ◦ gi and εi is an injective map, we deduce that fi(y) = gi(y), ∀y ∈ Y , i.e. fi = gi. (iii) This map is induced by the composition with t...

The well-known Banach’s fixed point theorem asserts that ifD X, f is contractive and X, d is complete, then f has a unique fixed point inX. It is well known that the Banach contraction principle 1 is a very useful and classical tool in nonlinear analysis. In 1969, Boyd and Wong 2 introduced the notion ofΦ-contraction. A mapping f : X → X on a metric space is called Φ-contraction if there exists...

In this paper, we shall generalize the definition of (φ− k) −B contraction to multi-valued mappings which was presented before in single valued case by Mihet. Then we shall prove two fixed point theorems for multi-valued (φ− k) − B contraction mappings in probabilistic metric space.