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

The paper is a natural continuation and generalization of the works of Fesenko and of the authors. Fesenko’s theory is carried over to infinite APF Galois extensions L over a local field K with a finite residue-class field κK of q = p f elements, satisfying μp(K) ⊂ K and K ⊂ L ⊂ Kφd , where the residue-class degree [κL : κK ] is equal to d. More precisely, for such extensions L/K and a fixed Lu...

We note that Theorem 2.3 [1] is a consequence of the same theorem for one map.

(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...

In this paper, new concepts of monotonicity, namely (Φ, ρ)-monotonicity, (Φ, ρ)-pseudo-monotonicity and (Φ, ρ)-quasi-monotonicityare introduced for functions defined in Banach spaces. Series of necessary conditions are also given that relate (Φ, ρ)-invexity and generalized (Φ, ρ)-invexity of the function with (Φ, ρ)monotonicity and generalized (Φ, ρ)-monotonicity of its gradient.

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...

Given an affine surjection of polytopes : P ! Q, the Generalized Baues Problem asks whether the poset of all proper polyhedral subdivisions of Q which are induced by the map has the homotopy type of a sphere. We extend earlier work of the last two authors on subdivisions of cyclic polytopes to give an affirmative answer to the problem for the natural surjections between cyclic polytopes : C(n; ...

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.

We present some fixed point results for mappings which satisfy Hardy–Rogers rational type, quasicontraction type, weak contraction type and generalized fψ type cyclic conditions in 0-complete partial metric spaces. Presented results generalize or improve many existing fixed point theorems in the literature. To demonstrate our results, we give throughout the paper some examples. One of the possi...

In this paper, we prove some common fixed point theorems for co-cyclic weak contractions in compact metric spaces. Keywords—Cyclic weak contraction, Co-cyclic weak contraction, Co-cyclic representation, Common fixed point.