in this paper we define weak $f$-contractions on a‎ ‎metric space into itself by extending $f$-contractions‎ ‎introduced by d‎. ‎wardowski (2012) and provide some fixed point‎ ‎results in complete metric spaces and in partially ordered complete ‎generalized metric spaces‎. ‎some relationships between weak‎ ‎$f$-contractions and $fi$-contractions are highlighted‎. ‎we also ‎give some application...

We give a new construction of cyclic homology of an associative algebra A that does not involve Connes’ differential. Our approach is based on an extended version of the complex Ω q A, of noncommutative differential forms on A, and is similar in spirit to the de Rham approach to equivariant cohomology. Indeed, our extended complex maps naturally to the equivariant de Rham complex of any represe...

The purpose of this study was to determine whether cyclic guanosine monophosphate inhibits contraction through inhibition of phosphatidylinositol hydrolysis. Sodium nitroprusside and atriopeptin II, agents which activate soluble and particulate guanylate cyclase, respectively, inhibited norepinephrine-induced contraction and accumulation of inositol monophosphate, a measure of phosphatidylinosi...

In this paper, we prove the existence and uniqueness of fixed points for cyclic (α,β)-admissible type F-contraction and F−weak contraction under the setting of modular spaces, where the modular is convex and satisfying the ∆2-condition. Later, we prove some periodic point results for self-mappings on a modular space. We also give some examples to s...

A positive integer n is called cyclic if there is a unique group of order n, which is necessarily cyclic. Using a characterisation of the cyclic integers as those n satisfying gcd(n, φ(n)) = 1, P. Erdős (1947) proved that the number of cyclic integers n ≤ x is asymptotic to z(x) = e−γ x log log log x , as x→∞, where γ is Euler’s constant. An ordered pair of integers (m,n) is called singular if ...

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.

Theorem 1.1 (Popa’s Cocycle Superrigity, Special Case). Let Γ be a discrete group with Kazhdan’s property (T), let Γ0 < Γ be an infinite index subgroup, (X0,μ0) an arbitrary probability space, and let Γ (X,μ) = (X0,μ0)0 be the corresponding generalized Bernoulli action. Then for any discrete countable group Λ and any measurable cocycle α : Γ × X → Λ there exist a homomorphism : Γ → Λ and a meas...

For a linear map from Mm to Mn, besides the usual positivity, there are two stronger notions, complete positivity and super-positivity. Given a positive linear map φ we study a decomposition φ = φ − φ with completely positive linear maps φ (j = 1, 2). Here φ + φ is of simple form with norm small as possible. The same problem is discussed with superpositivity in place of complete positivity.

We show that the general Levy process can be embedded in a suitable Fock space, classified by cocycles of the real line regarded as a group. The formula of de Finetti corresponds to coboundaries. Kolmogorov’s processes correspond to cocycles of which the derivative is a cocycle of the Lie algebra of R. The Lévy formula gives the general cocycle. 1 Cyclic representations of groups Let G be a gro...