The aim of this paper is to present some coincidence and common fixed point results for generalized (ψ, φ)-contractive mappings using partially weakly G-α-admissibility in the setup of G-metric space. As an application of our results, periodic points of weakly contractive mappings are obtained. We also derive certain new coincidence point and common fixed point theorems in partially ordered G-m...

Abstract. Let A and B be almost commuting (i.e., the commutator AB−BA belongs to trace class) self-adjoint operators. We construct a functional calculus φ 7→ φ(A,B) for functions φ in the Besov class B ∞,1(R ). This functional calculus is linear, the operators φ(A,B) and ψ(A,B) almost commute for φ, ψ ∈ B ∞,1(R ), and φ(A,B) = u(A)v(B) whenever φ(s, t) = u(s)v(t). We extend the Helton–Howe trac...

Let φ be a compactly supported refinable function in L2(R) such that the shifts of φ are stable and φ̂(2ξ) = â(ξ)φ̂(ξ) for a 2π-periodic trigonometric polynomial â. A wavelet function ψ can be derived from φ by ψ̂(2ξ) := e−iξ â(ξ + π)φ̂(ξ). If φ is an orthogonal refinable function, then it is well known that ψ generates an orthonormal wavelet basis in L2(R). Recently, it has been shown in the liter...

An efficient variant of the double-negation translation explains the relationship between Shoenfield’s and Gödel’s versions of the Dialectica interpretation. Fix a classical first-order language, based on the connectives ∨, ∧, ¬, and ∀. We will define a translation to intuitionistic (even minimal) logic, based on the usual connectives. The translation maps each formula φ to the formula φ∗ = ¬φ∗...

We derive and interpret some relations between the luminosity, mass, and age distributions of star clusters, denoted here by φ(L), ψ(M), and χ(τ), respectively. Of these, φ(L) is the easiest to determine observationally, whereas ψ(M) and χ(τ) are more informative about formation and disruption processes. For a population of young clusters, with a relatively wide range of ages, φ(L) depends on b...

We demonstrate experimentally the existence of Josephson junctions having a doubly degenerate ground state with an average Josephson phase ψ=±φ. The value of φ can be chosen by design in the interval 0<φ<π. The junctions used in our experiments are fabricated as 0-π Josephson junctions of moderate normalized length with asymmetric 0 and π regions. We show that (a) these φ Josephson junctions ha...

Thus φ is bi-Lipschitz on large scales. If there exists a constant C ′ such that every point of Y is within a distance C′ of a point of φ(X), then there is a quasi-isometric embedding ψ : Y → X which is a “coarse inverse of φ”, i.e. supx∈X dX(x, ψ(φ(x))) <∞ and supy∈Y dY (y, φ(ψ(y))) < ∞. In this case φ is called a quasi-isometry and the spaces X and Y are said to be quasi-isometric. A basic ex...

where dA is the normalized area measure in D. The case where α = 0 is known as the (unweighted) Bergman space, often simply denoted by A2. Let φ be an analytic map from the open unit disk D into itself. The operator that takes the analytic map f to f ◦ φ is a composition operator and is denoted by Cφ . A natural generalization of a composition operator is an operator that takes f to ψ · f ◦ φ, ...