We propose a formalization of the concept of ‘having the permission to say something to somebody’. For it, we introduce a notion of private announcement and define a permission operator with agency. We prove that this can be seen as a generalisation of the notion of permitted public announcement Balbiani and Seban (2011). We also add a notion of obligation with a new intuition. We illustrate th...

In this paper, we will use the notion of α-admissible mappings in Banach spaces, to introduce concept Tβ-contractive and establish a fixed point theorem for type contractions. Our theorems generalize improve many results literature. Moreover, apply main result prove existence solution Volterra-integral equation, under more general assumptions than previously made.

In this paper, we deal with the boundary value problem x′′ = f (t, x, xt , x′, x′ t ) , ( x0, x ′ 0 ) ∈ {(φ + c1,ψ + c2): c1, c2 ∈ R}, α(x|J )= 0, β (x′(1)− δx′|J ) = 0, where f ∈ Car(J × R × Cr × R × Cr), φ, ψ ∈ Cr , J := [0,1], δ = 1, α ∈ AJ , β ∈ A[0,1), AJ and A[0,1) are two special sets of functionals, and x|J is the restriction of x to J . We find sufficient conditions for the existence o...

Let Z be an analytic subvariety of pure codimension p of a pseudoconvex set X in C n. We introduce a formalism to generate weighted Koppelman formulas on Z that provide solutions to the ¯ ∂-equation. We prove that if φ is a smooth (0, q + 1)-form on Z with ¯ ∂φ = 0, then there is a smooth (0, q)-form ψ on Z reg with at most polynomial growth at Z sing such that ¯ ∂ψ = φ. The integral formulas a...

In this paper we present fixed point results for generalized α-ψ-contractive type mappings in dislocated metric spaces. We also provide some examples to illustrate our results. References 1. Banach S., “Surles operations dans les ensembles abstraites et leurs applications”, Fund. Math., 3 (1922), 133-187. 2. Kannan R., “Some results on fixed points”, Bull. Cal. Math. Soc., 60 (1968), 71-76. 3. ...

In this paper, fixed point theorems using ψ contractive mapping in C∗-algebra valued b-metric space are introduced. By stating multiple scenarios that illustrate the application domains, we demonstrate several applications from obtained results. particular, begin with definition of positive function and then recall some properties lay fundamental basis for research. We study a function.

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 study the following extremal problem and its relevance to the sum of the so-called superoptimal singular values of a matrix function: Given an m × n matrix function Φ, when is there a matrix function Ψ * in the set A n,m k such that Z T trace(Φ(ζ)Ψ * (ζ))dm(ζ) = sup Ψ∈A n,m k ˛ ˛ ˛ ˛ Z T trace(Φ(ζ)Ψ(ζ))dm(ζ) ˛ ˛ ˛ ˛ ? The set A n,m k is defined by A n,m k def = n Ψ ∈ H 1 0 (Mn...