Let (M,δ) be a metric space, f:M→M, and g:M→[0,+∞). In this paper, we obtain sufficient conditions under which the set of fixed points of f is g-admissible, i.e., Fix(f)≠∅ and Fix(f)⊂g−10. Some special cases of our main results are discussed and some...
In free probability, the theory of Cauchy–Stieltjes Kernel (CSK) families has recently been introduced. This theory is about a set of probability measures defined using the Cauchy kernel similarly to natural exponential families in classical pr...
The classical Belinskii theorem implies that any sufficiently regular function μ(z) on the extended complex plane C^ with a small C1+α norm generates via the two-dimensional Cauchy integral a quasiconformal automorphism w of C^ with the Belt...
We prove that a contact strongly pseudo-convex CR (Cauchy–Riemann) manifold M2n+1, n≥2, is locally pseudo-Hermitian symmetric and satisfies ∇ξh=μhϕ, μ∈R, if and only if M is either a Sasakian locally ϕ-symmetric space or...
In this paper, we investigate differential equations with generalized piecewise constant delay, DEGPCD in short, and establish the existence and stability of a unique almost periodic solution that is exponentially stable. Our results are derived by u...
This article delves into some properties of free and Boolean multiplicative convolutions, in connection with the theory of Cauchy–Stieltjes kernel (CSK) families and their respective variance functions (VFs). Consider K−(μ)={Qmμ(ds)...
Let μ be a self-similar measure with compact support K. The Hausdorff dimension of K is α. The Cauchy transform of μ is denoted by F(z). For 0<β<1, we define the function F[β], which compares with the fractional derivative...
This paper introduces a variant of differential evolution with micro-populations, called μ-DE-ERM, which incorporates a periodic elitist replacement mechanism with the aim of preserving diversity without the need to measure it explicitly. The prop...
In this article, we study the Cauchy problem of the chemotaxis-Navier–Stokes system with the consumption and production of chemosignals with a logistic source. The parameters χ≠0, ξ≠0, λ>0 and μ>0. The sys...
We further extend the results of other researchers on existence theory to homogeneous fractional Cauchy–Euler equations ∑i=1mdixαiDαiu(x)+μu(x)=0,αi>0, with the derivatives in Caputo or Riemann–Liouville sense....
Let F(νj)={Qmjνj,mj∈(m−νj,m+νj)}, j=1,2, be two Cauchy–Stieltjes Kernel (CSK) families induced by non-degenerate compactly supported probability measures ν1 and ν2. Introduce the set of measures F=F(ν1)⊞F(&...
This paper presents a rigorous solution of the Helmholtz equation for regular waveguide structures with the finite sizes of all cross-section elements that may have an arbitrary shape. The solution is based on the theory of Singular Integral Equation...
The target of the current research article is to investigate the solitonic attributes of relativistic magneto-fluid spacetime (MFST) if its metrics are Ricci–Yamabe soliton (RY-soliton) and gradient Ricci–Yamabe soliton (GRY-soliton). We...
Probability distributions for the center of gravity are fundamental tools for track fitting. The center of gravity is a widespread algorithm for position reconstruction in tracker detectors for particle physics. Its standard use is always accompanied...
In this paper, we analyze the well-posedness of the Cauchy–Dirichlet problem to an integro-differential equation on a multidimensional domain Ω⊂Rn in the unknown u=u(x,t), Dtν0(ϱ0u)−Dtν1(ϱ1u...