AI Networking Cookbook: Practical recipes for AI-assisted network automation and development
This work introduces two novel classes of bi-univalent functions, denoted by ℬΣ(μ,γ,λ;r) and ΡΣ(μ,γ,λ;r), linked to Lucas-Balancing polynomials within the open unit disk. For functions pertaining to these newly defined classes, we establish estimates for the early Taylor–Maclaurin coefficients |a2| and |a3|. Furthermor...
In one complex variable the Schwarzian derivative characterizes the M\"obius transformations, arises from a second-order linear equation, and controls univalence through the theorems of Nehari and of Ahlfors--Weill. This chapter presents what is known about these three properties for locally biholomorphic mappings in $...
In this paper, we introduce an extended two-factor q-differential multiplier operator denoted by ℳq,,n,mf(z). Using this operator, we define the associated subclasses Xq,,n,m() and Yq,,n,m(,) of analytic functions. We obtain upper bounds for the initial coefficients a2, a3 and FeketeSzeg inequalities for the functional...
We prove a surprisingly simple pointwise formula for the Frobenius norm of the tensor of $n$-th order partial derivatives of a radially symmetric function $f(x)=g(r(x))$. Using the iterations of the differential operator $\mathcal{D} g(r)=g'(r)/r$, we avoid technical difficulties usually caused by higher-order radial d...
Let G be a homogeneous Lie group of dimension ϰ. In this article, we investigate the mapping properties of the Wolff-type potential Wϑ,2 on G, associated with a homogeneous quasi-norm, and show that it coincides, up to an explicit dimensional constant, with the Riesz potential of doubled order 2ϑ on G. Using this ident...
Let d≥1, let Kd=[0,∞)d, and let B(A,R)⊂Kd be a closed Euclidean ball. For a continuous superquadratic function φ:Kd→R, we establish a corrected Hermite–Hadamard estimate that relates the integral mean of φ over the ball to its value at the center and its integral mean over the boundary sphere. The correction is given e...
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