On a General Conditional Cauchy Functional Equation by Elham Mohammadi, Abbas Najati, Yavar Khedmati Yengejeh

“…In this paper, we investigate the conditional Cauchy functional equation \[f(x+y)\neq af(x)+bf(y)\quad\Rightarrow \quad f(x+y)=f(x)+f(y),\quad x,y\in G,\] for functions $f:G\to Y$, where  $a,b\in \Bbb{F}$ are fixed constants. …”
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On the Cauchy Problem for the Two-Component Novikov Equation by Yongsheng Mi, Chunlai Mu, Weian Tao

“…We are concerned with the Cauchy problem of two-component Novikov equation, which was proposed by Geng and Xue (2009). …”
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A Generalization of Poly-Cauchy Numbers and Their Properties by Takao Komatsu, Vichian Laohakosol, Kálmán Liptai

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On Ulam's Type Stability of the Cauchy Additive Equation by Janusz Brzdęk

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Cauchy's functional equation in restricted complex domains by Watcharapon Pimsert, Vichian Laohakosol, Sajee Pianskool

“…Using a method modified from that used by Pisot and Schoenberg in 1964-1965, a Cauchy's functional equation with restricted domains in the complex field is solved for uniformly continuous solutions.…”
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Instability of Cauchy horizon induced by the graviton mass by Lu Chen, Shun Jiang

“…In the context of considering massless scalar field perturbations in a charged static black hole, our paper explores the impact of graviton mass on the stability of the Cauchy horizon. By employing numerical techniques such as the pseudospectral method, we calculated the quasinormal mode frequencies under various spacetime parameters. …”
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Order compatibility for Cauchy spaces and convergence spaces by D. C. Kent, Reino Vainio

Subjects: “…preordered Cauchy space…”
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On characterization of the Cauchy law by sample mean properties by Romanas Januškevičius

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Rational modules and higher order Cauchy transforms by James Li-Ming Wang

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Existence of Iterative Cauchy Fractional Differential Equation by Rabha W. Ibrahim

“…Our main aim in this paper is to use the technique of nonexpansive operators in more general iterative and noniterative fractional differential equations (Cauchy type). The noninteger case is taken in sense of the Riemann-Liouville fractional operators. …”
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Catherine Chauche, Langue et Monde. Grammaire géopoétique du paysage contemporain. by Sophie Chiari-Lasserre

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A Nonlocal Cauchy Problem for Fractional Integrodifferential Equations by Fang Li, Jin Liang, Tzon-Tzer Lu, Huan Zhu

“…This paper is concerned with a nonlocal Cauchy problem for fractional integrodifferential equations in a separable Banach space X. …”
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The Cauchy Problem for a Fifth-Order Dispersive Equation by Hongjun Wang, Yongqi Liu, Yongqiang Chen

“…This paper is devoted to studying the Cauchy problem for a fifth-order equation. We prove that it is locally well-posed for the initial data in the Sobolev space Hs(R) with s≥1/4. …”
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Approximation of Analytic Functions by Solutions of Cauchy-Euler Equation by Soon-Mo Jung

“…We investigate the approximation properties of a special class of twice continuously differentiable functions by solutions of the Cauchy-Euler equation.…”
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Estimates for the Cauchy matrix of perturbed linear impulsive equation by P. S. Simeonov, D. D. Bainov

“…Estimates for the Cauchy matrix of a perturbed linear impulsive equation are obtained for given estimates for the Cauchy matrix of the corresponding unperturbed linear impulsive equation.…”
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Quasilinear Stochastic Cauchy Problem in Abstract Colombeau Spaces by Irina V. Melnikova, Uljana A. Alekseeva

“…Generalized solutions to the abstract Cauchy problem for a quasilinear equation with the generator of an integrated semigroup and with terms reflecting nonlinear perturbations and white noise type perturbations are under consideration. …”
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Stability of Functional Inequalities with Cauchy-Jensen Additive Mappings by Young-Sun Cho, Hark-Mahn Kim

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Fast Analytic Sampling Approximation from Cauchy Kernel by Youfa Li, Jing Shang, Honglei Yang, Gengrong Zhang, Shouzhi Yang

“…Here, Bk(f) is an approximation to f we recently constructed by applying the multiscale transform to the Cauchy kernel. We establish the matrix expression of Bk(f) and find that it has the structure of a multilevel Hankel matrix. …”
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Generalized Moisil-Théodoresco Systems and Cauchy Integral Decompositions by Ricardo Abreu Blaya, Juan Bory Reyes, Richard Delanghe, Frank Sommen

“…Furthermore, if Ω is bounded with boundary Γ, where Γ is an Ahlfors-David regular surface, and if W is a ℝ0,m+1(r,p,q)-valued Hölder continuous function on Γ, then necessary and sufficient conditions are given under which W admits on Γ a Cauchy integral decomposition W=W++W−.…”
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