A convergent Deep Learning algorithm for approximation of polynomials by Després, Bruno

“…We start from the contractive functional equation proposed in [4], where it was shown that the polynomial solution of functional equation can be used to initialize a Neural Network structure, with a controlled accuracy. …”
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Approximate Generalized Cubic *-Derivations by Heejeong Koh, Dongseung Kang

“…We will show the general solution of the functional equation f(ax+by)+f(ax-by) = ab2[f(x+y)+f(x-y)]+2a(a2-b2)f(x) and investigate the stability of cubic *-derivations associated with the given functional equation on Banach *-algebras.…”
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On Pexider Differences in Topological Vector Spaces by Abbas Najati, M. R. Abdollahpour, Gwang Hui Kim

“…We consider also the Pexiderized Cauchy functional equation.…”
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Higher Ring Derivation and Intuitionistic Fuzzy Stability by Ick-Soon Chang

“…We take account of the stability of higher ring derivation in intuitionistic fuzzy Banach algebra associated to the Jensen type functional equation. In addition, we deal with the superstability of higher ring derivation in intuitionistic fuzzy Banach algebra with unit.…”
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Analytic Solutions of an Iterative Functional Differential Equations Near Regular Points by Lingxia Liu

“…By reducing the equation to another functional equation without iteration of the unknown function an existence theorem is established for analytic solutions of the original equation.…”
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Approximation of Generalized Left Derivations by Sheon-Young Kang, Ick-Soon Chang

“…., generalized derivations) associated with a Jensen-type functional equation, and we also deal with problems for the Jacobson radical ranges of left derivations (resp., derivations).…”
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Stability in Generalized Functions by Young-Su Lee

“…We consider the following additive functional equation with 𝑛-independent variables: ∑𝑓(𝑛𝑖=1𝑥𝑖∑)=𝑛𝑖=1𝑓(𝑥𝑖∑)+𝑛𝑖=1𝑓(𝑥𝑖−𝑥𝑖−1) in the spaces of generalized functions. …”
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On Ulam's Type Stability of the Cauchy Additive Equation by Janusz Brzdęk

“…We prove a general result on Ulam's type stability of the functional equation fx+y=fx+fy, in the class of functions mapping a commutative group into a commutative group. …”
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On the Stability Problem in Fuzzy Banach Space by G. Zamani Eskandani, P. Găvruţa, Gwang Hui Kim

“…We investigate the generalized Ulam-Hyers stability of the Cauchy functional equation and pose two open problems in fuzzy Banach space.…”
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On the stability estimation of Wang's characterization theorem by Romanas Januškevičius

“…The technique commonly employed in proving this characterization is the well-known Cauchy functional equ­ation φ(a√(xa + ya)) = φ(x)φ(y). The stability estimation in this characterization of the Weibull distribution is analysied. …”
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Approximate Cubic Lie Derivations on ρ-Complete Convex Modular Algebras by Hark-Mahn Kim, Hwan-Yong Shin

“…In this article, we present generalized Hyers–Ulam stability results of a cubic functional equation associated with an approximate cubic Lie derivations on convex modular algebras χρ with Δ2-condition on the convex modular functional ρ.…”
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Solutions of the neutral differential-difference equation αx′(t)+βx′(t−r)+γx(t)+δx(t−r)=f(t) by Ll. G. Chambers

“…Particular solutions and complementary functions are obtained for the functional equation αx′(t)+βx′(t−r)+γx(t)+δx(t−r)=f(t) in the forms of a convolution type integral and of infinite series.…”
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Homomorphisms and Derivations in C*-Algebras by Choonkil Park, Abbas Najati

“…Using the Hyers-Ulam-Rassias stability method of functional equations, we investigate homomorphisms in C*-algebras, Lie C*-algebras, and JC*-algebras, and derivations on C*-algebras, Lie C*-algebras, and JC*-algebras associated with the following Apollonius-type additive functional equation f(z−x)+f(z−y)+(1/2)f(x+y)=2f(z−(x+y)/4).…”
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Approximate Quartic and Quadratic Mappings in Quasi-Banach Spaces by M. Eshaghi Gordji, H. Khodaei, Hark-Mahn Kim

“…we establish the general solution for a mixed type functional equation of aquartic and a quadratic mapping in linear spaces. …”
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Certain Geometric Properties of the Canonical Weierstrass Product of an Entire Function Associated with Conic Domains by K. A. Selvakumaran, P. Rajaguru, S. D. Purohit, D. L. Suthar

“…In this paper, we determine the radius of λ-uniform convexity, λ-starlikeness, and α-convexity of order δ for the Weierstrass canonical product of an entire function as a root having smallest modulus and argument ϕ of a functional equation. As special cases, we also determine the radius of λ-uniform convexity, λ-starlikeness, and α-convexity of order δ for the entire function 1/Γ.…”
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Optimal Design of Tooth Profile Parameter of Straight-conjugate Internal Gear Pair by Hu Hanlin, Cui Jiankun, Xu Jinbo

“…The optimal design of the straight-conjugate internal gear pair tooth profile parameter is carried out,the performance parameter functional equation of the straight-conjugate internal gear pair is analyzed.The optimization design mathematical model is set up,and the design variables are decided.By making use of the Matlab optimizing software tool,the optical calculation to the whole gear pair and he detailed comparison about the performance and tooth profile parameters of the before and after are carried out.…”
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On the Abstract Subordinated Exit Equation by Hassen Mejri, Ezzedine Mliki

“…A ℙ-exit law is a ℬ-valued function 𝑡∈]0,∞[→𝜑𝑡∈ℬ satisfying the functional equation: 𝑃𝑡𝜑𝑠=𝜑𝑡+𝑠, 𝑠,𝑡>0. Let 𝛽 be a Bochner subordinator and let ℙ𝛽 be the subordinated semigroup of ℙ (in the Bochner sense) by means of 𝛽. …”
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Stability of generalized additive Cauchy equations by Soon-Mo Jung, Ki-Suk Lee

“…A familiar functional equation f(ax+b)=cf(x) will be solved in the class of functions f:ℝ→ℝ. …”
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Stability and Global Hopf Bifurcation Analysis on a Ratio-Dependent Predator-Prey Model with Two Time Delays by Huitao Zhao, Yiping Lin, Yunxian Dai

“…By using the theory of functional equation and Hopf bifurcation, the conditions on which positive equilibrium exists and the quality of Hopf bifurcation are given. …”
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Approximate Quadratic-Additive Mappings in Fuzzy Normed Spaces by Ick-Soon Chang, Yang-Hi Lee

“…We examine the generalized Hyers-Ulam stability of the following functional equation: 2fx+y+z+w+f-x-y+z+w+f-x+y-z+w+f-x+y+z-w+fx-y-z+w+fx-y+z-w+fx+y-z-w-5fx-3f-x-5fy-3f-y-5fz-3f-z-5fw-3f-w=0, in the fuzzy normed spaces with the fixed point method.…”
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