Results 51 to 60 of about 4,267,250 (176)
On the quasilinear Cauchy problem for a hyperbolic functional differential equation [PDF]
Opuscula Mathematica, 2015 The Cauchy problem for hyperbolic functional differential equations is considered. Volterra and Fredholm dependence are considered. A theorem on the local existence of generalized solutions defined on the Haar pyramid is proved.
Elżbieta Puźniakowska-Gałuch
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Extracta Mathematicae, 2018 We obtained a generalization of the stability of some Banach lattice-valued functional equation with the addition replaced in the Cauchy functional equation by lattice operations and their combinations.
Nutefe Kwami Agbeko, Patrícia Szokol
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Alternative Functional Equations. A Survey
Annales Mathematicae SilesianaeThis paper provides a survey of several results on alternative functional equations, related to the Cauchy equation and to the quadratic equation, and involving one or more unknown functions.
Forti Gian Luigi
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Weighted Cauchy-type problem of a functional differ-integral equation
Electronic Journal of Qualitative Theory of Differential Equations, 2007 In this work, we are concerned with a nonlinear weighted Cauchy type problem of a differ-integral equation of fractional order. We will prove some local and global existence theorems for this problem, also we will study the uniqueness and stability of ...
Ahmed El-Sayed +1 more
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Paradigmatic well posedness in some generalized characteristic Cauchy problems [PDF]
By means of convenient regularization for an ill posed Cauchy problem, we deï¬ne an associated generalized problem and discuss the conditions for the solvability of it.
Emmanuel Allaud +4 more
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On Pexider Differences in Topological Vector Spaces
Abstract and Applied Analysis, 2011 Let 𝑋 be a normed space and 𝑌 a sequentially complete Hausdorff topological vector space over the field ℚ of rational numbers. Let 𝐷1={(𝑥,𝑦)∈𝑋×𝑋∶‖𝑥‖+‖𝑦‖≥𝑑}, and 𝐷2={(𝑥,𝑦)∈𝑋×𝑋∶‖𝑥‖+‖𝑦‖0.
Abbas Najati +2 more
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Cauchy's functional equation in the mean
Advances in Mathematics, 1984 The following theorem is proved. If \(\alpha \geq 1\) and \(f\in L^{\alpha}(0,z)\) for every \(z>0\) and if \[ \lim_{z\to \infty}(z^{- 2}\int^{z}_{0}\int^{z}_{0}| f(x+y)-f(x)- f(y)|^{\alpha}dxdy)=0, \] then there exists an A such that \(\lim_{z\to \infty}(z^{-1}\int^{z}_{0}| f(x)- Ax|^{\alpha}dx)=0.\) Similar theorems and connections to \textit{D.
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Stability of generalized additive Cauchy equations
International Journal of Mathematics and Mathematical Sciences, 2000 A familiar functional equation f(ax+b)=cf(x) will be solved in the class of functions f:ℝ→ℝ. Applying this result we will investigate the Hyers-Ulam-Rassias stability problem of the generalized additive Cauchy equation f(a1x1+⋯+amxm+x0)=∑i=1mbif(ai1x1 ...
Soon-Mo Jung, Ki-Suk Lee
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On restricting Cauchy–Pexider functional equations to submanifolds [PDF]
Aequationes mathematicae, 2012 The author considers the restricted Cauchy-Pexider functional equation \(f(x)g(y)=h(x+y)\) for complex-valued functions on subsets of Euclidean spaces. The functions are assumed to be measurable and non-vanishing almost everywhere. The main result is that if the functional equation is satisfied almost everywhere on a hypersurface which is nowhere flat ...
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Some generalization of Cauchy’s and the quadratic functional equations [PDF]
Aequationes mathematicae, 2011 Suppose that \((S,+)\) is an abelian group and \(\Lambda\) is a finite subgroup of the automorphism group of \(S\), \(L=\text{card} \Lambda\). Let \((H,+)\) be an abelian group uniquely divisible by \((L+1)!\). The author finds the solutions \(f, , h:S \to H\) of the equation \[ \sum_{\lambda \in \Lambda}f(x+\lambda y)=Lg(x)+h(y)\,\,(x,y\in S). \]
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