Results 221 to 230 of about 152,222 (241)

107.31 Obtaining a more general result from a functional equation by not differentiating

Mathematical Gazette, 2023
3. M. Levi, A Water-Based Proof of the Cauchy–Schwarz Inequality, Amer. Math. Monthly 127 (2020) p. 572. 4. N. J. Lord, Cauchy–Schwarz via collisions, Math. Gaz. 99 (November 2015) pp. 541-542. 5. T.
Steven J. Kilner, David L. Farnsworth
semanticscholar   +1 more source

Fuzzy stability of the Jensen functional equation

Fuzzy Sets and Systems, 2008
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Alireza Kamel Mirmostafaee, Madjid Mirzavaziri, Mohammad Sal Moslehian   +2 more
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Hyperstability of the Jensen functional equation

Acta Mathematica Hungarica, 2013
\textit{S.-M. Jung}, \textit{M. S. Moslehian} and \textit{P. K. Sahoo} [J. Math. Inequal. 4, No. 2, 191--206 (2010; Zbl 1219.39016)] investigated the conditional stability of the generalized Jensen functional equation \(f(ax+by)=af(x)+bf(y)\). Based on a fixed point method, the authors of the present paper consider the hyperstability problem of the ...
Bahyrycz, A., Piszczek, M.
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On a Mikusiński—Jensen Functional Equation

2002
The following Mikusinski-Jensen type functional equation is investigated. The main result states that if I is an open real interval, or more generally, if I is a convex subset of a linear space whose intersection with straight lines is an open segment, then the above equation is equivalent to the so called Jensen functional equation.
Károly Lajkó, Zsolt Páles
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An interplay between Jensen's and Pexinder's functional equations on semigroups

Annales Universitatis Scientiarum Budapestinensis de Rolando Eötvös Nominatae. Sectio computatorica, 2011
. Let (S, +) and (G, +) be two commutative semigroups. Assuming that the latter one is cancellative we deal with functions f : S −→ G satisfying the Jensen functional equation written in the form 2f(x + y) = f(2x) + f(2y).
Roman Ger, Z. Kominek
semanticscholar   +1 more source

Innovative Neural Network Approach for Solving TDKS Equations with Jensen’s Inequality

Punjab University journal of mathematics
. We propose a novel neural network-based approach for solv-ing the Time Dependent Kohn-Sham (TDKS) equations, central to Time-Dependent Density Functional Theory (TDDFT).
Adeel Farooq, M. T. Chaudhary, M. Yousaf, Samra Sarwar, Farooq Ahmad   +4 more
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On Jensen-like form of Mikusiński's functional equation

Acta Mathematica Hungarica
The paper investigates the following conditional version of Mikusiński's functional equation \[f(x+y)\neq 0 \quad \Rightarrow \quad 2f\left(\frac{x+y}{2}\right)= f(x)+f(y), \] for functions between uniquely 2-divisible groups, with the codomain being abelian.
Imani, E., Najati, A., Tareeghee, M. A.
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Alienation and stability of Jensen’s and other functional equations

Aequationes mathematicae
\textit{J. Dhombres} [Aequationes Math. 35, No. 2--3, 186--212 (1988; Zbl 0654.39003)] introduced the notion of alienation of functional equations: consider the functional equation \(E(f,g)=0\) obtained by summing up two functional equations \(E_1(f)=0\) and \(E_2(g)=0\) side by side. If the equation \(E(f,g)=E_1(f)+E_2(g)=0\) splits back to the system
Tial, Mohamed, Zeglami, Driss
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Jensen and Quadratic Functional Equations on Semigroups

2012
Let S be a commutative semigroup, σ:S→S an endomorphism of order 2, G a 2-cancellative abelian group, and n a positive integer. One of the goals of this paper is to determine the general solutions of the functional equations f 1(x+y)+f 2(x+σy)=f 3(x) and also f 1(x+y)+f 2(x+σy)=f 3(x)+f 4(y) for all x,y∈S n , where f 1,f 2,f 3,f 4:S n →G are unknown ...
Esteban A. Chávez, Prasanna K. Sahoo
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On the stability of a generalization of Jensen functional equation

Acta Mathematica Hungarica, 2017
The author uses the fixed point method to prove the stability and the hyperstability of a generalization of Jensen functional equation \[ \sum_{k=0}^{n-1}f(x+b_ky)=nf(x) \] in the setting of Banach spaces. Here \(n \geq 2\), \(b_k=\exp(2i\pi k/n)\) for \(0\leq k \leq n-1\).
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