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Ulam Stability of a Quartic Functional Equation [PDF]
Abstract and Applied Analysis, 2012 The oldest quartic functional equation was introduced by J. M. Rassias in (1999), and then was employed by other authors. The functional equation 𝑓(2𝑥+𝑦)+𝑓(2𝑥−𝑦)=4𝑓(𝑥+𝑦)+4𝑓(𝑥−𝑦)+24𝑓(𝑥)−6𝑓(𝑦) is called a quartic functional equation, all of its solution is
Abasalt Bodaghi +2 more
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General quartic β-function at three loops
Journal of High Energy PhysicsWe determine the three-loop MS ¯ $$ \overline{\textrm{MS}} $$ quartic β-function for the most general renormalisable four-dimensional theories. A general parametrisation of the β-function is compared to known β-functions for specific theories to fix all ...
Tom Steudtner, Anders Eller Thomsen
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Fuzzy Stability Results of Generalized Quartic Functional Equations
Mathematics, 2021 In the present paper, we introduce a new type of quartic functional equation and examine the Hyers–Ulam stability in fuzzy normed spaces by employing the direct method and fixed point techniques.
Sang Og Kim, Kandhasamy Tamilvanan
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Some Implications of a Quartic Loss Function [PDF]
SSRN Electronic Journal, 2006 Motivated by a central banker with a symmetric but non-quadratic loss function, we show in this note that the approximations of two plausible loss functions of this type will include a quartic term. For skewed distributions, we establish that such a loss function implies a systematic inflation bias even when the bank targets the natural rate. Moreover,
Aretz, Kevin, Peel, David
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ON THE GENERAL SOLUTION OF A QUARTIC FUNCTIONAL EQUATION [PDF]
Bulletin of the Korean Mathematical Society, 2003 Using a classical result of M. Hosszú and applying elegant and elementary arguments the authors find the general solution of the functional equation: \[ f(x + 2y) + f(x-2y) + 6 f(x) = 4 (f (x+y) + f(x-y) + 6 f(y)), \] i.e., \( f(x) = A^4 (x)\) which is the diagonal of a 4-additive symmetric function from \(R^4\) into \(R\). By means of some results due
Prasanna K Sahoo
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Value-distribution of quartic Hecke L-functions [PDF]
Moscow Journal of Combinatorics and Number Theory, 2021 11 ...
Gao, Peng, Zhao, Liangyi
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Results in Physics, 2020 This paper applies exp-function expansion algorithm to secure to cubic-quartic dark and singular optical solitons in birefringent fibers that are studied with four forms of nonlinear refractive index.
Yakup Yıldırım +7 more
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Green’s Function for the Quartic Oscillator
Applied Mathematics, 2016 This paper has been withdrawn by the author due to many errors that need ...
exaly +4 more sources
General Cubic‐Quartic Functional Equation [PDF]
Abstract and Applied Analysis, 2011 We obtain the general solution and the generalized Hyers‐Ulam stability of the general cubic‐quartic functional equation for fixed integerskwithk≠ 0, ±1:f(x+ky) +f(x−ky) =k2(f(x+y) +f(x−y)) + 2(1 −k2)f(x)+((k4−k2)/4)(f(2y) − 8f(y)), where .
M. Eshaghi Gordji +2 more
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Slow-Time Ambiguity Function Shaping With Spectral Coexistence for Cognitive Radar
IEEE Journal of Selected Topics in Applied Earth Observations and Remote Sensing, 2023 In the spectrum-congested environment, weak target obscuration can be addressed by simultaneously shaping the ambiguity function and waveform spectrum based on cognitive radar a priori information. In this article, we investigate joint waveform design to
Cui Zhang +6 more
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