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A Gauss type functional equation
... case n = 1 and p = log was studied in [2]. The essential step was done in [4] by the consideration of the definition (1.12) fo r n = 2 with an arbitrary p. The values n = −1 and n = 1 were studied in [5, 6]. The general ... See full document
5
On the stability of set-valued functional equations with the fixed point alternative
... the functional Equation (1.1), which is called a Cauchy-Jensen type additive functional equation and every solution of the Cauchy-Jensen type additive functional ... See full document
17
Solution and Stability of a Mixed Type Additive, Quadratic, and Cubic Functional Equation
... 1 S. M. Ulam, Problems in Modern Mathematics, chapter 6, John Wiley & Sons, New York, NY, USA, 1940. 2 D. H. Hyers, G. Isac, and Th. M. Rassias, Stability of Functional Equations in Several Variables, Progress ... See full document
17
On Cauchy type functional equations
... 1. Introduction. Let G be a locally compact Hausdorff group, that is, a locally com- pact group which satisfies the following separation axiom: every pair of distinct points in G have disjoint neighborhoods. Let µ be a ... See full document
13
Generalised Hyers-Ulam Product-Sum Stability of a Cauchy Type Additive Functional Equation
... Abstract. In 1940 (and 1964) S.M. Ulam proposed the well-known Ulam stability problem. In 1941 D.H. Hyers solved the Hyers-Ulam problem for linear mappings. In 2008, J. M. Rassias introduced the generalised Hyers-Ulam ... See full document
9
General Stability of a Reciprocal Type Functional Equation in Three Variables
... for functional equations is solved by direct method in which the exact solution of the functional equation is explicitly con- structed as a limit of a (Hyers) sequence, starting from the given ... See full document
18
On analytic continuation and functional equation of certain Dirichlet series
... Analytic continuation and functional equation of Riemann’s type are proved for a class of Dirichlet series associated to rational functions... KEY WORDS AND PHRASES.[r] ... See full document
6
A new analogue of Gauss' functional equation
... The purpose of this paper is to obtain new results for the solution of 1.2 by following the theory on Gauss’ functional equation.. The main result is to solve 1.2 under suitable natural [r] ... See full document
8
Non-Archimedean stability of Cauchy-Jensen Type functional equation
... functional equation. In particular, every solution of the qua- dratic functional equation is said to be a quadratic ...quadratic functional equation was proved by Skof [34] for ... See full document
11
A generalized Hyers Ulam stability of a Pexiderized logarithmic functional equation in restricted domains
... of functional equations go back to 1940 when Ulam proposed a question concerning the approximate homomorphisms from a group to a metric group (see ...numerous functional equations in various directions ... See full document
10
A Variational Approach to the Establishment of a Lubrication Equation for a Non-Newtonian Thin Film
... Non-Newtonian lubricants are commonly found in engineering. Here we illustrate the utility of a derivation of a Reynolds-type equation from a variational functional. The technique developed can be ... See full document
5
The Importance of Gauss-Jordan Elimination Methods for Balancing Chemical Reaction Equation
... chemical equation for a reaction gives two important types of information: the nature of the reactants and products and the relative numbers of ...each type of atom must occur on both sides of the ...an ... See full document
7
Fixed Points and Random Stability of a Generalized Apollonius Type Quadratic Functional Equation
... The stability problem of functional equations was originated from a question of Ulam 1 concerning the stability of group homomorphisms. Hyers 2 gave a first affirmative partial answer to the question of Ulam for ... See full document
11
On the stability of a mixed type quadratic additive functional equation
... 2. Hyers, DH: On the stability of the linear functional equation. Proc. Natl. Acad. Sci. USA 27, 222-224 (1941) 3. Rassias, TM: On the stability of the linear mapping in Banach spaces. Proc. Am. Math. Soc. ... See full document
10
On the Stability of a Generalized Quadratic and Quartic Type Functional Equation in Quasi Banach Spaces
... The generalized Hyers-Ulam stability problem for the quadratic functional equation 1.3 was proved by Skof for mappings f : A → B, where A is a normed space and B is a Banach space see 8. Cholewa 9 noticed ... See full document
26
On the Probabilistic Stability of the 2-variable $k$-AC-mixed Type Functional Equation
... for functional equations concerns deriving conditions under which, given an approximate solution of a functional equation, one may find an exact solution that is near it in some ... See full document
13
Fuzzy Stability of Generalized Mixed Type Cubic, Quadratic, and Additive Functional Equation
... This paper is organized as follows: In Section 3, we prove the generalized Hyers- Ulam stability of the functional equation (1.5) in fuzzy Banach spaces for an even case. In Section 4, we prove the ... See full document
22
Stability of a mixed type cubic and quartic functional equation in fuzzy Banach spaces
... function equation and they established the solution of Hyers- Ulam-Rassias stability for the functional equation ...this equation is called the cubic function equation, if the cubic ... See full document
11
Stability of a Jensen type quadratic additive functional equation under the approximately conditions
... 2. Hyers, DH: On the stability of the linear functional equation. Proc. Natl. Acad. Sci. USA 27, 222-224 (1941) 3. Aoki, T: On the stability of the linear transformation in Banach spaces. J. Math. Soc. Jpn. ... See full document
20
The solution of the functional equation of D'Alembert's type for commutative groups
... A solution of D’Alembert’s functional equation on a locally compact Abelian group, Aequationes Math.. The families with a universal Bayesian estimator of the transformation parameter, Sy[r] ... See full document
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