Results 31 to 40 of about 360 (83)
Journal of Inequalities and Applications, 2012 Let ℝ+ and B be the set of positive real numbers and a Banach space, respectively, f, g, h : ℝ+ → B and ψ:ℝ+2→ℝ be a nonnegative function of some special forms.
Jaeyoung Chung
semanticscholar +2 more sources
On the stability of generalized gamma functional equation
International Journal of Mathematics and Mathematical Sciences, Volume 23, Issue 8, Page 513-520, 2000., 2000 We obtain the Hyers‐Ulam stability and modified Hyers‐Ulam stability for the equations of the form g(x + p) = φ(x)g(x) in the following settings: |g(x + p) − φ(x)g(x) | ≤ δ, | g(x + p) − φ(x)g(x) | ≤ ϕ(x), | (g(x + p)/φ(x)g(x)) − 1 | ≤ ψ(x). As a consequence we obtain the stability theorems for the gamma functional equation.
Gwang Hui Kim
wiley +1 more source
Non-Archimedean Hyers-Ulam-Rassias stability of m-variable functional equation
Advances in Differential Equations, 2012 The main goal of this paper is to study the Hyers-Ulam-Rassias stability of the following Euler-Lagrange type additive functional equation: ∑j=1mf(−rjxj+∑1≤i≤m,i≠jrixi)+2∑i=1mrif(xi)=mf(∑i=1mrixi), where r1,…,rm∈R, ∑i=kmrk≠0,
H. Azadi Kenary +4 more
semanticscholar +2 more sources
Algebraic and topological structures on the set of mean functions and generalization of the AGM mean [PDF]
, 2010 In this paper, we present new structures and results on the set MD of mean functions on a given symmetric domain D of R 2 . First, we construct on MD a structure of abelian group in which the neutral element is simply the Arithmetic mean; then we study ...
Bakir Farhi
semanticscholar +1 more source
Stability of generalized additive Cauchy equations
International Journal of Mathematics and Mathematical Sciences, Volume 24, Issue 11, Page 721-727, 2000., 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+⋯+aimxm) in connection with the question of Rassias and Tabor.
Soon-Mo Jung, Ki-Suk Lee
wiley +1 more source
Improved Poincar\'e inequalities [PDF]
, 2011 Although the Hardy inequality corresponding to one quadratic singularity, with optimal constant, does not admit any extremal function, it is well known that such a potential can be improved, in the sense that a positive term can be added to the quadratic
Dolbeault, Jean, Volzone, Bruno
core +2 more sources
On generalizations of the Pompeiu functional equation
International Journal of Mathematics and Mathematical Sciences, Volume 21, Issue 1, Page 117-124, 1998., 1997 In this paper, we determine the general solution of the functional equations and which are generalizations of a functional equation studied by Pompeiu. We present a method which is simple and direct to determine the general solutions of the above equations without any regularity assumptions.
Pl. Kannappan, P. K. Sahoo
wiley +1 more source
Potentials Unbounded Below [PDF]
, 2010 Continuous interpolates are described for classical dynamical systems defined by discrete time-steps. Functional conjugation methods play a central role in obtaining the interpolations.
Curtright, Thomas
core +4 more sources
Quasi‐homogeneous associative functions
International Journal of Mathematics and Mathematical Sciences, Volume 21, Issue 2, Page 351-357, 1998., 1997 A triangular norm is a special kind of associative function on the closed unit interval [0, 1]. Triangular norms (or t‐norms) were introduced in the context of probabilistic metric space theory, and they have found applications also in other areas, such as fuzzy set theory.
Bruce R. Ebanks
wiley +1 more source
A new analogue of Gauss′ functional equation
International Journal of Mathematics and Mathematical Sciences, Volume 18, Issue 4, Page 749-756, 1995., 1994 Gauss established a theory on the functional equation (Gauss′ functional equation) , where f : R+ × R+ → R is an unknown function of the above equation. In this paper we treat the functional equation where f : R+ × R+ → R is an unknown function of this equation.
Hiroshi Haruki, Themistocles M. Rassias
wiley +1 more source