Results 21 to 30 of about 323 (78)
On a functional equation related to a generalization of Flett′s mean value theorem
International Journal of Mathematics and Mathematical Sciences, Volume 23, Issue 2, Page 103-107, 2000., 2000 In this paper, we characterize all the functions that attain their Flett mean value at a particular point between the endpoints of the interval under consideration. These functions turn out to be cubic polynomials and thus, we also characterize these.
T. Riedel, Maciej Sablik
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Approximate Hermite-Hadamard type inequalities for approximately convex functions [PDF]
, 2012 In this paper, approximate lower and upper Hermite--Hadamard type inequalities are obtained for functions that are approximately convex with respect to a given Chebyshev ...
Makó, Judit, Páles, Zsolt
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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
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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
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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
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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
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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
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, 2013 This paper shows a simple construction of the continuous involutions of real intervals in terms of the continuous even functions. We also study the smooth involutions defined by symmetric equations. Finally, we review some applications, in particular the
Zampieri, Gaetano
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On extension of solutions of a simultaneous system of iterative functional equations [PDF]
, 2009 Some sufficient conditions which allow to extend every local solution of a simultaneous system of equations in a single variable of the form \[ \varphi(x) = h (x, \varphi[f_1(x)],\ldots,\varphi[f_m(x)]),\] \[\varphi(x) = H (x, \varphi[F_1(x)],\ldots ...
Janusz Matkowski
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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
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