Results 31 to 40 of about 16,630 (273)
On a Jensen Type Functional Equation [PDF]
Journal of Applied Analysis, 2007 Suppose that \(M\) is a Abelian group in which the unique division by 2 and 3 is performable and \(S\) is an abstract cone satisfying the cancellation law. In this paper the author proves that if \(f:M\to S\) is a solution of the Jensen functional equation, then it is a solution of the following equation \[ 3(b-1) f\biggl(\frac{x+y+z}{3}\biggr)+ f(x)+f(
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Jensen’s and the quadratic functional equations with an endomorphism [PDF]
Proyecciones (Antofagasta), 2017 We determine the solutions f : S → H of the generalized Jensen’s functional equation f (x + y) + f (x + φ(y)) = 2f (x), x,y ∈ S,and the solutions f : S → H of the generalized quadratic functional equation f (x + y) + f (x + φ(y)) = 2f (x) + 2f (y), x,y ∈ S,where S is a commutative semigroup, H is an abelian group (2-torsion free in the first ...
Sabour, KH, Kabbaj, S
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On the stability of a quadratic Jensen type functional equation [PDF]
, 2002 In this paper we obtain the general solution of the quadratic Jensen type functional equation 9fx+y+z3+f(x)+f(y)+f(z)=4fx+y2+fy+z2+fz+x2 and prove the stability of this equation in the spirit of Hyers, Ulam, Rassias, and ...
Lee, Young Whan
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On Jensen's functional equation
Aequationes Mathematicae, 1992 The following is offered as main result. Let \((G,\cdot)\) and \((H,+)\) be abelian groups, and \(e\) the neutral element of \((G,\cdot)\). The solutions \(f: G\to H\) of \(f(xy)+f(xy^{-1})=2f(x)\), \(f(e)=0\) are exactly the homomorphisms of \(G\to H\) if, and only if, either \(H\) has no element of order 2 or \([G:G^ 2]\leq 2\), where \(G^ 2:=\{x^ 2 ...
Vasudeva, H.L., Parnami, J.C.
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On Jensen’s and the quadratic functional equations with involutions [PDF]
Proyecciones (Antofagasta), 2017 We determine the Solutions f : S → H of the generalized Jensen’s functional equation f( x + σ(y)) + f( x + τ(y)) = 2f(x), x , y∈ Sand the solutions f : S → H of the generalized quadratic functional equationf ( x + σ(y)) + f (x + τ(y)) = 2f (x) + 2f (y), x, y ∈ S,where S is a commutative semigroup, H is an abelian group (2-torsion free in the first ...
Fadli, B. +3 more
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A Fixed Point Approach to the Stability of a Cauchy-Jensen Functional Equation [PDF]
, 2020 We find out the general solution of a generalized Cauchy-Jensen functional equation and prove its stability. In fact, we investigate the existence of a Cauchy-Jensen mapping related to the generalized Cauchy-Jensen functional equation and prove its ...
Won-Gil Park, Jae-Hyeong Bae
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Functional Differential Equations and Jensen’s Inequality [PDF]
Journal of Mathematical Analysis and Applications, 1987 The authors study various types of stability of the functional differential equations \(x'(t)=F(t,x_ t)\) where \(x_ t(s)=x(t+s),\)- h\(\leq s\leq 0\), and h is a positive constant. The main tool is the Lyapunov functionals. These functionals satisfy certain conditions involving functions which verify Jensen's inequality.
Becker, Leigh C +2 more
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ON CONDITIONAL JENSEN EQUATION
Demonstratio Mathematica, 2001 The author extends some results of \textit{C. Alsina} and \textit{J. L. Garcia-Roig} [in `Functional analysis, approximation theory and numerical analysis', Singapore: World Scientific, 5-7 (1994; Zbl 0877.39015)], \textit{R. Ger} and \textit{J. Sikorska} [Pr. Nauk. Univ. Śląsk. Katowicach, Ann. Math. Silesianae 1665, No.
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On a Jensen-Hosszú equation, II [PDF]
Mathematical Inequalities & Applications, 2012 We solve functional equation of the form f (x+ y− xy)+ f (xy) = 2 f ( x+ y 2 ) in the class of functions transforming the unit interval into the space of all reals. We also prove that this equation is stable in the Hyers-Ulam’s sense. Mathematics subject classification (2010): 39B82, 39B62, 26A61.
Zygfryd Kominek, Justyna Sikorska
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A Fixed Point Approach to the Stability of Quadratic Functional Equation with Involution
Fixed Point Theory and Applications, 2008 Cădariu and Radu applied the fixed point method to the investigation of Cauchy and Jensen functional equations. In this paper, we will adopt the idea of Cădariu and Radu to prove the Hyers-Ulam-Rassias stability of the quadratic functional equation
Zoon-Hee Lee, Soon-Mo Jung
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