Results 11 to 20 of about 153,653 (286)

Stability of a Bi-Jensen Functional Equation II

Journal of Inequalities and Applications, 2009
We investigate the stability of the bi-Jensen functional equation II f((x+y)/2,z)−f(x,z)−f(y,z)=0,  2f(x,(y+z)/2)−f(x,y)−f(x,z)=0 in the spirit of Găvruta.
Lee Yang-Hi, Jun Kil-Woung, Jung Il-Sook
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On the stability of set-valued functional equations with the fixed point alternative [PDF]

, 2012
Using the fixed point method, we prove the Hyers-Ulam stability of a Cauchy-Jensen type additive set-valued functional equation, a Jensen type additive-quadratic set-valued functional equation, a generalized quadratic set-valued functional equation and a
Choonkil Park, Hamid Rezaei, Hassan Azadi Kenary, Yousof Gheisari   +3 more
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Fuzzy Stability of Jensen‐Type Quadratic Functional Equations [PDF]

Abstract and Applied Analysis, 2009
We prove the generalized Hyers‐Ulam stability of the following quadratic functional equations 2f((x + y)/2) + 2f((x − y)/2) = f(x) + f(y) and f(ax + ay) + (ax − ay) = 2a2f(x) + 2a2f(y) in fuzzy Banach spaces for a nonzero real number a with a ≠ ±1/2.
Jang, Sun-Young, Lee, Jung Rye, Park, Choonkil, Shin, Dong Yun   +3 more
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A Fixed Point Approach to the Stability of a Cauchy-Jensen Functional Equation

Abstract and Applied Analysis, 2012
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 ...
Jae-Hyeong Bae, Won-Gil Park
doaj   +1 more source

Asymptotic stability of the Cauchy and Jensen functional equations [PDF]

, 2016
The aim of this note is to investigate the asymptotic stability behaviour of the Cauchy and Jensen functional equations. Our main results show that if these equations hold for large arguments with small error, then they are also valid everywhere with a ...
A. Bahyrycz, A. Bahyrycz, D.G. Bourgin, D.H. Hyers, G.-L. Forti, G.-L. Forti, J. Brzdȩk, K. Nikodem, L. Losonczi, L. Maligranda, L. Székelyhidi, M. Piszczek, R. Badora, R. Badora, R. Badora, S.-M. Jung, T. Aoki, Th.M. Rassias, Zs. Páles, Á. Száz   +19 more
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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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Some hyperstability and stability results for the Cauchy and Jensen equations

Journal of Inequalities and Applications, 2022
In this paper we give some hyperstability and stability results for the Cauchy and Jensen functional equations on restricted domains. We provide a simple and short proof for Brzdȩk’s result concerning a hyperstability result for the Cauchy equation.
Mohammad Bagher Moghimi, Abbas Najati
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Scaling function and universal amplitude combinations for self-avoiding polygons [PDF]

, 2001
We analyze new data for self-avoiding polygons, on the square and triangular lattices, enumerated by both perimeter and area, providing evidence that the scaling function is the logarithm of an Airy function.
A J Guttmann, Bousquet-Mélou M, Brak R, C Richard, Cardy J L, Enting I G, Enting I G, Fisher M E, I Jensen, Janse van Rensburg E J, Jensen I, Jensen I, Prellberg T, Prellberg T, Prellberg T, Prellberg T, Richard C, Richard C   +17 more
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Fuzzy Stability of Quadratic Functional Equations

Advances in Difference Equations, 2010
The fuzzy stability problems for the Cauchy additive functional equation and the Jensen additive functional equation in fuzzy Banach spaces have been investigated by Moslehian et al.
Dong Yun Shin, Choonkil Park, Sun-Young Jang, Jung Rye Lee   +3 more
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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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