Approximation of the Quadratic and Cubic Functional Equations in RN-spaces

Madjid Eshaghi-Gordji, John Michael Rassias, Meysam Bavand Savadkouhi · European Journal of Pure and Applied Mathematics · 2009

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Type: article
Published: 2009-10-09
Cited by: 23
References: 31
Access: Open access
OpenAlex: https://openalex.org/W88137520
Semantic Scholar: https://api.semanticscholar.org/CorpusID:115385476

Keywords

Mathematics, Quadratic equation, Functional equation, Applied mathematics, Mathematical analysis

References

Countable extension of triangular norms and their applications to the fixed point theory in probabilistic metric spacesOlga Hadžić, Endre Pap, Mirko Budinčević — 2002
Probabilistic Metric SpacesB. Schweizer, A. Sklar — 2011
Problems in modern mathematicsStanislaw M. Ulam — 1964
Solution of the Ulam stability problem for quartic mappingsJohn Michael Rassias — 1999
On approximation of approximately linear mappings by linear mappingsJohn Michael Rassias — 1982
Fuzzy versions of Hyers-Ulam-Rassias theoremAlireza Kamel Mirmostafaee, Mohammad Sal Moslehian — 2008
Fuzzy approximately cubic mappingsAlireza Kamel Mirmostafaee, Mohammad Sal Moslehian — 2008
On the stability of the linear mapping in Banach spacesThemistocles M. Rassias — 1978
On the stability of the additive Cauchy functional equation in random normed spacesDorel Miheţ, Viorel Radu — 2008
Classes of transformations and bordering transformationsD. G. Bourgin — 1951
Generalized quadratic mappings in several variablesChun-Gil Park — 2004
On the Stability of the Linear Functional Equation.D. H. Hyers — 1941
Proprieta’ locali e approssimazione di operatoriFulvia Skof — 1983
Quadratic Functional Equation and Inner Product SpacesPl. Kannappan — 1995
On the Stability of the linear Transformation in Banach Spaces.Tosio Aoki — 1950
Solution of a problem of UlamJohn Michael Rassias — 1989
Variational Problem of Some Quadratic Functionals in Complex AnalysisThemistocles M. Rassias, Keiichi SHIBATA — 1998
On the stability of the quadratic mapping in normed spacesSt. Czerwik — 1992
A Generalization of the Hyers-Ulam-Rassias Stability of Approximately Additive MappingsP. Găvruţa — 1994
On stability of additive mappingsZbigniew Gajda — 1991

Cited by

Random Stability of a Functional Equation Related to an Inner Product SpaceDong Yun Shin, Jung Rye Lee, Choonkil Park — 2012
HYERS-ULAM-RASSIAS STABILITY OF FUNCTIONAL EQUATIONS IN MENGER PROBABILISTIC NORMED SPACESNasrin Eghbali, Masoud Ganji — 2012
Approximate n-Lie Homomorphisms and Jordan n-Lie Homomorphisms on n-Lie AlgebrasM‎. ‎Eshaghi Gordji, Gwang Hui Kim — 2012
Generalized Ulam-Hyers Stability of Jensen Functional Equation in Šerstnev PN SpacesM‎. ‎Eshaghi Gordji, Mohammad Bagher Ghaemi, Hamid Majani — 2010
A fixed points approach to stability of the Pexider equationElhoucien Elqorachi, John Michael Rassias, Belaid Bouikhalene — 2014
The Fixed Point Method for Fuzzy Approximation of a Functional Equation Associated with Inner Product SpacesM‎. ‎Eshaghi Gordji, H. Khodaei — 2010
Generalized Hyers-Ulam-Rassias Theorem in Menger Probabilistic Normed SpacesM‎. ‎Eshaghi Gordji, Mohammad Bagher Ghaemi, Hamid Majani — 2010
GENERALIZED HYERS-ULAM-RASSIAS THEOREM OF QUADRATIC FUNCTIONAL EQUATION IN MENGER PROBABLISTIC NORMED SPACESV. Arasu, J.B. Stalin — 2013
Generalized Ulam—Hyers stabilities of quartic derivations on Banach algebrasM‎. ‎Eshaghi Gordji, N. Ghobadipour — 2010
On nonlinear stability in various random normed spacesJohn Michael Rassias, Reza Saadati, Ghadir Sadeghi — 2011
Stabilities of Cubic Mappings in Fuzzy Normed SpacesAli Ghaffari, Ahmad Alinejad — 2010
Quadratic-Quartic Functional Equations in RN-SpacesMEshaghi Gordji, MBavand Savadkouhi, Choonkil Park — 2009
On the stability of an AQCQ-functional equation in random normed spacesChoonkil Park, Sun Young Jang, Jung Rye Lee — 2011
On the Stability of a General Mixed Additive-Cubic Functional Equation in Random Normed SpacesTian-Zhou Xu, JohnMichael Rassias, Wanxin Xu — 2010
On the stability of a nonic functional equation in quasi-normed spacesSoo Hwan Kim — 2016
Stability of Cubic Functional Equation in Random Normed SpaceSandra Pinelas, Vediyappan Govindan, K. Tamilvanan — 2018
A note on second order linear functional equations in random normed spacesMongkhon Tuntapthai — 2019
Ulam stability of a functional equation deriving from quadratic and additive mappings in random normed spacesK. Tamilvanan, Jung Rye Lee, Choonkil Park — 2021
Hyers-Ulam stability of an n-variable quartic functional equationVediyappan Govindan, In-Ho Hwang, Choonkil Park — 2021
Hyers-Ulam Stability of the Functional Equation ( 1 ) : An Odd CaseDong-Yun Shin, Jung Rye Lee, Choonkill Park — 2012

Related papers

On the Stability of the Linear Functional Equation.D. H. Hyers — 1941
On the stability of the linear mapping in Banach spacesThemistocles M. Rassias — 1978
On the Stability of the linear Transformation in Banach Spaces.Tosio Aoki — 1950
A Generalization of the Hyers-Ulam-Rassias Stability of Approximately Additive MappingsP. Găvruţa — 1994
On approximation of approximately linear mappings by linear mappingsJohn Michael Rassias — 1982
Problems in modern mathematicsStanislaw M. Ulam — 1964
On stability of additive mappingsZbigniew Gajda — 1991
Solution of a problem of UlamJohn Michael Rassias — 1989
On the stability of the additive Cauchy functional equation in random normed spacesDorel Miheţ, Viorel Radu — 2008
Solution and Stability of a Mixed Type Cubic and Quartic Functional Equation in Quasi-Banach SpacesM‎. ‎Eshaghi Gordji, S. Zolfaghari, John Michael Rassias — 2009