In this paper we study general solutions of the following Pexider functional equation (4 − k)f1 Xk i=1 xi + Xk j=2 fj Xk i=1,i6=j xi − xj + fk+1 − x1 + Xk i=2 xi = 4Xk j=1 fk+j+1 xj ,
on a vector space over a field of characteristic different from 2, for k ≥ 3
Acz´el, J. Lectures on Functional Equations and their Applications (Academic Press, New York, London, 1966).
Acz´el, J. and Dhombers, J. Functional Equations in Several Variables (Encyclopedia of Mathematics and its Applications 31, Cambridge University Press, Cambridge, 1989).
Baak, C., Boo, D. and Rassias, Th. M. Generalized additive mapping in Banach modules and isomorphisms between C*-algebras, J. Math. Anal. Appl. 314, 150–161, 2006.
Baak, C., Hong, S. and Kim, M. Generalized quadratic mappings of r-type in several vari- ables, J. Math. Anal. Appl. 310, 116–127, 2005.
Chu, H. and Kang, D. On the stability of an n-dimensional cubic functional equation, J. Math. Anal. Appl. 325, 595–607, 2007.
Gordji, M. E. and Khodaei, H. On the generalized Hyers-Ulam-Rassias stability of quadratic functional equations, Abstr. Appl. Anal. 2009, 11 pages, 2009.
Hyers, D., Isac, G. and Rassias, Th. M. Stability of Functional Equations in Several Variables (Birkh¨auser Boston Inc., Boston, MA, 1998).
Janfada, M. and Shourvazi, R. On solutions and Hyers–Ulam–Rassias stability of a gener- alized quadratic equation, Internat. J. Nonlinear Science 10 (2), 231–237, 2010.
Jun, K. and Kim, H. Ulam stability problem for generalized A-quadratic mappings, J. Math. Anal. Appl. 305, 466–476, 2005.
Jun, K. and Kim, H. On the generalized A-quadratic mappings associated with the variance of a discrete-type distribution, Nonlinear Analysis-TMA 62, 975–987, 2005.
Jun, K. and Kim, H. Stability problem of Ulam for generalized forms of Cauchy functional equation, J. Math. Anal. Appl. 312, 535–547, 2005.
Jung, S. Quadratic functional equations of Pexider type, Internat. J. Math. Math. Sci. 24 (5), –359, 2000.
Kang, D. and Chu, H. Stability problem of Hyers-Ulam-Rassias for generalized forms of cubic functional equation, Acta Mathematica Sinica 24 (3), 491–502, 2007.
Kannappan, P. Quadratic functional equation and inner product spaces, Results Math. (3-4), 368–372, 1995.
Kuczma, M. An Introduction to the Theory of Functional Equations and Inequalities (Birk¨auser Verlag AG, ???, 2009).
Lee, J. and Shin, D. On the Cauchy-Rassias stability of a generalized additive functional equation, J. Math. Anal. Appl. 339, 372–383, 2008.
Najati, A. and Rassias, Th. M. Stability of a mixed functional equation in several variables on Banach modules, Nonlinear Analysis-TMA, 72 (3-4), 1755–1767, 2010.
Park, C. and Rassias, Th. M. HyersˆuUlam stability of a generalized Apollonius type quadratic mapping, J. Math. Anal. Appl. 322, 371–381, 2006.
Park, C. Cauchy-Rassias stability of a generalized TrifÆs mapping in Banach modules and its applications, Nonlinear Analysis-TMA 62, 595–613, 2005.
Park, C. Generalized quadratic mappings in several variables, Nonlinear Analysis-TMA 57, –722, 2004.
Zhang, D. and Cao, H. Stability of functional equations in several variables, Acta Mathe- matica Sinica 23 (2), 321–326, 2007.
ON SOLUTIONS OF A GENERALIZED QUADRATIC FUNCTIONAL EQUATION OF PEXIDER TYPE
Year 2012,
Volume: 41 Issue: 2, 265 - 270, 01.02.2012
Acz´el, J. Lectures on Functional Equations and their Applications (Academic Press, New York, London, 1966).
Acz´el, J. and Dhombers, J. Functional Equations in Several Variables (Encyclopedia of Mathematics and its Applications 31, Cambridge University Press, Cambridge, 1989).
Baak, C., Boo, D. and Rassias, Th. M. Generalized additive mapping in Banach modules and isomorphisms between C*-algebras, J. Math. Anal. Appl. 314, 150–161, 2006.
Baak, C., Hong, S. and Kim, M. Generalized quadratic mappings of r-type in several vari- ables, J. Math. Anal. Appl. 310, 116–127, 2005.
Chu, H. and Kang, D. On the stability of an n-dimensional cubic functional equation, J. Math. Anal. Appl. 325, 595–607, 2007.
Gordji, M. E. and Khodaei, H. On the generalized Hyers-Ulam-Rassias stability of quadratic functional equations, Abstr. Appl. Anal. 2009, 11 pages, 2009.
Hyers, D., Isac, G. and Rassias, Th. M. Stability of Functional Equations in Several Variables (Birkh¨auser Boston Inc., Boston, MA, 1998).
Janfada, M. and Shourvazi, R. On solutions and Hyers–Ulam–Rassias stability of a gener- alized quadratic equation, Internat. J. Nonlinear Science 10 (2), 231–237, 2010.
Jun, K. and Kim, H. Ulam stability problem for generalized A-quadratic mappings, J. Math. Anal. Appl. 305, 466–476, 2005.
Jun, K. and Kim, H. On the generalized A-quadratic mappings associated with the variance of a discrete-type distribution, Nonlinear Analysis-TMA 62, 975–987, 2005.
Jun, K. and Kim, H. Stability problem of Ulam for generalized forms of Cauchy functional equation, J. Math. Anal. Appl. 312, 535–547, 2005.
Jung, S. Quadratic functional equations of Pexider type, Internat. J. Math. Math. Sci. 24 (5), –359, 2000.
Kang, D. and Chu, H. Stability problem of Hyers-Ulam-Rassias for generalized forms of cubic functional equation, Acta Mathematica Sinica 24 (3), 491–502, 2007.
Kannappan, P. Quadratic functional equation and inner product spaces, Results Math. (3-4), 368–372, 1995.
Kuczma, M. An Introduction to the Theory of Functional Equations and Inequalities (Birk¨auser Verlag AG, ???, 2009).
Lee, J. and Shin, D. On the Cauchy-Rassias stability of a generalized additive functional equation, J. Math. Anal. Appl. 339, 372–383, 2008.
Najati, A. and Rassias, Th. M. Stability of a mixed functional equation in several variables on Banach modules, Nonlinear Analysis-TMA, 72 (3-4), 1755–1767, 2010.
Park, C. and Rassias, Th. M. HyersˆuUlam stability of a generalized Apollonius type quadratic mapping, J. Math. Anal. Appl. 322, 371–381, 2006.
Park, C. Cauchy-Rassias stability of a generalized TrifÆs mapping in Banach modules and its applications, Nonlinear Analysis-TMA 62, 595–613, 2005.
Park, C. Generalized quadratic mappings in several variables, Nonlinear Analysis-TMA 57, –722, 2004.
Zhang, D. and Cao, H. Stability of functional equations in several variables, Acta Mathe- matica Sinica 23 (2), 321–326, 2007.
Janfada, M., & Shourvazi, R. (2012). ON SOLUTIONS OF A GENERALIZED QUADRATIC FUNCTIONAL EQUATION OF PEXIDER TYPE. Hacettepe Journal of Mathematics and Statistics, 41(2), 265-270.
AMA
Janfada M, Shourvazi R. ON SOLUTIONS OF A GENERALIZED QUADRATIC FUNCTIONAL EQUATION OF PEXIDER TYPE. Hacettepe Journal of Mathematics and Statistics. February 2012;41(2):265-270.
Chicago
Janfada, Mohammad, and Rahele Shourvazi. “ON SOLUTIONS OF A GENERALIZED QUADRATIC FUNCTIONAL EQUATION OF PEXIDER TYPE”. Hacettepe Journal of Mathematics and Statistics 41, no. 2 (February 2012): 265-70.
EndNote
Janfada M, Shourvazi R (February 1, 2012) ON SOLUTIONS OF A GENERALIZED QUADRATIC FUNCTIONAL EQUATION OF PEXIDER TYPE. Hacettepe Journal of Mathematics and Statistics 41 2 265–270.
IEEE
M. Janfada and R. Shourvazi, “ON SOLUTIONS OF A GENERALIZED QUADRATIC FUNCTIONAL EQUATION OF PEXIDER TYPE”, Hacettepe Journal of Mathematics and Statistics, vol. 41, no. 2, pp. 265–270, 2012.
ISNAD
Janfada, Mohammad - Shourvazi, Rahele. “ON SOLUTIONS OF A GENERALIZED QUADRATIC FUNCTIONAL EQUATION OF PEXIDER TYPE”. Hacettepe Journal of Mathematics and Statistics 41/2 (February 2012), 265-270.
JAMA
Janfada M, Shourvazi R. ON SOLUTIONS OF A GENERALIZED QUADRATIC FUNCTIONAL EQUATION OF PEXIDER TYPE. Hacettepe Journal of Mathematics and Statistics. 2012;41:265–270.
MLA
Janfada, Mohammad and Rahele Shourvazi. “ON SOLUTIONS OF A GENERALIZED QUADRATIC FUNCTIONAL EQUATION OF PEXIDER TYPE”. Hacettepe Journal of Mathematics and Statistics, vol. 41, no. 2, 2012, pp. 265-70.
Vancouver
Janfada M, Shourvazi R. ON SOLUTIONS OF A GENERALIZED QUADRATIC FUNCTIONAL EQUATION OF PEXIDER TYPE. Hacettepe Journal of Mathematics and Statistics. 2012;41(2):265-70.