Random Stability of Quadratic Functional Equations


  • Mee Kwang Kang Dong-eui University, Busan




Random P-Normed Space, Quadratic Functional Equation, Generalized Hyers-Ulam Stability, Direct Method, Fixed Point Method


In this paper, we investigate the generalized Hyers-Ulam stability on random -normed spaces associated with the following generalized quadratic functional equation 8373_11.PNG8373_2.PNG,where  is a fixed positive integer via two methods


Download data is not yet available.

Author Biography

Mee Kwang Kang, Dong-eui University, Busan

Department of Mathematics, Dong-eui University, Busan 47340, Republic of Korea


S.M. Ulam, Problems in Modern Mathematics, Science Editions, John Wiley & Sons, New York, USA, 1940.

D.H. Hyers, On the stability of the linear functional equation, Proc. Nat. Acad. Sci. USA 27 (1941), 222-224.

T. Aoki, On the stability of the linear transformation in Banach spaces, J. Math. Soc. Japan. 2 (1950), 64-66.

Th.M. Rassias, On the stability of the linear mapping in Banach spaces, Proc. Amer. Math. Soc. 72 (1978), 297-300.

P. Ga ̃vruta, A generalization of the Hyers-Ulam-Rassias stability of approximately additive mappings, J. Math. Anal. Appl. 184 (1994), 431-436.

L. Ca ̆dariu, V. Radu, Fixedoints, and the stability of Jensen's functional equation, J. Iraq. Pure Appl. Math. 4 (2003), No. 1, Art. 4.

P.W. Cholewa, Remarks on the stability of functional equations, Aeq. Math. 27(1984), 76-86.

P. Czerwik, On the stability of the quadratic mapping in normed spaces, Abh. Math. Sem. Univ. Hamburg, 62(1992), 59-64.

F. Skof, Proprieta locali e approssimazione di operatori, Rend. Sem. Mat. Fis. Milano, 53(1983), 113-129.

Y.J. Cho, TM. Rassias, R. Saadati, Stability of Functional Equations in Random Normed Spaces, Springer Optimization and Its Application 86, Springer New York, 2013.

Khodaei, ME. Gordji, S.S. Kim and Y.J. Cho, Approximation of radical functional equations related to quadratic and quartic mappings, J. Math. Anal. Appl. 395(2012), 284-297.

D. Mihet, V. Radu, On the stability of the additive Cauchy functional equation in random normed spaces, J. Math. Anal. Appl. 343(2008), 567-572.

J.M. Rassias, R. Saadati, G. Sadeghi, J. Vahidi, On nonlinear stability in various random normed spaces, J. Ineq. Appl. 2011, 2011:62.

B. Schweizer, A. Skar, Probability Metric Spaces, North-Holland Series in Probability and Applied Math. New York, USA 1983.

A.N. Sherstnev, On the notion of s random normed spaces, Dpkl. Akad. Nauk SSSR 149, 280-283 (in Russian).

O. Hadz ̃ic ́, E. Pap, M. Budincevi'{c}, Countable extension of triangular norms and their applications to the fixed-point theory in probabilistic metric spaces, Kybernetika 38(2002), 363-381.

Golet, Random $p$-normed spaces and applications to random functions, Istanbul Univ. Fen Fak. Mat. Fiz. Astro. Derg. 1(2004-2005), 31-42.

J.B. Dias, B. Margolis, A fixed point theorem of the alternative for contractions on a generalized complete metric space, Bull. Amer. Math. Soc. 74 (1968), 305-309.



How to Cite

Kang, M. K. (2019). Random Stability of Quadratic Functional Equations. JOURNAL OF ADVANCES IN PHYSICS, 16(1), 498-507. https://doi.org/10.24297/jap.v16i1.8373