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A Fixed Point Approach to the Stability of Quadratic Equations in Quasi Normed Spaces

Alireza Kamel Mirmostafaee
경북대학교 자연과학대학 수학과|2009.12|Kyungpook Mathematical Journal|제49권 제4호|pp. 691-700

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참고문헌

키워드

Hyers-Ulam-Rassias stabilityquadratic functional equationfixed point alternativequasi p-norm
주제분류수학

초록

We use the xed alternative theorem to establish Hyers{Ulam{Rassias stabil- ity of the quadratic functional equation where functions map a linear space into a complete quasi p-normed space. Moreover, we will show that the continuity behavior of an approximately quadratic mapping, which is controlled by a suitable continuous function, implies the continuity of a unique quadratic function, which is a good approximation to the mapping. We also give a few applications of our results in some special cases.

Abstract

We use the xed alternative theorem to establish Hyers{Ulam{Rassias stabil- ity of the quadratic functional equation where functions map a linear space into a complete quasi p-normed space. Moreover, we will show that the continuity behavior of an approximately quadratic mapping, which is controlled by a suitable continuous function, implies the continuity of a unique quadratic function, which is a good approximation to the mapping. We also give a few applications of our results in some special cases.

참고문헌 (25)

  1. T. Aoki, "bounded linear topological spaces", Proc. Imp. Acad. Tokyo, 18, pp.588~594 (1942)
  2. T. Aoki, "On the stability of the linear transformation in Banach spaces", J. Math. Soc. Japan, 2, pp.64~66 (1950)
  3. Y. Benyamini, "Geomertic nonlineat functional analysis volume 1", Coll. Pub. ( Amer. Math. Soc.), 48 (2000)
  4. L. Cadariu, "Fixed points in generalized metric space and the stability of a quartic func-tional equation", Bul. Stiint. Univ. Politeh. Timis. Ser. Mat. Fiz, 50(64), pp.25~34 (2005)
  5. L. Cadariu, "Fixed points and the stability of quadratic functional equa-tions", An. Univ. Timisoara Ser. Mat.-Inform, 41(1), pp.25~48 (2003)
  6. P. W. Cholewa, "Remarks on the stability of functional equations", Aequationes Math, 27, pp.76~86 (1984)
  7. S. Czerwik, "On the stability of the quadratic mapping in normed spaces", Abh. Math. Sem. Univ. Hamburg, 62, pp.59~64 (1992)
  8. S. Czerwik, "The stability of the quadratic functional equation, in: Stability of map- pings of Hyers{Ulam type", pp.81~91 (1994), Hadronic Press Collect. Orig. Artic., Hadronic Press
  9. S. Czerwik, "Functional Equations and Inequalities in Several Variables" (2002), World Scien-tific
  10. J. B. Diaz, "A xed point theorem of the alternative for the contractions on generalized complete metric space", Bull. Amer. Math. Soc, 74, pp.305~309 (1968)
  11. P. Gavruta, "A generalization of the Hyers{Ulam{Rassias stability of approximately additive mappings", J. Math. Anal. Appl, 184, pp.431~436 (1994)
  12. D. H. Hyers, "On the stability of the linear functional equation", Proc. Nat. Acad. Sci. U. S. A, 27, pp.222~224 (1941)
  13. S. -M. Jung, "Hyers{Ulam{Rassias Stability of Functional Equations in Mathematical Analysis" (2001), Hadronic Press
  14. 정순모, "A fixed point approach to the stability of quadratic functional equation", 대한수학회보, 43(3), pp.531~541 (2006), 대한수학회
  15. S. -M. Jung, "Hyers{Ulam stability of the quadratic equation of Pexider type", J. Korean Math. Soc, 38(3), pp.645~656 (2001)
  16. A. K. Mirmostafaee, "Stability of quartic mappings in non-Archimedean normed spaces", to be appear in Kyungpook Mathematical Journal(KMJ), ~
  17. A. K. Mirmostafaee, "Fuzzy stability of the Jensen functional equation", Fuzzy Sets and Systems, 159, pp.730~738 (2008)
  18. A. K. Mirmostafaee, "Fuzzy approximately cubic mappings", In- formation Sciences, 78(19), pp.3791~3798 (2008)
  19. A. K. Mirmostafaee, "Fuzzy almost quadratic functions Result", Math, 52, pp.161~177 (2008)
  20. V. Radu, "The xed point alternative and stability of functional equations", Fixed Point Theory, 4(1), pp.91~96 (2003)
  21. J. M. Rassias, "Alternative contraction principle and Ulam stability problem", Math. Sci. Res. J, 9(7), pp.190~199 (2005)
  22. Th. M. Rassias, "On the stability of the linear mapping in Banach spaces", Proc. Amer. Math. Soc, 72, pp.297~300 (1978)
  23. Th. M. Rassias, "Functional equations, inequalities and applications" (2003), Kluwer Academic Publishers
  24. F. Skof, "Local properties and approximations of operators", Rend. Sem. Mat. Fis. Mi- lano, 53, pp.113~129 (1983)
  25. S. M. Ulam, "Problems in Modern Mathematics (Chapter VI, Some Questions in Analysis: x1, Stability)" (1964), John Wiley & Sons

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On the Stability of a Quadratic Functional EquationJae-Hyeong Bae, Kil-Woung Jun, Soon-Mo Jung경북대학교 자연과학대학 수학과 · Kyungpook Mathematical Journal2003 · 제43권 제3호ON THE STABILITY OF RADICAL FUNCTIONAL EQUATIONS IN QUASI- -NORMED SPACES김성식, 양영오, 조열제, Madjid Eshaghi Gordji대한수학회 · 대한수학회보2014 · 제51권 제5호A FIXED POINT APPROACH TO THE CAUCHY-RASSIAS STABILITY OF GENERAL JENSEN TYPE QUADRATIC-QUADRATIC MAPPINGS박춘길, H. Khodaei, M. Eshaghi Gordji대한수학회 · 대한수학회보2010 · 제47권 제5호The Hyers-Ulam stability of a quadratic functional equation with involution in paranormed spaces김창일, 신창협강원경기수학회 · 한국수학논문집2016 · 제24권 제1호A Fixed Point Approach to the Stability of a Functional Equation박원길, 배재형경북대학교 자연과학대학 수학과 · Kyungpook Mathematical Journal2010 · 제50권 제4호Solution and stability of a functional equation deriving from additive, quadratic and quartic in quasi-Banach spaces박춘길, Mohammad Golestani, Norouz Ghobadipour강원경기수학회 · 한국수학논문집2025 · 제33권 제4호

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