International Journal of
Physical Sciences

  • Abbreviation: Int. J. Phys. Sci.
  • Language: English
  • ISSN: 1992-1950
  • DOI: 10.5897/IJPS
  • Start Year: 2006
  • Published Articles: 2578

Full Length Research Paper

A fixed point approach to the stability of a general mixed additive-cubic functional equation in quasi fuzzy normed spaces

Tian Zhou Xu1*, John Michael Rassias2 and Wan Xin Xu3
1Department of Mathematics, School of Science, Beijing Institute of Technology, Beijing  100081, People’s Republic of China. 2Pedagogical Department E.E., Section of Mathematics and Informatics, National and Capodistrian University of Athens, 4 Agamemnonos Str., Aghia Paraskevi, Athens  15342, Greece. 3School of Communication and Information Engineering, University of Electronic Science and Technology of China, Chengdu 611731, People’s Republic of China.
Email: [email protected]

  •  Accepted: 25 February 2010
  •  Published: 18 January 2011

Abstract

In this paper, we use the fixed point alternative theorem to establish Hyers-Ulam-Rassias stability of the general mixed additive-cubic functional equation where functions map a linear space into a complete quasi fuzzy p-normed space. In addition, some applications of our results in the stability of general mixed additive-cubic mappings from a linear space into a quasi p-normed space will be exhibited. Finally, we establish some results of continuous approximately general mixed additive-cubic mappings in quasi fuzzy p-normed spaces.

 

Key words: Fuzzy normed space, fuzzy stability, Hyers-Ulam-Rassias stability, additive function, cubic function, fixed point alternative.

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