Sometime in modeling applied problems there may be a degree of uncertainty in the parameters used in the model or some measurements may be imprecise. Due to such features, we are tempted to consider the study of functional equations in the fuzzy setting. The notion of fuzzy sets was first introduced by Zadeh [31] in 1965 which is a powerful hand set for modeling uncertainty and vagueness in var...

The stability problem of functional equations is originated from a question of Ulam 1 concerning the stability of group homomorphisms. Hyers 2 gave a first affirmative partial answer to the question of Ulam for Banach spaces. Hyers’ Theorem was generalized by Aoki 3 for additive mappings and by Th. M. Rassias 4 for linear mappings by considering an unbounded Cauchy difference. The paper of Th. ...

Katsaras 1 defined a fuzzy norm on a vector space to construct a fuzzy vector topological structure on the space. Some mathematicians have defined fuzzy norms on a vector space from various points of view 2–4 . In particular, Bag and Samanta 5 , following Cheng and Mordeson 6 , gave an idea of fuzzy norm in such a manner that the corresponding fuzzy metric is of Kramosil and Michálek type 7 . T...

In any dimension [Formula: see text], for given mass text] and when the energy functional is coercive on constraint we are interested in searching constrained critical points at positive levels. Under general conditions suitable ranges of mass, manage to construct such which appear as a local minimizer or correspond mountain pass symmetric level. particular, our results shed some light cubic–qu...

1 Department of Mathematics, School of Science, Beijing Institute of Technology, Beijing 100081, China 2 Pedagogical Department E.E., Section of Mathematics and Informatics, National and Kapodistrian University of Athens, 4, Agamemnonos Str., Aghia Paraskevi, 15342 Athens, Greece 3 School of Communication and Information Engineering, University of Electronic Science and Technology of China, Che...

In this paper, we obtain the general solution and the stability result for the following functional equation in random normed spaces (in the sense of Sherstnev) under arbitrary t-norms f(x + 3y) + f(x− 3y) = 9(f(x + y) + f(x− y))− 16f(x).

in this article, a numerical approximation to the solution of the newell-whitehead equation (nwe) and cauchy problem of ill-posed non-linear diffusion equation have been studied. the presented scheme is obtained by using the derivative of the cubic b-spline quasi-interpolation (bsqi) to approximate the spatial derivative of the dependent variable and first order forward difference to approximat...

the srk two-parameter cubic equation of state has been used for the calculation of the equilibrium constant using the liquid and vapor fugacity coefficients for three binary mixtures. dew and bubble points have been determined using the equilibrium constants and the phase envelope has been plotted showing dearly that retrograde condenstaion occurs. the following percent deviations have been obt...

the stability problem of the functional equation was conjectured by ulam and was solved by hyers in the case of additive mapping. baker et al. investigated the superstability of the functional equation from a vector space to real numbers.in this paper, we exhibit the superstability of $m$-additive maps on complete non--archimedean spaces via a fixed point method raised by diaz and margolis.