[PDF] Top 20 Approximate homomorphisms and derivations on random Banach algebras

... The study of stability problems originated from a famous talk Under what condition does there exist a homomorphism near an approximate homomorphism? given by S. M. Ulam [] in . Next year, in , D. H. ... See full document

... of derivations on random Banach ∗-algebras are exactly derivations by using a fixed point ...on random Banach ∗-algebras are exactly quadratic ...of ... See full document

... and approximate homomorphisms have been extensively investigated by a number of authors, and there are many interesting results concerning this problem (see ... See full document

... 2. Hyers, DH: On the stability of the linear functional equation. Proc. Natl. Acad. Sci. USA 27, 222-224 (1941) 3. Aoki, T: On the stability of the linear transformation in Banach spaces. J. Math. Soc. Jpn. 2, ... See full document

... sequence in fuzzy normed space is Cauchy. If each Cauchy sequence is convergent, then the fuzzy norm is said to be complete and the fuzzy normed space is called a fuzzy Banach space. Let X be an algebra and (X, N) ... See full document

... In this paper, using the fixed point method, we prove the generalized Hyers-Ulam stability of homomorphisms and derivations in non-Archimedean random C * -algebras and non-Archimedean ran[r] ... See full document

... The basic problem of the stability of functional equations asks whether an approximate solution of the Cauchy functional equation f (x + y) = f (x) + f (y) can be approximated by a solution of this equation []. ... See full document

... commutative Banach algebra and D : A → A is a continuous linear derivation, then DA ⊆ ...linear derivations on a semisimple commutative Banach algebra, which had been proved by Johnson ...ring ... See full document

... We can say that a mathematical property is stable if any mathematical object satisfying a certain mathematical property approximately is near to the object exactly satisfying the mathematical property. On the stability ... See full document

... A basic question in the theory of functional equations is as follows: when is it true that a function, which approximately satisfies a functional equation, must be close to an exact solution of the equation? If the ... See full document

... -Jordan homomorphisms on Banach ...each approximate 3-Jordan homomorphism h from a Banach algebra into a semisimple commutative Banach algebra there corresponds a unique 3-ring ... See full document

... In this paper, we introduce functional equations of *-derivations and of quadratic *-derivations. we prove the stability of *-derivations associated with the Cauchy func- tional equation and the ... See full document

... Park, Fixed points and Hyers-Ulam- Rassias stability of Cauchy-Jensen func- tional equations in Banach algebras , Fixed Point Theory Appl.. Saa- dati, Random homomorphisms and random der[r] ... See full document

... every approximate linear left derivation on a semisimple Banach algebra is ...linear derivations on Banach algebras and we first study the conditions for a linear derivation on a ... See full document

... These three automatic continuity questions of when homomorphisms, derivations, and point derivations from a Banach algebra are continuous have been extensively studied for various specia[r] ... See full document

... I would like to thank Professor Gábor Elek for the many fun conversations (math- ematical or otherwise) and for his (futile) efforts to talk some sense into me about picking up an interest in more fashionable areas of ... See full document

... 1. Ulam, SM: Problems in Modern Mathematics. Science ed. Wiley, New York (1940) (Chapter VI) 2. Hyers, DH: On the stability of the linear functional equation. Proc. Natl. Acad. Sci. USA 27, 222-224 (1941) 3. Aoki, T: On ... See full document

... The stability problem of functional equations originated from the question of Ulam [] concerning the stability of group homomorphisms. Hyers [] gave the first affirmative par- tial answer to the question of Ulam ... See full document

... points of view [–]. We use the definition of fuzzy normed spaces given in [, ] to in- vestigate the stability of derivation in the fuzzy Banach ∗ -algebra setting. The stability of functional equations in ... See full document

... We say that a functional equation E is stable if any function f which approximately satisfies the equation E is near to an exact solution of E . The problem of stability of functional equations was formulated by Ulam in ... See full document