Approximation theory and functional equations (II)
نویسندگان
چکیده
منابع مشابه
fragmentability and approximation
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متن کاملQuadratic $alpha$-functional equations
In this paper, we solve the quadratic $alpha$-functional equations $2f(x) + 2f(y) = f(x + y) + alpha^{-2}f(alpha(x-y)); (0.1)$ where $alpha$ is a fixed non-Archimedean number with $alpha^{-2}neq 3$. Using the fixed point method and the direct method, we prove the Hyers-Ulam stability of the quadratic $alpha$-functional equation (0.1) in non-Archimedean Banach spaces.
متن کاملSome functional equations originating from number theory
If the answer is affirmative, the functional equation for homomorphisms is said to be stable in the sense of Hyers and Ulam because the first result concerning the stability of functional equations was presented by Hyers. Indeed, he has answered the question of Ulam for the case where G1 and G2 are assumed to be Banach spaces (see [8]). We may find a number of papers concerning the stability re...
متن کاملApproximation of Mixed-Type Functional Equations in Menger PN-Spaces
and Applied Analysis 3 Clearly, every Menger PN-space is probabilistic metric space having a metrizable uniformity on X if supa<1T a, a 1. Definition 1.3. Let X,Λ, T be a Menger PN-space. i A sequence {xn} in X is said to be convergent to x in X if, for every > 0 and λ > 0, there exists positive integer N such that Λxn−x > 1 − λ whenever n ≥ N. ii A sequence {xn} in X is called Cauchy sequence ...
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ژورنال
عنوان ژورنال: Journal of Approximation Theory
سال: 1973
ISSN: 0021-9045
DOI: 10.1016/0021-9045(73)90101-9