Stability of a Jensen Type Logarithmic Functional Equation on Restricted Domains and Its Asymptotic Behaviors
نویسندگان
چکیده
Let R be the set of positive real numbers, B a Banach space, f : R → B, and > 0, p, q, P,Q ∈ R with pqPQ/ 0. We prove the Hyers-Ulam stability of the Jensen type logarithmic functional inequality ‖f xy − Pf x − Qf y ‖ ≤ in restricted domains of the form { x, y : x > 0, y > 0, xy ≥ d} for fixed k, s ∈ R with k / 0 or s / 0 and d > 0. As consequences of the results we obtain asymptotic behaviors of the inequality as xy → ∞.
منابع مشابه
On a new type of stability of a radical cubic functional equation related to Jensen mapping
The aim of this paper is to introduce and solve the radical cubic functional equation $fleft(sqrt[3]{x^{3}+y^{3}}right)+fleft(sqrt[3]{x^{3}-y^{3}}right)=2f(x)$. We also investigate some stability and hyperstability results for the considered equation in 2-Banach spaces.
متن کاملNon-Archimedean stability of Cauchy-Jensen Type functional equation
In this paper we investigate the generalized Hyers-Ulamstability of the following Cauchy-Jensen type functional equation$$QBig(frac{x+y}{2}+zBig)+QBig(frac{x+z}{2}+yBig)+QBig(frac{z+y}{2}+xBig)=2[Q(x)+Q(y)+Q(z)]$$ in non-Archimedean spaces
متن کاملSTABILITY OF THE JENSEN'S FUNCTIONAL EQUATION IN MULTI-FUZZY NORMED SPACES
In this paper, we define the notion of (dual) multi-fuzzy normedspaces and describe some properties of them. We then investigate Ulam-Hyers stability of Jensen's functional equation for mappings from linear spaces into multi-fuzzy normed spaces. We establish an asymptotic behavior of the Jensen equation in the framework of multi-fuzzy normed spaces.
متن کاملStability of Jensen-Type Functional Equations on Restricted Domains in a Group and Their Asymptotic Behaviors
متن کامل
stability of the quadratic functional equation
In the present paper a solution of the generalizedquadratic functional equation$$f(kx+ y)+f(kx+sigma(y))=2k^{2}f(x)+2f(y),phantom{+} x,yin{E}$$ isgiven where $sigma$ is an involution of the normed space $E$ and$k$ is a fixed positive integer. Furthermore we investigate theHyers-Ulam-Rassias stability of the functional equation. TheHyers-Ulam stability on unbounded domains is also studied.Applic...
متن کامل