فهرست مطالب jung rye lee
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International Journal Of Nonlinear Analysis And Applications, Volume:14 Issue: 1, Jan 2023, PP 193 -204In this article, we introduce a new generalized Euler-Lagrange $(m,n)$-cubic functional equation with its general solution. Also, we investigate its various stabilities related to the Ulam problem in fuzzy normed linear spaces using Felbin's concept. Also, we provide a counter-example for the non-existence of stability of a generalized Euler-Lagrange $(m,n)$-cubic functional equation.Keywords: Euler-Lagrange cubic functional equation, Hyers-Ulam stability, generalized Hyers-Ulam- stability, Fuzzy normed linear space}
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International Journal Of Nonlinear Analysis And Applications, Volume:13 Issue: 2, Summer-Autumn 2022, PP 1747 -1755
Let A be a unital C∗-algebra. In this paper, we investigate the additive (u,β)-functional equation f(x)+u∗f(uy)+f(z)=β−1f(β(x+y+z)) for all unitary elements u in A and for a fixed nonzero complex number β. Using the fixed point method and the direct method, we prove the Hyers-Ulam stability of the additive (u,β)-functional equation (???) in Banach modules.
Keywords: Hyers-Ulam stability, additive (u beta)-functional equation, A-linear mapping fixed point method, direct method, Banach module} -
International Journal Of Nonlinear Analysis And Applications, Volume:13 Issue: 1, Winter-Spring 2022, PP 3239 -3248
In this paper, the lattice derivatives and their properties are introduced and next to the generalized stability of lattice derivatives is investigated using the direct and fixed point method.
Keywords: Banach lattice, stability functional equation, f-algebra, lattice derivation.2010 MSC: Primary 39B82, 46A40, Secondary 97H50, 46B42} -
International Journal Of Nonlinear Analysis And Applications, Volume:12 Issue: 2, Summer-Autumn 2021, PP 1157 -1161
In the present article, we prove some result using $C_*$-class function in the notion of C*-algebra valued metric space which is more general than metric space. The obtained results extend and generalize some of the results in the literature.
Keywords: C∗-algebra valued metric space, C∗-class function, fixed point} -
In cite{p}, Park introduced the quadratic $rho$-functional inequalities begin{eqnarray} && |f(x+y)+f(x-y)-2f(x)-2f(y)| && qquad le left|rholeft(2 fleft(frac{x+y}{2}right) + 2 flef (frac{x-y}{2}right)- f(x) - f(y)right)right|, nonumber end{eqnarray} where $rho$ is a fixed complex number with $|rho|and begin{eqnarray} && left|2 fleft(frac{x+y}{2}right) + 2 fleft(frac{x-y}{2}right)- f(x) - f(y)right| && qquad le |rho(f(x+y)+f(x-y)-2f(x)-2f(y))|, nonumber end{eqnarray} where $rho$ is a fixed complex number with $|rho| In this paper, we prove the Hyers-Ulam stability of the quadratic $rho$-functional inequalities (0.1) and (0.2) in $beta$-homogeneous complex Banach spaces and prove the Hyers-Ulam stability of quadratic $rho$-functional equations associated with the quadratic $rho$-functional inequalities (0.1) and (0.2) in $beta$-homogeneous complex Banach spaces.Keywords: Hyers, Ulam stability, $beta$, homogeneous space, quadratic $rho$, functional equation, quadratic $rho$, functional inequality}
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