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ISSN : 1226-0657
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Vol.24 No.1
Abstract
In this paper we obtain some integral inequalities by using Stieltjes derivatives, and we apply our results to the study of asymptotic behavior of a certain second-order integro-differential equation.
Abstract
In this paper, we introduce and solve the following additive (<TEX>${\rho}_1$</TEX>, <TEX>${\rho}_2$</TEX>)-functional inequality <TEX>$${\Large{\parallel}}2f(\frac{x+y}{2})-f(x)-f(y){\Large{\parallel}}{\leq}{\parallel}{\rho}_1(f(x+y)+f(x-y)-2f(x)){\parallel}+{\parallel}{\rho}_2(f(x+y)-f(x)-f(y)){\parallel}$$</TEX> where <TEX>${\rho}_1$</TEX> and <TEX>${\rho}_2$</TEX> are fixed nonzero complex numbers with <TEX>$\sqrt{2}{\mid}{\rho}_1{\mid}+{\mid}{\rho}_2{\mid}<1$</TEX>. Using the fixed point method and the direct method, we prove the Hyers-Ulam stability of the additive (<TEX>${\rho}_1$</TEX>, <TEX>${\rho}_2$</TEX>)-functional inequality (1) in complex Banach spaces.
Abstract
<TEX>$Fo{\check{s}}ner$</TEX> [1] defined a module left (m, n)-derivation and proved the Hyers-Ulam stability of module left (m, n)-derivations. In this note, we prove that every module left (m, n)-derivation is trival if the algebra is unital and <TEX>$m{\neq}n$</TEX>.
Abstract
The present paper aims at harnessing the technique of Lie Algebra and operational methods to derive and interpret generating relations for the three-variable Hermite Polynomials <TEX>$H_n$</TEX>(x, y, z) introduced recently in [2]. Certain generating relations for the polynomials related to <TEX>$H_n$</TEX>(x, y, z) are also obtained as special cases.
Abstract
In this paper, we propose an accelerating scheme of convergence of numerical solutions of fuzzy non-linear equations. Numerical experiments show that the new method has significant acceleration of convergence of solutions of fuzzy non-linear equation. Three-dimensional graphical representation of fuzzy solutions is also provided as a reference of visual convergence of the solution sequence.