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ISSN : 1226-0657
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Vol.24 No.3
Abstract
In this paper, we establish lower estimates for the modulus of the non-tangential derivative of the holomorphic functionf(z) at the boundary of the unit disc. Also, we shall give an estimate below |f''(b)| according to the first nonzero Taylor coefficient of about two zeros, namely z = 0 and <TEX>$z_0{\neq}0$</TEX>.
Abstract
In this paper, we propose a numerical method to solve fuzzy differential equations. Numerical experiments show that when the step size is small, the new method has significantly good approximate solutions of fuzzy differential equation. Graphical representation of fuzzy solutions in three-dimension is also provided as a reference of visual convergence of the solution sequence.
Abstract
In this paper we obtain some integral inequalities involving impulses and apply our results to a certain integro-differential equation with impulses. First, we obtain a bound of the equation, and we use the bound to study some qualitative properties of the equation.
Abstract
In this paper, we define <TEX>$C^*-ternary$</TEX> quadratic 3-Jordan homomorphisms associated with the quadratic mapping f(x + y) + f(x - y) = 2f(x) + 2f(y), and prove the Hyers-Ulam stability of <TEX>$C^*-ternary$</TEX> quadratic 3-Jordan homomorphisms.
Abstract
In this paper, we introduce and solve the following quadratic (<TEX>${\rho}_1$</TEX>, <TEX>${\rho}_2$</TEX>)-functional inequality (0.1) <TEX>$$N\left(2f({\frac{x+y}{2}})+2f({\frac{x-y}{2}})-f(x)-f(y),t\right){\leq}min\left(N({\rho}_1(f(x+y)+f(x-y)-2f(x)-2f(y)),t),\;N({\rho}_2(4f(\frac{x+y}{2})+f(x-y)-2f(x)-2f(y)),t)\right)$$</TEX> in fuzzy normed spaces, where <TEX>${\rho}_1</TEX><TEX>$</TEX> and <TEX>${\rho}_2$</TEX> are fixed nonzero real numbers with <TEX>${{\frac{1}{{4\left|{\rho}_1\right|}}+{{\frac{1}{{4\left|{\rho}_2\right|}}$</TEX> < 1, and f(0) = 0. Using the fixed point method, we prove the Hyers-Ulam stability of the quadratic (<TEX>${\rho}_1$</TEX>, <TEX>${\rho}_2$</TEX>)-functional inequality (0.1) in fuzzy Banach spaces.