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ISSN : 1226-0657
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Vol.27 No.1
Abstract
In this paper we determine conditions which a function a(t) must satisfy to insure that the function a'(t) is an element of the separable Hilbert space L<sup>2</sup><sub>a,b</sub>[0, T]. We then proceed to illustrate our results with several pertinent examples and counter-examples.
Abstract
In this article, we investigate the solvability of nonlinear fractional integro-differential equations of the Hammerstein type. The results are obtained using the technique of measure of noncompactness and the Darbo theorem in the real Banach space of continuous and bounded functions in the interval [0, a]. At the end, an example is presented to illustrate the effectiveness of the obtained results.
Abstract
In this paper, we consider the following quadratic (ρ<sub>1</sub>, ρ<sub>2</sub>)-functional equation (0, 1) <TEX>$$N(2f({\frac{x+y}{2}})+2f({\frac{x-y}{2}})-f(x)-f(y)-{\rho}_1(f(x+y)+f(x-y)-2f(x)-2f(y))-{\rho}_2(4f({\frac{x+y}{2}})+f(x-y)-f(x)-f(y)),t){\geq}{\frac{t}{t+{\varphi}(x,y)}}$$</TEX>, where ρ<sub>2</sub> are fixed nonzero real numbers with ρ<sub>2</sub> ≠ 1 and 2ρ<sub>1</sub> + 2ρ<sub>2</sub>≠ 1, in fuzzy normed spaces. Using the fixed point method, we prove the Hyers-Ulam stability of the quadratic (ρ<sub>1</sub>, ρ<sub>2</sub>)-functional equation (0.1) in fuzzy Banach spaces.
Abstract
In this paper, numerical algorithms for solving a fuzzy system of linear equations with crisp coefficients are presented. We illustrate the efficiency and accuracy of the proposed methods by solving some numerical examples. We also provide a graphical representation of the fuzzy solutions in three-dimension as a visual reference of the solution of the fuzzy system.
Abstract
We investigate the domain of influence of the local volatility function on the solutions of the general Black-Scholes model. First, we generate the sample paths of underlying asset using the Monte Carlo simulation. Next, we define the inner and outer domains to find the effective volatility region. To confirm the effect of the inner domain, we use the root mean square error for the European call option prices, and then change the values of volatility in the proposed domain. The computational experiments confirm that there is an effective region which dominates the option pricing.
Abstract
In this note, we investigate the Hyers-Ulam stability and the hyperstability of the Pexider type functional equation g(x + y + xy) = g(x) + f(y) + xf(y) + yg(x).
Abstract
In this paper, we introduce a new concept of stability of coincidence iterative algorithm for three mappings and derive a new three-step Jungck-type iterative algorithm. And, we prove a stability result and a strong convergence result for the Jungck-type algorithm using the M<sub>J</sub>-contractive condition. Our results extend and unify the corresponding ones in [3, 6, 7, 13].