But by the regularization method, there are a few papers with strict theoretical analysis on identifying the unknown source.
This property has a close relation to the use of topological degree in eigenvalue theory by the regularization method.
To the authors' knowledge, there were few papers for identifying an unknown source for a fractional diffusion equation by the regularization method.
The initial equation (1) is reduced to the Abel integral equation (23) by the regularization method of Carleman-Vekua [4], which was developed for solving singular integral equations.
By the regularization method in [2], Lemma 4.2, we can prove that (xin C^{2+nu,1+frac{nu}{2} overline{Omega}timesmathbb{R}^^)) is a classical time 2π-periodic solution of the boundary value problem (4.1).
From Table 2, we easily see that by using the regularization method and with iterative number increasing, (x_{n}) approaches to (x^) and the errors gradually approach to zero.
On the other hand, by combining the regularization method, Korpelevich's extragradient method, the hybrid steepest-descent method, and the viscosity approximation method, Ceng et al. [2] introduced and analyzed implicit and explicit iterative schemes for computing a common element of the solution set of system of variational inequalities and a set of zeros of an accretive operator in Banach space.
On the other hand, by combining the regularization method, the hybrid steepest-descent method, and the projection method, Ceng et al. [29] proposed an iterative algorithm that generates a sequence via the explicit scheme and proved that this sequence converges strongly to a unique solution of the following problem.
Very recently, by combining the regularization method and extragradient method due to Nadezhkina and Takahashi [13], Ceng, Ansari and Yao [34] proposed an extragradient algorithm with regularization and proved that the sequences generated by the proposed algorithm converge weakly to an element of Fix ( S ) ∩ Γ, where S : C → C is a nonexpansive mapping.
Very recently, some approximation methods are proposed in [13, 14, 32, 48] to solve the vector optimization problem and split feasibility problem by virtue of the regularization method.
The size distribution of scattering particles was reconstructed from the scattered light correlation function using PrecisionDeconvolve software (Precision Detectors) based on the regularization method by Tikhonov and Arsenin (Tikhonov and Arsenin, 1977).
