Based on Cauchy criteria, the regularized sparse inversion can be made by using pre-conditional conjugate gradient algorithm (PCGA) in simultaneously iterative inversion of reflection factor and wavelet.

The purpose of this paper is to introduce the concept of Φ-Pseudo contractive type of mappings and to study the fixed points approximation problem of the Iskikawa iterative process for the single-valued Φ-Pseudo contractive mapping.

We give two iterative processes for perturbations accretive operator.

The existence of positive radial solution is proved for a class of generalized Gelfand problems on the unite ball when the nonlinear term is partly subject to an exponential function and the corresponding iterative process is also given.

Without Lipschitz assumption in real uniformly smooth Banach space,by virtue of some analysis theory and Ishikawa iteration techniques,the stable results of the Ishikawa iteration procedures have been given for one class of contiuous and Φ-generalized pseudocontractive mapping with a bounded range.

In uniformly smooth Banach space,the stable of the Ishikawa iteration procedures are researched for one class of nonLipschitz and Φstongly pseudocontractive operator,By virtue of supply the basis of structure and theory for further discussing stability of iteration procedures,the results improve and extened the recent corresponding results.