The purpose of this work is to establish the weak convergence results of the generalized Mann iterates for finding coincidence points of two self maps satis- fying certain conditions in Banach spaces. An appli- cation of our results to the approximation of a solu- tion of certain nonlinear operator equation with pseu- domonotone operator is also given. Such problems arise in the description of steady state filtration pro- cesses. The results generalizes the corresponding the- orems in [12].

The purpose of this work is to establish the weak convergence results of the generalized Mann iterates for finding coincidence points of two self maps satis- fying certain conditions in Banach spaces. An appli- cation of our results to the approximation of a solu- tion of certain nonlinear operator equation with pseu- domonotone operator is also given. Such problems arise in the description of steady state filtration pro- cesses. The results generalizes the corresponding the- orems in [12].

The main aim of this paper is to present the concept of general Mann type doubly sequence iteration process with errors to approximate fixed points. We prove that the general Mann type doubly sequence iteration process with errors converges strongly to a coincideness point of two continuous pseudo-contractive mappings both of them which maps a bounded closed convex nonempty subset of a real Hilbert space into itself. Moreover, we discuss equivalence from the S,T-stability point of view under certain restrictions between general Mann type doubly sequence iteration process with errors and general Ishikawa iterations with errors. An application is also given to support our idea using compatible-type of mappings.

The stability of periodic solutions of non-linear differential equations with periodic coefficients has been of interest in mathematical physics for many years. The goal of this work is to continue our investigations to stability properties of some fundamental periodic solutions of strongly non-linear coupled Hill’s equations.
c achieve this goal, we first solve analytically the differential equations using modified version of the generalized averaging method which has been developed for strongly non-linear problems.
We test the validity of these approximate solutions numerically and a good agreement is found for large values of the coefficient of nonlinearity. A transformation is used to write our equations in the form which we can use the multiple-scaling technique. The stability analysis of solutions are studied as on example, and a good agreement is found between the analytical and numerical results.