In [4] the authors considered equation (1.1) with q ≤ 0, b = c ( t ), c = 0, α = 1, β = 1 for all t ≥ t 0, and classified all solutions into four classes and obtained the solutions in these classes.
The results show that the proposed approach can converge to the optimum solution, and obtains the solution with high accuracy.
Following the nomenclature of the singular perturbation theory, we define the degenerate (DG) system and the boundary-layer (BL) system and obtain the solution of the sampled-data system as an approximation of the solutions of the lower-order subsystems.
In this article, we shall extend this concept to two mappings and obtain the solution of common fixed point equations and hence coincidence point equations in the framework of vector lattices.
Step 1: Solve the nonlinear system bigl u_{n}',overline{Psi}_{k}' bigr -A u_{n},overline{Psi}_{k}) = 0,quad text{for all } k=1, 2, ldots, dim S_{n} and obigr -A u_{n}ution (u_{n}).
Here, we consider a Cauchy-type singular integral equation of the first kind in the intervals (−∞,b), (a,∞), and and obtain the solutions by a limiting process applied to the solutions of similar equations associated with finite intervals.
and obtained the result that every solution of equation (1.6) oscillates or converges to zero.
In [1] the boundary conditions are local, the solution is obtained locally and the authors obtained the solution in Holder classes using iteration method.
In 1989, Aczél and Dhombres [10] obtained the solution of (1.1) for the case that acts on.
