ON SOME PROJECTION METHODS FOR THE SOLUTION OF NONLINEAR EQUATIONS WITH NONDIFFERENTIABLE OPERATORS

Main Article Content

IOANNIS K. ARGYROS

Abstract







We consider a nonlinear equation with a nondifferentiable operator in a Banach space. We approximate a solution of the nonlinear equation using an iteration, whose iterates can be obtained by solving a certain operator equation in a finite dimensional space.





 




Article Details

How to Cite
ARGYROS, I. K. (1993). ON SOME PROJECTION METHODS FOR THE SOLUTION OF NONLINEAR EQUATIONS WITH NONDIFFERENTIABLE OPERATORS. Tamkang Journal of Mathematics, 24(1), 1–7. https://doi.org/10.5556/j.tkjm.24.1993.4466
Section
Papers

References

I. K. Argyros, "On Newton's method and nondiscrete mathematical induction", Bull. Austral. Math. Soc., 38, (1988), 131-140.

M. Balazs and G. Goldner, "On the method of the cord and on a modification of it for the solution of nonlinear operator equations", Stud. Ger. Mat., 20 (1968), 981-990.

F. M. Migovich, "On the convergence of projection-iterative methods for solving nonlinear operator equation", Dopov. Akad. Nauk. Ukr. RSR, Ser. A, No. 1, (1970), 20-23.

M. N. Prisyazhnyuk, "The convergence of some approximate methods for solving non- linear operator equations with non-differentiable operators", Ukrainskii Mathematicheskii Zhurnal, Vol. 30, No. 2, {1978), 261-265.

W. C. Rheinholdt, "A unified convergence theory for a class of iterative processes", SIAM J. Numer. Anal. 5 (1968), 42-63.

J. W. Schmidt, "Unter Fehrerschranker fiir regular-falsi-verfahren", Period. Math. Hung., 9, (1978), 241-247.

T. Yamamoto, "A note on a posteriori error bound of Zabreiko and Nguen for Zincenko's iteration", Numer. Funct. Anal. and Optimiz., 9, (9and 10), (1987), 987-994.

P. P. Zabrejko and D. F. Nguen, "The majorant method in the theory of Newton- Kantorovich approximations and the Ptâk error estimates", Numer. Funct. Anal. Optimiz., 9, (1987), 671-684.

A. I. Zincenko, "Some approximate methods of solving equations with non-differentiable operators", (Ukrainian). Dopovidi Akad. Nav.k. Ukrain., RSR (1963), 156-161.