Previous |  Up |  Next


In this paper is studied the equation $(^*)x=Tx+f$ in a complex Banach space $X$, its ordering being given by a normal reproducing cone $K$. Under the assumption that $(^*)$ has exactly one solution in $K$ it is shown that a certain sequence $(w_p)$ (given by iterations - which is an analogue of Marsal's method) converges to $x^*$. The paper is a generalization of Marsal's results.
[1] M. G. Krein M. A. Rutman: Linear operators leaving invariant a cone in a Banach space. Uspekhi Mat. Nauk III (1948), N 3, 3-95 (Russian). MR 0027128
[2] I. Marek: Iterations of linear bounded operators in non self-adjoint eigenvalue problems and Kellogg's iterations. Czech. Math. J. 12 (1962), 536-554. MR 0149297
[3] D. Marsal: Konvergenzbeschleunigte Iteration von linearen Gleichungssystemen bei Divergenz des klassischen Verfahren und besonderer Berücksichtigung von Randwertproblemen. Computing 4 (1969), 234-245. DOI 10.1007/BF02234772 | MR 0248972
[4] H. Schaefer: Halbgeordnete lokalkonvexe Vektorräume. Math. Ann. 135 (1958), 115-141. DOI 10.1007/BF01343098 | MR 0106401 | Zbl 0080.31501
Partner of
EuDML logo