Convergence and stability of the three-step iterative schemes for a class of general quasivariational-like inequalities.
Convergence comparison of several iteration algorithms for the common fixed point problems.
Convergence conditions for Secant-type methods
We provide new sufficient convergence conditions for the convergence of the secant-type methods to a locally unique solution of a nonlinear equation in a Banach space. Our new idea uses recurrent functions, and Lipschitz-type and center-Lipschitz-type instead of just Lipschitz-type conditions on the divided difference of the operator involved. It turns out that this way our error bounds are more precise than earlier ones and under our convergence hypotheses we can cover cases where earlier conditions...
Convergence domains under Zabrejko-Zinčenko conditions using recurrent functions
We provide a semilocal convergence analysis for Newton-type methods using our idea of recurrent functions in a Banach space setting. We use Zabrejko-Zinčenko conditions. In particular, we show that the convergence domains given before can be extended under the same computational cost. Numerical examples are also provided to show that we can solve equations in cases not covered before.
Convergence of a random iteration scheme to a random fixed point.
Convergence of a sequence of sets in a Hadamard space and the shrinking projection method for a real Hilbert ball.
Convergence of discretization procedures for problems whose entropy solutions are uniquely characterized by additional relations
Weak solutions of given problems are sometimes not necessarily unique. Relevant solutions are then picked out of the set of weak solutions by so-called entropy conditions. Connections between the original and the numerical entropy condition were often discussed in the particular case of scalar conservation laws, and also a general theory was presented in the literature for general scalar problems. The entropy conditions were realized by certain inequalities not generalizable to systems of equations...
Convergence of fixed point of asymptotically quasi-nonexpansive type mappings in convex metric space.
Convergence of implicit iterates with errors for mappings with unbounded domain in Banach spaces.
Convergence of inexact iterative schemes for nonexpansive set-valued mappings.
Convergence of Ishikawa iterates for a multi-valued mapping with a fixed point
Existence of fixed points of multivalued mappings that satisfy a certain contractive condition was proved by N. Mizoguchi and W. Takahashi. An alternative proof of this theorem was given by Peter Z. Daffer and H. Kaneko. In the present paper, we give a simple proof of that theorem. Also, we define Mann and Ishikawa iterates for a multivalued map with a fixed point and prove that these iterates converge to a fixed point of under certain conditions. This fixed point may be different from...
Convergence of Ishikawa iterates of generalized nonexpansive mappings.
Convergence of iterates with errors of uniformly quasi-Lipschitzian mappings in cone metric spaces
Convergence of iterative algorithms to common random fixed points of random operators.
Convergence of iterative sequences for common zero points of a family of -accretive mappings in Banach spaces.
Convergence of iterative sequences for fixed point and variational inclusion problems.
Convergence of iterative sequences for generalized equilibrium problems involving inverse-strongly monotone mappings.
Convergence of Newton-like methods for singular operator equations using outer inverses.
Convergence of three-step iterations scheme for nonself asymptotically nonexpansive mappings.
Convergence of two-step iterative scheme with errors for two asymptotically nonexpansive mappings.