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2000 Mathematics Subject Classification: 65G99, 65K10, 47H04.We provide a local convergence analysis for Steffensen's method in order to solve a generalized equation in a Banach space setting. Using well known fixed point theorems for set-valued maps [13] and Hölder type conditions introduced by us in [2] for nonlinear equations, we obtain the superlinear local convergence of Steffensen's method. Our results compare favorably with related ones obtained in [11].
We are concerned with first order set-valued problems with very general boundary value conditions
involving the Stieltjes derivative with respect to a left-continuous nondecreasing function , a Carathéodory multifunction and a continuous . Using appropriate notions of lower and upper solutions, we prove the existence of solutions via a fixed point result for condensing mappings. In the periodic single-valued case, combining an existence theory for the linear case with a recent result involving...
The paper introduces a notion of strictly convex metric space and strictly convex metric space with round balls. These objects generalize the well known concept of strictly convex Banach space. We prove some fixed point theorems in strictly convex metric spaces with round balls.
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