Abstract
A fixed point theorem for weakly inward A-proper maps defined on cones in Banach spaces is established using a fixed point index for such maps. The result generalizes a theorem in Deimling (Nonlinear Functional Analysis, 1985) for weakly inward maps defined on a cone in $\mathbb{R}^{n}$ . We then apply the theorem to a Picard boundary value problem and obtain the existence of a positive solution.
Highlights
1 Introduction The purpose of this paper is to establish a fixed point theorem for weakly inward A-proper maps defined on cones in Banach spaces that generalizes a result in Deimling [ ], p. , for weakly inward maps defined on a cone in Rn
We use the fixed point index for weakly inward A-proper maps introduced by Lan and Webb [ ] to obtain our new result
We obtain a positive solution to the Picard boundary value problem
Summary
The purpose of this paper is to establish a fixed point theorem for weakly inward A-proper maps defined on cones in Banach spaces that generalizes a result in Deimling [ ], p. , for weakly inward maps defined on a cone in Rn. 1 Introduction The purpose of this paper is to establish a fixed point theorem for weakly inward A-proper maps defined on cones in Banach spaces that generalizes a result in Deimling [ ], p. For weakly inward maps defined on a cone in Rn. We use the fixed point index for weakly inward A-proper maps introduced by Lan and Webb [ ] to obtain our new result.
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