Approximation Theorems and Fixed Point Theorem in Cones
Copyright policy )Approximation Theorems and Fixed Point Theorem in Cones
In this paper, we investigate the validity of an interesting theorem of Fan [3, Theorem 2] in cones. We prove that it is true for a continuous condensing map defined on a closed ball in cones. A more interesting case is that we prove that it is true on an annulus if suitable inner boundary conditions are posed. As applications of our theorems, some new fixed point theorems in the norm form are derived.
- University of Wisconsin–Milwaukee United States
Best approximation, Chebyshev systems, Schauder's fixed point theorem, Fixed-point theorems, Fixed-point and coincidence theorems (topological aspects), Monotone and positive operators on ordered Banach spaces or other ordered topological vector spaces, continuous condensing maps on a closed ball or annulus in cones
Best approximation, Chebyshev systems, Schauder's fixed point theorem, Fixed-point theorems, Fixed-point and coincidence theorems (topological aspects), Monotone and positive operators on ordered Banach spaces or other ordered topological vector spaces, continuous condensing maps on a closed ball or annulus in cones
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