Convexity of nonlinear mappings between bounded linear operator spaces
AIMS MATHEMATICS(2024)
摘要
Motivated by the work [7], in which the author studied the convexity of nonlinear mappings defined between bounded linear operator spaces, our research extends this inquiry. In this work, we continue the study of the convexity of nonlinear mappings defined between bounded linear operator spaces and we establish a characterization in terms of the second order directional derivative. We apply the main result to prove the convexity and the nonconvexity of well-known nonlinear mappings. The case of nondifferentiable mappings is also treated in the last section.
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关键词
nonlinear mapping,directional derivative,second order directional derivative,Bounded,linear operators,nondi ff erentiable convex mappings
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