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Some criteria for maximal abstract monotonicity |
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| Authors: | H Mohebi J-E Martínez-Legaz M Rocco |
| Institution: | 1. Department of Mathematics, Shahid Bahonar University of Kerman, Kerman, Iran 2. School of Mathematical and Geospatial Sciences, RMIT University, Melbourne, VIC, 3001, Australia 3. Departament d??Economia i d??Hist??ria Econ??mica, Universitat Aut??noma de Barcelona, 08193, Bellaterra, Spain 4. Department of Mathematics, Statistics, Computer Science and Applications, University of Bergamo, 24127, Bergamo, Italy |
| Abstract: | In this paper, we develop a theory of monotone operators in the framework of abstract convexity. First, we provide a surjectivity result for a broad class of abstract monotone operators. Then, by using an additivity constraint qualification, we prove a generalization of Fenchel??s duality theorem in the framework of abstract convexity and give some criteria for maximal abstract monotonicity. Finally, we present necessary and sufficient conditions for maximality of abstract monotone operators. |
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