Monotone Bifunctions and Monotone Operators - Alizadeh, Mohammad hossein
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Our purpose is to study and advance in the research area of monotone and generalized monotone operators and bifunctions. To each bifunction we will correspond an operator and for every operator will correspond a bifunction. We also show that each monotone operator is inward locally bounded at every point of the closure of its domain, a property which collapses to ordinary local boundedness at interior points of the domain. Moreover, we derive some properties of cyclically monotone bifunctions. A considerable part of this thesis is devoted to introducing and studying of the Fitzpatrick…mehr

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Produktbeschreibung
Our purpose is to study and advance in the research area of monotone and generalized monotone operators and bifunctions. To each bifunction we will correspond an operator and for every operator will correspond a bifunction. We also show that each monotone operator is inward locally bounded at every point of the closure of its domain, a property which collapses to ordinary local boundedness at interior points of the domain. Moreover, we derive some properties of cyclically monotone bifunctions. A considerable part of this thesis is devoted to introducing and studying of the Fitzpatrick transform of a bifunction and its properties. Whenever the monotone bifunction is lower semi-continuous and convex with respect to its second variable, the Fitzpatrick transform permits to obtain results on its maximal monotonicity
Autorenporträt
I received my bachelor's degree in Pure Mathematics from the University of Tehran and my master's degree in Pure Mathematics (Functional Analysis) from the Kharazmi University of Tehran. Then, I completed my PhD in Convex and Nonlinear Analysis at University of the Aegean where I worked under the supervision of Professor Nicolas Hadjisavvas.