On the Semi-monotone Operator Theory and Applications

Recent progress on Monotone Operator Theory

In this paper, we survey recent progress on the theory of maximally monotone operators in general Banach space. We also extend various of the results and leave some open questions. 2010 Mathematics Subject Classification: Primary 47H05; Secondary 46B10, 47A06, 47B65, 47N10, 90C25

Operator theory and its applications

Solving the Power Flow Equations: A Monotone Operator Theory Approach

The AC power flow equations are fundamental in all aspects of power systems planning and operations. They are routinely solved using Newton-Raphson like methods. However, there is little theoretical understanding of when these algorithms are guaranteed to find a solution of the power flow equations or how long they may take to converge. Further, it is known that in general these equations have ...

Some Extensions of Loewner’s Theory of Monotone Operator Functions

Several extensions of Loewner’s theory of monotone operator functions are given. These include a theorem on boundary interpolation for matrix-valued functions in the generalized Nevanlinna class. The theory of monotone operator functions is generalized from scalarto matrix-valued functions of an operator argument. A notion of κ-monotonicity is introduced and characterized in terms of classical ...

A Class of nonlinear $(A,eta)$-monotone operator inclusion problems with iterative algorithm and fixed point theory

A new class of nonlinear set-valued variationalinclusions involving $(A,eta)$-monotone mappings in a Banachspace setting is introduced, and then based on the generalizedresolvent operator technique associated with$(A,eta)$-monotonicity, the existence and approximationsolvability of solutions using an iterative algorithm and fixedpint theory is investigated.