ON A SURJECTIVITY FOR THE SUM OF TWO MAPPINGS OF MONOTONE TYPE

In this paper the sum(T+S)of two nonlinear mappings is considered,where T ismaximal monotone or generalized pseudomonotone and S is generalized pseudomonotone orof type(M).By using the concepts of T-boundedness,T-generalized pseudomonotonemappings and mappings of type T--(M) introduced by the author,it is proved that(T+S) is of type (M).A new surjectivity result for multivalued pseudo A-propermappings is given.As a consequence,it is obtained that the coercive mappings of type(M)whose effective domain contains a dense linear subspace are surjectivity. In particular,the author answers affirmatively a part of Browder's question(see[1],p.70).     

ON THE TOPOLPGICAL DEGREE FOR THE SUM OF MAXIMAL MOMOTONE OPERATOR AND GENERALIZED PSEUDOMONOTONE OPERATOR

Let X be a real separable reflexive Banach space, $${X^*}$$ its dual space, and let T: $X \to {X^*}$ be a maximal monotone operator, P ：$X \to {X^*}$ a quasi-bounded generalized pseudomonotone operator or T-pseudomonotone operator. In this paper, We have constructed a topological degree for the operator(T+P). As a by products surjectvity result is obtained. In particular, we have given a partially affirmative answer to a Browder''s question by using a topological method (of., Mathematical Developments arising from Hilbert Problems, Vol. 1(1976), 68—73 AMS)