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    STUDIA MATHEMATICA - Issue no. 1 / 2015  
         
  Article:   ITERATES OF INCREASING LINEAR OPERATORS, VIA MAIA’S FIXED POINT THEOREM.

Authors:  IOAN A. RUS. 		 
       
         
  Abstract:  Abstract. Let X be a Banach lattice. In this paper we give conditions in which an increasing linear operator, A∶X→X is weakly Picard operator (see I.A. Rus, Picard operators and applications, Sc. Math. Japonicae, 58(2003), No. 1, 191-219). To do this we introduce the notion of “invariant linear partition of X with respect to A” and we use contraction principle and Maia’s fixed point theorem. Some applications are also given.
Mathematics Subject Classification (2010): 47H10, 46B42, 47B65, 47A35, 34K06.
Keywords: Banach lattice, order unit, increasing linear operator, invariant linear partition of the space, fixed point, weakly Picard operator, Maia’s fixed point theorem, functional differential equation. 		 
         
     
         
         
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