Abstract. The purpose of this paper is to deal with generalizations of ratio ergodic theorems due to R.V. Chacon, G. Baxter, and K. Jacobs. We prove two weighted generalizations of the Chacon ergodic theorem and the Jacobs random ergodic theorem. L. Sucheston has formulated a general principle yielding simultaneous proofs of many almost everywhere multiparameter convergence theorems. This principle will allow us to derive multiparameter Chacon's type ergodic theorems for positive linear contractions on $L_{1}.$ The advantage is that we can inquire further into the problem of improving the multiparameter Chacon--Ornstein ergodic theorem due to Frangos and Sucheston. A multiparameter generalization of the Dunford--Schwartz ergodic theorem is also obtained. In addition, our consideration comes to the a.e. convergence for sectorially restricted averages in the commutative case, as in the Brunel--Dunford--Schwartz theorem. Moreover, we establish two Chacon's type nonlinear ergodic theorems for the nonlinear sums of affine operators on $L_{1}$.

AMS Subject Classification (1991): 47A35, 28A35

Keyword(s): positive linear contraction, linear modulus, Sucheston principle, Chacon ergodic theorem, Jacobs random ergodic theorem, multiparameter Chacon's type nonlinear ergodic theorem, affine operator

Received July 18, 2011, and in final form February 9, 2012. (Registered under 38/2011.)