Abstract. Monotone triangles are certain triangular arrays of integers, which correspond to n × n alternating sign matrices when prescribing (1, 2, . . . , n) as bottom row of the monotone triangle. In this article we define halved monotone triangles, a specialization of which correspond to vertically symmetric alternating sign matrices. We derive an operator formula for the number of halved mo...

The notions of a quasi-monotone operator and of a cyclically quasi-monotone operator are introduced, and relations between such operators and quasi-convex functions are established.

and Applied Analysis 3 Since weak convergence is not good for an effective algorithm, our purpose in this paper is to modify algorithm 1.3 in such a way that strong convergence is guaranteed. More precisely, for any two maximal monotone operators A and B, we define an iterative process in the following way: For x0, u ∈ H given, a sequence xn is generated using the rule x2n 1 αnu δnx2n γnJ βnx2n...

In this paper, we study an iterative scheme for two different types of resolvents of a monotone operator defined on a Banach space. These resolvents are generalizations of resolvents of a monotone operator in a Hilbert space. We obtain iterative approximations of a zero point of a monotone operator generated by the shrinking projection method with errors in a Banach space. Using our result, we ...