We propose two very simple methods, the first one with constant step sizes and second self-adaptive sizes, for finding a zero of sum monotone operators in real reflexive Banach spaces. Our methods require only evaluation single-valued operator at each iteration. Weak convergence results are obtained when set-valued is maximal Lipschitz continuous, strong either these required, addition, to be s...

This paper derives several novel properties of conditional quantiles viewed as nonlinear operators. The results are organized in parallel to the usual expectation operator. We first define a τ-conditional quantile random set, relative any sigma-algebra, set solutions an optimization problem. Then, well-known unconditional quantiles, translation invariance, comonotonicity, and equivariance monot...

The theory of maximal monotone operators is utilized to prove the existence of weak periodic solutions for a coupled nonlinear parabolic-elliptic system.The diffusion term in the parabolic equation contains a Leray-Lions operator.This system may be regarded as a generalized version of the evolution thermistor model.

The notion of monotone operator in a Hilbert space is extended, and a considerably broader class of possibly multivalued operators is introduced. It is shown that well-known Minty's theorems on maximal monotone operators in Hilbert spaces can be extended to the cases of operators belonging to the class. Typical examples of partial differential operators are given to illustrate that the results ...

In this paper, by using Bregman’s technique, we introduce and study the hybrid proximal-point methods for finding a common element of the set of solutions to a system of generalized equilibrium Problems and zeros of a finite family of maximal monotone operators in reflexive Banach spaces. Strong convergence results of the proposed hybrid proximal-point algorithms are also established under some...