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FINDING A ZERO OF THE SUM OF TWO MAXIMAL MONOTONE OPERATORS WITH MINIMIZATION PROBLEM
Abdallah Beddani 경남대학교 수학교육과 2022 Nonlinear Functional Analysis and Applications Vol.27 No.4
The aim of this paper is to construct a new method for finding the zeros of the sum of two maximally monotone mappings in Hilbert spaces. We will define a simple function such that its set of zeros coincide with that of the sum of two maximal monotone operators. Moreover, we will use the Newton-Raphson algorithm to get an approximate zero.In addition, some illustrative examples are given at the end of this paper.
Aicha Ouali,Abdallah Beddani,Yamina Miloudi 경남대학교 수학교육과 2024 Nonlinear Functional Analysis and Applications Vol.29 No.3
In this paper, we study the existence and uniqueness of solutions for a class of fractional differential inclusion including a maximal monotone operator in real space with an initial condition. The main results of the existence and uniqueness are obtained by using resolvent operator techniques and multivalued fixed point theory.