General hybrid (A,η,m)(A,η,m)-proximal point algorithm frameworks for finding common solutions of nonlinear operator equations and fixed point problems

In this paper, we introduce and study a new general class of hybrid (A,η,m)(A,η,m)-proximal point algorithm frameworks for finding the common solutions of nonlinear operator equations and fixed point problems of Lipschitz continuous operators in Hilbert spaces. Further, by using the generalized resolvent operator technique associated with (A,η,m)(A,η,m)-maximal monotone operators, we discuss the approximation solvability of the operator equation problems and the convergence of iterative sequences generated by the algorithm frameworks. Finally, using software Matlab 7.0, the numerical simulation examples are given to illustrate the validity of main results presented in this paper.

► General hybrid (A,η,m)(A,η,m)-proximal point algorithm frameworks were constructed. ► Common solutions of nonlinear equations and fixed point problems were found. ► Resolvent operator technique with (A, η, m)-maximal monotonicity was used. ► Approximation and convergence for this algorithm frameworks were discussed. ► Numerical simulation examples were given to illustrate the main results.