Two New Algorithms For Solving Fixed Point Problems Of Nonexpansive Mappings And Their Applications

Fixed point iterative algorithm is an important component of fixed point theory.Its convergence analysis and applications in specific optimization problems have attracted extensive attention.This paper mainly studies two new algorithms for solving fixed point problems of nonexpansive mappings in Hilbert spaces.On one hand,inspired by the existing work on generalized viscous approximation algorithm and Ishikawa iterative algorithm,we propose a generalized Ishikawa viscosity approximation algorithm,prove that the algorithm is strongly convergent,and apply it to solve bilevel optimization problems.Compared with other existing algorithms,the aforementioned algorithm is more flexible in parameter selection.On the other hand,we propose an inertial generalized Mann-Halpern algorithm.The selection of coefficients in the iterative sequence can be relaxed to less than or equal to 1 compared with previous algorithms.We prove its strong convergence and apply it to solve the Fermat-Weber location problem.