Abstract
We introduce an iterative algorithm which converges strongly to a common element of fixed point sets of nonexpansive mappings and sets of zeros of maximal monotone mappings. Our iterative method is quite general and includes a large number of iterative methods considered in recent literature as special cases. In particular, we apply our algorithm to solve a general system of variational inequalities, convex feasibility problem, zero point problem of inverse strongly monotone and maximal monotone mappings, split common null point problem, split feasibility problem, split monotone variational inclusion problem and split variational inequality problem. Under relaxed conditions on the parameters, we derive some algorithms and strong convergence results to solve these problems. Our results improve and generalize several known results in the recent literature.
Highlights
Fixed point theory has been revealed as a very powerful and effective method for solving a large number of problems which emerge from real world applications and can be translated into equivalent fixed point problems
We present a new iterative algorithm for finding a common point of fixed point sets of nonexpansive mappings and sets of zeros of maximal monotone mappings
We introduced a new general system of variational inequalities which comprises some existing general system of variational inequalities and it is shown that our algorithm converges strongly to a solution of this variational inequality problem
Summary
Fixed point theory has been revealed as a very powerful and effective method for solving a large number of problems which emerge from real world applications and can be translated into equivalent fixed point problems. In order to obtain approximate solution of the fixed point problems various iterative methods have been proposed (see, e.g., [1,2,3,4,5,6,7,8,9,10] and the reference therein). The most popular method for finding zeros of a maximal monotone operator is the proximal point algorithm (PPA). Introduced the SFP for modeling phase retrieval problems This problem has large number of applications in optimization problems, signal processing, image reconstruction, intensity-modulated radiation therapy (IMRT). Motivated and inspired by the above work, we propose an iterative algorithm for finding common element of fixed point sets of nonexpansive mappings and sets of zeros of maximal monotone mappings. We solve all the problems discussed above under weaker conditions
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
