On common solution of fixed point problem and convex minimization problem through modified proximal point algorithm

Abstract

The study of finding common elements from the set of fixed point and set of solutions of convex minimization problems for nonlinear operators increase rapidly due to its applications in different branches of mathematics and engineering. In optimization theory, the proximal point algorithm plays an important role in solving problems with nonlinear operators. Several modifications of proximal point algorithm are introduced. We introduced the modified proximal point algorithm (MPPA) and studied the strong convergence of MPPA in Hilbert spaces.