Fixed point approximation methods for nonlinear operators

Abstract

The main objective of the thesis is to discuss fixed point approximation method efor single valued and multivalued nonlinear operators. New iterative algorithms are introduced to establish the weak and strong convergence theorems of newly defined nonlinear operators such as multivalued nearly asymptotically nonexpan- sive mapping, multivalued -demicontractive and -hemicontractive mappings. A three step iteration process is introduced to prove common fixed point theorem of nonexpansive and strongly pseudocontractive mapping. To support and applica-bility of the theorems, we have presented numerical examples and demonstrated the proposed iterative algorithm converges to the fixed point. We have defined modified proximal point algorithm to find fixed point of nonexpansive mapping and minimizing convex function. Using this modified iteration process strong and newline -convergence theorems are proved in CAT(0) spaces.