To investigate various properties of important classes of nonlinear mappings that related to fixed point problem and give some sufficient conditions in order to obtain new existence theorems for those nonlinear mappings in Hilbert spaces, Banach spaces, complete metric spaces, convex metric spaces, R-tree and CAT(k) spaces.
2.2 To construct new iterative methods for approximation fixed points of various kinds of nonlinear mappings and finding a common fixed point of a finite and infinite family of those nonlinear mappings studied in the objective (1), and give some sufficient conditions for proving weak and strong convergence theorems of the studied iterative methods for those mappings. Moreover, we also study the rate of convergence and stability of the studied iterative methods.
2.3 To prove existence results concerning equilibrium and optimization problems and construct new iterative methods for finding a solution of those problems and a common element of the set of equilibrium problems, variational inequality problems and fixed point problems, and give some control conditions to prove weak and strong convergence theorems of those methods.
2.4 To construct and study new types of monotone multi-valued mappings in partially ordered metric spaces and find some sufficient conditions for which each types of the studied mappings has a fixed point and a maximal and minimal fixed points.
2.5 To construct and study new classes of graph-preserving multi-valued mappings in complete metric spaces with graphs and find some sufficient conditions for which each type of the studied mappings has a fixed point.
2.6 To construct and investigate new types mixed monotone multi-valued mappings in partially ordered metric spaces and find some sufficient conditions for which each type of mappings has a coupled fixed point, coupled coincidence point and a coupled common fixed point.
2.7 To construct and investigate new types mixed graph-preserving multi-valued mappings in complete metric spaces with graphs and find some sufficient conditions for which each type of mappings has a coupled fixed point,h a coupled coincidence point and a coupled common fixed point.
2.8 To investigate existence of common fixed points for semigroup of nonlinear mappings in Hilbert spaces, Banach spaces, complete metric spaces, convex metric spaces, R-tree and CAT(k) spaces.
2.9 To apply the new knowledge (new theorems) obtained from the project for solving some problems in game theory, Nash equilibria of non-cooperative games, existence problems for ordinary differential equations.
2.10 To develop software program for solving fixed point problems, equilibrium problems and optimization problems.
2.11 To build and develop new and young researchers in the area of fixed point
theory and applications for developing human resource and high standard
academic researches.
2.12. To create research network both inside and outside of the country for making
