An iterative procedure for solving the common solution of two total quasi-ϕ-asymptotically nonexpansive multi-valued mappings in Banach spaces

In this paper, we introduce a new iterative procedure which is constructed by the shrinking hybrid projection method for solving the common solution of fixed point problems for two total quasi-?-asymptotically nonexpansive multi-valued mappings. Under suitable conditions, the strong convergence theorems are established in a uniformly smooth and strictly convex real Banach space with Kadec-Klee property. Our result improves and extends the corresponding ones announced by some authors.     

Two block hybrid projection method for solving a common solution for a system of generalized equilibrium problems and fixed point problems for two countable families

In this paper, we introduce a new iterative sequence which is constructed by using the new modified two block hybrid projection method for solving the common solution problem for a system of generalized equilibrium problems of inverse strongly monotone mappings and a system of bifunctions satisfying certain conditions, and the common fixed point problems for families of uniformly quasi - ${\phi}$ - asymptotically nonexpansive and locally uniformly Lipschitz continuous. Strong convergence theorems are proved on approximating a common solution of a system of generalized equilibrium problems and fixed point problems for two countable families in Banach spaces. Our results presented in this paper improve and extend many recent results in this area.