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In this paper, a new algorithm for finding a common element of a split equality fixed point problem for nonexpansive mappings and split equality equilibrium problem in three Banach spaces is introduced. Also, some strong and weak convergence theorems for the proposed algorithm are proved. Finally, the main results obtained in this paper are applied to solve the split equality convex minimization problem.

In this paper, we introduce a new algorithm for solving split equality mixed equilibrium problems in the framework of infinite-dimensional real Hilbert spaces. The strong and weak convergence theorems are obtained. As application, we shall utilize our results to study the split equality mixed variational inequality problem and the split equality convex minimization problem. Our results presented in this paper improve and extend some recent corresponding results. MSC: 47H09; 47J25Keywords: split equality mixed equilibrium problems; split equality mixed variational inequality problem; split equality convex minimization problem

In this paper, we introduce the concept of total asymptotically nonexpansive nonself mappings and prove the demiclosed principle for this kind of mappings in CAT(0) spaces. As a consequence, we obtain a -convergence theorem of total asymptotically nonexpansive nonself mappings in CAT(0) spaces. Our results extend and improve the corresponding recent results announced by many authors. MSC: 47H09; 47J25