The authors have obtained the following results: 1 the definition of uniformly closed countable family of nonlinear mappings, 2 strong convergence theorem by the monotone hybrid algorithm for two countable families of hemirelatively nonexpansive mappings in a Banach space with new method of proof, 3 two examples of uniformly closed countable families of nonlinear mappings and applications, 4 an...

and Applied Analysis 3 If θ ≡ 0, the problem 1.4 reduces into the minimize problem, denoted by arg min φ , which is to find x ∈ C such that φ ( y ) − φ x ≥ 0, ∀y ∈ C. 1.7 The above formulation 1.5 was shown in 11 to covermonotone inclusion problems, saddle point problems, variational inequality problems, minimization problems, optimization problems, variational inequality problems, vector equil...