In this paper, a regularization method for treating zero points of the sum of two monotone operators is investigated. Strong convergence theorems are established in the framework of Hilbert spaces.

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.

The purpose of this paper is to introduce the implicit midpoint rule of nonexpansive mappings in CAT(0) spaces. The strong convergence of this method is proved under certain assumptions imposed on the sequence of parameters. Moreover, it is shown that the limit of the sequence generated by the implicit midpoint rule solves an additional variational inequality. Applications to nonlinear Volterra integral equations and nonlinear variational inclusion problem are included. The results presented in the paper extend and improve some recent results announced in the current literature.

In this paper, we study periodic solutions for a seasonally forced SIR model with impact of media coverage. Usually, media reports, information processing, and individuals' alerted responses to the information can only arise as the number of infected individuals reaches and exceeds a certain level. The piecewise smooth righthand side is introduced to describe the impact of this kind of media coverage. Using Leray-Schauder degree theory, we establish new results on the existence of at least one positive periodic solution for a seasonally forced SIR model with impact of media coverage. Some numerical simulations are presented to illustrate the effectiveness of such media coverage. MSC: 34C25; 37J45; 92B05

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