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In this paper, we alter Wang's new iterative method as well as apply it to find the common solution of fixed point problem (FPP) and split variational inclusion problem ( S p VIP) in Hilbert space. We discuss the weak convergence for ( S p VIP) and strong convergence for the common solution of ( S p VIP) and (FPP) using appropriate assumptions. Some consequences of the proposed methods are studied. We compare our iterative schemes with other existing related schemes. [ABSTRACT FROM AUTHOR]

In this work, we study iterative methods for the approximation of common attractive points of two widely more generalized hybrid mappings in Hilbert spaces and obtain weak and strong convergence theorems without assuming the closedness for the domain. A numerical example supporting our main result is also presented. As a consequence, our main results can be applied to solving a common fixed point problem. [ABSTRACT FROM AUTHOR]

In this paper, we propose two modified two-step proximal methods that are formed through the proximal-like mapping and inertial effect for solving two classes of equilibrium problems. A weak convergence theorem for the first method and the strong convergence result of the second method are well established based on the mild condition on a bifunction. Such methods have the advantage of not involving any line search procedure or any knowledge of the Lipschitz-type constants of the bifunction. One practical reason is that the stepsize involving in these methods is updated based on some previous iterations or uses a stepsize sequence that is non-summable. We consider the well-known Nash–Cournot equilibrium models to support our well-established convergence results and see the advantage of the proposed methods over other well-known methods. [ABSTRACT FROM AUTHOR]

In this work, we study the inclusion problem of the sum of two monotone operators and the fixed-point problem of nonexpansive mappings in Hilbert spaces. We prove the weak and strong convergence theorems under some weakened conditions. Some numerical experiments are also given to support our main theorem. [ABSTRACT FROM AUTHOR]