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In this paper, we will consider the coincidence point problem for a pair of single-valued operators satisfying to some contraction and expansion type conditions. Existence, uniqueness and qualitative properties of the solution will be presented. The results are based on some fixed point theorems for nonlinear contractions in complete b-metric spaces. An application illustrates the theoretical results. [ABSTRACT FROM AUTHOR]

In this paper, we introduce an iteration method for solving pseudomonotone variational inequalities and related pseudoconvex optimization problems in Hilbert spaces. The iterative scheme is based on inertial ideas and subgradient-extragradient ideas. A main feature of the method is that it formally requires only one projection step onto the feasible set. We prove a weak convergence of sequences generated by our method. In the end, some numerical examples are provided to illustrate the effectiveness and performance of the proposed algorithm. Meanwhile, we make some detailed comparisons with the known related schemes. [ABSTRACT FROM AUTHOR]

In this paper, we investigate three new relaxed single projection methods with alternating inertial extrapolation steps and adaptive non-monotonic step sizes for solving pseudo-monotone variational inequalities in real Hilbert spaces. The proposed algorithms need to compute the projection on the feasible set only once in each iteration and they can work adaptively without the prior information of the Lipschitz constant of the mapping. The weak convergence theorems of the proposed iterative schemes are established under some appropriate conditions imposed on the parameters. These methods recover the Fejer monotonicity of the even subsequence with respect to the solution and obtain linear convergence rates. Finally, some numerical experiments and applications to optimal control problems are provided to demonstrate the advantages and efficiency of the proposed methods compared to some recent related ones. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to consider a system of N -fixed point equations in metric spaces. The existence and uniqueness of solution and an iterative algorithm for approximating the solution are studied. This system of N -fixed point equations is an extension of the classical of fixed point equation x = T x. The results of this paper improve several important works recently published in the literature. [ABSTRACT FROM AUTHOR]