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In this paper, we deal with the control systems governed by the systems of fractional evolution hemivariational inequalities involving Riemann-Liouville fractional derivatives. We establish suitable sufficient conditions to guarantee the existence of mild solutions. Under these conditions, the approximate controllability of the associated fractional evolution systems involving Riemann-Liouville fractional derivatives is formulated and proved. [ABSTRACT FROM AUTHOR]

We introduce two new iterative algorithms with line-search process for solving a variational inequality problem with pseudomonotone and Lipschitz continuous mapping and a common fixed-point problem of an asymptotically nonexpansive mapping and a strictly pseudocontractive mapping. The proposed algorithms are based on inertial subgradient extragradient method with line-search process, hybrid steepest-descent method, and viscosity approximation method. Under mild conditions, we prove strong convergence of the proposed algorithms in a real Hilbert space. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a modified inertial subgradient extragradient method for solving a variational inequality problem with Lipschitz pseudomonotone mapping and a common fixed-point problem of a family of nonexpansive mappings. Under mild conditions, we obtain strong convergence theorems in a real Hilbert space. An application is also provided. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to introduce a general viscosity implicit iterative method for finding a solution of a split variational inclusion problem (SVIP) with a hierarchical variational inequality (HVI) constraint for a countable family of nonexpansive mappings in Hilbert spaces. Strong convergence theorem is obtained under some mild assumptions [ABSTRACT FROM AUTHOR]

In this paper, some existence results for generalized vector equilibrium-like problems (for short, GVELPs) are established by virtue of a generalized KKM-Fan theorem in topological vector spaces. In addition, some applications to vector optimization problems are also given. The results presented in this paper are the extension and improvement of the corresponding results of other authors. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to investigate the problems of the well-posedness for a system of mixed quasivariational-like inequalities in Banach spaces. First, we generalize the concept of a-well-posedness to the system of mixed quasivariational-like inequalities, which includes symmetric quasi-equilibrium problems as a special case. Second, we establish some metric characterizations of a-well-posedness for the system of mixed quasivariational-like inequalities. Under some suitable conditions, we prove that the a-well-posedness is equivalent to the existence and uniqueness of solution for the system of mixed quasivariational-like inequalities. The corresponding concept of a-well-posedness in the generalized sense is also considered for the system of mixed quasivariational-like inequalities having more than one solution. The results presented in this paper generalize and improve some known results in the literature. [ABSTRACT FROM AUTHOR]

The article presents a discussion that looks into the wide class of inexact proximal-type methods for handling the generalized variational inequality problem with maximal monotone operator in a reflexive Banach space. An extension of Kamimura and Takahashi's algorithm is also provided with the aim of developing a generic inexact proximal point algorithm. A convergence analysis which unifies a broad class of proximal-type methods associated with finding Hilbert spaces or Banach spaces is also included.