Iterative approximation of a common solution of a split equilibrium problem, a variational inequality problem and a fixed point problem

Strong and weak convergence theorems for split equilibrium problems and fixed point problems in Banach spaces

“…Recently, split feasibility problems [3,4,6,9,29,34,35], split variational inequality problems [10,21] and split equilibrium problems [2,17,31] have been investigated by many authors. However, most of the results on these kinds of these problems are investigated only in Hilbert spaces, only a few works are considered in Banach spaces.…”

Cloud hybrid methods for solving split equilibrium and fixed point problems for a family of countable quasi-Lipschitz mappings and applications

“…Moreover, they gave some examples and mentioned that there exist many SEPs and the new methods for solving it further need to be explored in the future. Later, in 2013, Kazmi and Rizvi [14] considered the iterative method to compute the common approximate solution of a split equilibrium problem, a variational inequality problem and a fixed point problem for a nonexpansive mapping in the framework of real Hilbert spaces. They generated the sequence iteratively as follows: r n − I)A)x n , y n = P C (u n − λ n Du n ), x n+1 = α n v + β n x n + γ n Sy n , for each n 0, where A : H 1 → H 2 is a bounded linear operator, D : C → H 1 is a τ-inverse strongly monotone mapping, F 1 : C × C → R, F 2 : Q × Q → R are two bifunctions.…”

“…In 2015 [24], motivated and inspired by the results [3,10,14] and the recent works in this field, Witthayarat et al introduced a shrinking projection method for solving split equilibrium problems and fixed point problems for asymptotically nonexpansive mappings in the framework of Hilbert spaces and proved some strong convergence theorems for the proposed new iterative method. They proved the following strong convergence theorem.…”

A viscosity Cesàro mean approximation method for split generalized vector equilibrium problem and fixed point problem

“…In the last two decades, EP(1.1) has been generalized and extensively studied in many directions due to its importance; see for example [2][3][4][5][6][7][8][9][10] for the literature on the existence and iterative approximation of solution of the various generalizations of EP(1.1). Recently, Kazmi and Rizvi [11] considered the following pair of equilibrium problems in different spaces, which is called split equilibrium problem (in short, SEP): Let F 1 : C Â C ! R and F 2 : Q Â Q !…”

“…Motivated by the work of Shimizu and Takahashi [20], Colao et al [23], Shan and Haung [26] and Kazmi and Rizvi [11,12,14] and by the on going research in this direction, we introduce and study the strong convergence of an explicit iterative method for approximating a common solution of SGVEP(1.4) and (1.5) and FPP(1.9) for a finite family of nonexpansive mappings in real Hilbert spaces using viscosity Cesa`ro mean approximation in Hilbert spaces. The results presented in this paper generalize, improve and unify many previously known results in this research area, see instance [5,[10][11][12][13]22,23].…”