The combination of the set of solutions of equilibrium problem for convergence theorem of the set of fixed points of strictly pseudo-contractive mappings and variational inequalities problem

Abstract

For the purpose of this article, we introduce a new problem using the concept of equilibrium problem and prove the strong convergence theorem for finding a common element of the set of fixed points of an infinite family of κ i -strictly pseudo contractive mappings and of a finite family of the set of solutions of equilibrium problem and variational inequalities problem. Furthermore, we utilize our main theorem for the numerical example.

Convergence analysis for combination of equilibrium problems and k-nonspreading multi-valued mappings

“…Furthermore, we give a numerical example to illustrate the main result. By making use of iteration method presented in this paper, we can find the strong convergence theorems for the problems considered in [17].…”

“…Therefore, inspired and motivated by the work of [6,[14][15][16][17]19], in this paper, we propose shrinking projection hybrid method for finding a common solution of the set of CEP (1.3), a combination of CQ-method and shrinking projection method and the set of fixed points of a k-nonspreading multi-valued mapping with k ∈ (0, 1 2 ], which is more general than 1 2 -nonspreading multi-valued mapping. Further, we prove a strong convergence theorem for the sequences generated by iterative method and derive some consequences.…”

“…This theoery has helped in many ways of developing several thrust areas in physics, optimization, economics and transportation problems. In recent past, various classes and forms of equilibrium problems and their applications have been studied by many authors; see for instance [1][2][3][4][7][8][9][10]12,15,[17][18][19][20]. As a result various techniques and iterative schemes have been developed over the year to solve equilibrium problems; see for examples [1][2][3][4]7,9,10,12,15,[17][18][19] and references therein.…”

“…Recently, Suwannaut and Kangtunyakarn [17] proposed the following combination of equilibrium problems: For each i = 1, 2, ..., N , let G i : E × E → R be a bifunction and a i ∈ (0, 1) with…”