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.

In this paper, we propose an iterative scheme modified from the work of Ceng et al. (Nonlinear Anal. Hybrid Syst. 4:743-754, 2010) and Plubtieng and Punpaeng (J. Math. Anal. Appl. 336(1): [455][456][457][458][459][460][461][462][463][464][465][466][467][468][469] 2007) to prove the strong convergence theorem for approximating a common element of the set of fixed points of nonspreading mappings and a finite family of the set of solutions of the equilibrium problem. Using this result, we obtain the strong convergence theorem for a finite family of nonspreading mappings and a finite family of the set of solutions of equilibrium problem. Moreover, in order to compare numerical results between the combination of the equilibrium problem and the classical equilibrium problem, some examples are given in one-and two-dimensional spaces of real numbers.

The purpose of this paper is to modify the generalized equilibrium problem introduced by Ceng et al. (J. Glob. Optim. 43:487-502, 2012) and to introduce the K-mapping generated by a finite family of strictly pseudo-contractive mappings and finite real numbers modifying the results of Kangtunyakarn and Suantai (Nonlinear Anal. 71:4448-4460, 2009). Then we prove the strong convergence theorem for finding a common element of the set of fixed points of a finite family of strictly pseudo-contractive mappings and a finite family of the set of solutions of the modified generalized equilibrium problem. Moreover, using our main result, we obtain the additional results related to the generalized equilibrium problem.

In Thai mathematics classrooms, there is a lack of attention to support students’ mathematical problem-solving skills by working from real-world contexts that make sense to students. This study aimed to investigate how pre-service mathematics teachers’ problem solving can be explored in their content course, intervening with technology and Realistic Mathematics Education (RME) through the Mean Value Theorem (MVT) lesson. The study included nine pre-service mathematics teachers purposively selected from a public university in Thailand who attended a Calculus course. Data was collected from classroom artifacts, observation notes, and interviews. It was found in this study that the intervention of technology and RME in pre-service mathematics teachers’ content courses has the potential to build pre-service mathematics teachers’ problem-solving abilities. It was also discussed that the intervention could use RME to conceptualize mathematics theorem and cultivate Polya’s problem-solving steps. The findings provide light on the efficacy of using technology and RME in enhancing problem-solving skills among other content courses and could be used to inform the creation of mathematics curricula and instructional strategies in undergraduate content courses for mathematics education programs.

In this research, we introduced the S -mapping generated by a finite family of contractive mappings, Lipschitzian mappings and finite real numbers using the results of Kangtunyakarn (2013). Then, we prove the strong convergence theorem for fixed point sets of finite family of contraction and Lipschitzian mapping and solution sets of the modified generalized equilibrium problem introduced by Suwannaut and Kangtunyakarn (2014). Finally, numerical examples are provided to illustrate our main theorem.