In this paper, we introduce the notions of cyclic (?,?)-admissible mappings, (?,?)-(?,?)-contractive and weak ? - ? - ? - rational contraction mappings via cyclic (?,?)-admissible mappings. We prove some new fixed point results for such mappings in the setting of complete metric spaces. The obtained results generalize, unify and modify some recent theorems in the literature. Some examples and an application to integral equations are given here to illustrate the usability of the obtained results.

In this paper, we introduce a new modified Ishikawa iteration for finding a common element of the set of solutions of an equilibrium problem and the set of fixed points of generalized hybrid mappings in a Hilbert space. Our results generalize, extend and enrich some existing results in the literature. Mathematics Subject Classification.Primary 47H10, 47H09, 47J25, 47J05.

In this paper, we prove a weak convergence theorem of Ishikawa's type for m-generalized hybrid mappings in a Hilbert space. Further, by using a new modification of Ishikawa iteration, we prove a strong convergence theorem for m-generalized hybrid mappings in a Hilbert space.

Abstract. In this paper, we propose a new modified Ishikawa iteration for finding a common element of the set of solutions of an equilibrium problem and the set of fixed points of 2-generalized hybrid mappings in a Hilbert space. Our results generalize and improve some existing results in the literature. A numerical example is given to illustrate the usability of our results.

In this paper, we prove a strong convergence theorem for finding a common element of the set of solutions of an equilibrium problem and the set of fixed points of a symmetric generalized hybrid mapping by using modified hybrid method. Our results extend and improve some existing results in the literature.