In this paper, we first prove the weak convergence for the Moudafi’s iterative scheme of two quasi-nonexpansive mappings. Then we prove the weak convergence for the Moudafi’s iterative scheme of quasi-nonexpansive mapping and nonexpansive mapping. Finally, we prove the strong convergence for the Moudafi’s iterative scheme of two quasi-nonexpansive mappings. Our results generalize the recent res...

In this paper, we introduce a new class of set-valued mappings which is called MD-type mappings. This class of mappings is a set-valued case of a class of the D-type mappings. The class of D-type mappings is a generalization of nonexpansive mappings that recently introduced by Kaewkhao and Sokhuma. The class of MD-type mappings includes upper semi-continuous Suzuki type mappings, upper semi-con...

We discuss the concept of probabilistic quasi-nonexpansive mappings in connection with the mappings of Nishiura. We also prove a result regarding the convergence of the sequence of successive approximations for probabilistic quasi-nonexpansive mappings.

Let K be a nonempty closed convex subset of a reflexive real Banach space E which has a uniformly Gâteaux differentiable norm. Assume that K is a sunny nonexpansive retract of E with Q as the sunny nonexpansive retraction. Let Ti : K → E, i = 1, . . . ,r, be a family of nonexpansive mappings which are weakly inward. Assume that every nonempty closed bounded convex subset of K has the fixed poin...

We introduce a general implicit algorithm for finding a common element of the set of solutions of systems of equilibrium problems and the set of common fixed points of a sequence of nonexpansive mappings and a continuous representation of nonexpansive mappings. Then we prove the strong convergence of the proposed implicit scheme to the unique solution of the minimization problem on the solution...

In this paper, we study the iterations of quasi $phi$-nonexpansive mappings and its applications in Banach spaces. At the first, we prove strong convergence of the sequence generated by the hybrid proximal point method to a common fixed point of a family of quasi $phi$-nonexpansive mappings.  Then, we give  applications of our main results in equilibrium problems.

There are two important connections between the classes of nonexpansive and of accretive mappings which give rise to a strong connection between the fixed point theory of nonexpansive mappings and the mapping theory of accretive maps. These are: (1) If U is a nonexpansive mapping of D(U) into X, and if we set T — I--U, D(T)=D(U), then T is an accretive mapping of D{T) into X. (2) If { U(i)f t^O...

the aim of this paper is to prove a common fixed point theorem for nonexpansive type single valued mappings which include both continuous and discontinuous mappings by relaxing the condition of continuity by weak reciprocally continuous mapping. our result is generalize and extends the corresponding result of jhade et al. [p.k. jhade, a.s. saluja and r. kushwah, coincidence and fixed points of ...

We study the asymptotic behavior of the sequence of the iterates for a nonexpansive mapping, defined on a suitable subset of a Banach space with Opial's condition. Some results are stated also for semigroups of nonexpansive mappings and for mappings of asymptotically nonexpansive type in uniformly convex Banach spaces with Opial's condition.

We introduce a new composite iterative scheme by the viscosity approximation method for nonexpansive mappings andmonotone mappings in a Hilbert space. It is proved that the sequence generated by the iterative scheme converges strongly to a common point of set of fixed points of nonexpansive mapping and the set of solutions of variational inequality for an inversestrongly monotone mappings, whic...