The purpose of this paper is to introduce two implicit iteration schemes for approximating fixed points of nonexpansive mapping T and a finite family of nonexpansive mappings {Ti}i 1, respectively, in Banach spaces and to prove weak and strong convergence theorems. The results presented in this paper improve and extend the corresponding ones of H.-K. Xu and R. Ori, 2001, Z. Opial, 1967, and oth...

In this paper, we first obtain a weak mean convergence theorem of Baillon’s type for generalized hybrid mappings in a Hilbert space. Further, using an idea of mean convergence, we prove a strong convergence theorem of Halpern’s type for generalized hybrid mappings in a Hilbert space.

In this paper, we first introduce a class of nonlinear mappings called extended hybrid in a Hilbert space containing the class of generalized hybrid mappings. The class is different from the class of super hybrid mappings which was defined by Kocourek, Takahashi and Yao [12]. We prove a fixed point theorem for generalized hybrid nonself-mapping in a Hilbert space. Next, we prove a nonlinear erg...

In this paper, we modify the KF-iteration process into hyperbolic metric spaces where symmetry condition is satisfied and establish weak w2-stability data dependence results for contraction mappings. We also prove some Δ-convergence strong convergence theorems generalized (α,β)-nonexpansive type 1 Finally, offer a numerical example of mappings show that more effective than other iterations. Our...

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, a shrinking projection algorithm based on the prediction correction method for equilibrium problems and weak Bregman relatively nonexpansive mappings is introduced and investigated in Banach spaces, and then the strong convergence of the sequence generated by the proposed algorithm is derived under some suitable assumptions. These results are new and develop some recent results i...

* Correspondence: [email protected] Department of Mathematics, Faculty of Science, Imam Khomeini International University, P.O. Box 34149-16818, Qazvin, Iran Full list of author information is available at the end of the article Abstract In this paper, an iterative sequence for relatively nonexpansive multi-valued mappings by using the notion of generalized projection is introduced, and th...

where {rn} ⊂ (0,∞) and Jr = (I + rA)−1 for all r > 0. This algorithm was first introduced by Martinet [9]. In [16], Rockafellar proved that if liminfn→∞ rn > 0 and A−10 = ∅, then the sequence {xn} defined by (1.2) converges weakly to an element of solutions of (1.1). On the other hand, Kamimura and Takahashi [4] considered an algorithm to generate a strong convergent sequence in a Hilbert space...

Very recently, Moudafi proposed the following new convex feasibility problem in [10,11]: find x ∈ C, y ∈ Q such that Ax = By, where the two closed convex sets C and Q are the fixed point sets of two firmly quasi-nonexpansive mappings respectively, H1, H2 and H3 are real Hilbert spaces, A : H1 → H3 and B : H2 → H3 are two bounded linear operators. However, they just obtained weak convergence for...

LetK be a nonempty closed convex subset of a real Hilbert space H , and assume that Ti : K → H, i = 1, 2...N be a finite family of ki-strictly pseudo-contractive mappings for some 0 ≤ ki ≤ 1 such that ⋂N i=1 F (Ti) = {x ∈ K : x = Tix, i = 1, 2...N} = ∅. For the following iterative algorithm in K, for x1, x ′ 1 ∈ K and u ∈ K, { yn = PK [kxn + (1− k)Σi=1λiTixn] xn+1 = βnxn + (1− βn)yn and { y′ n ...