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.

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 ...

The focus of this article, reviewed a generalized contraction mapping and nonexpansive maps recall some theorems about the existence uniqueness common fixed point coincidence fixed-point for such under conditions. Moreover, schemes different types as one-step ,two-step three step (Mann scheme algorithm, Ishukawa noor .scheme algorithm Modified arahan others. convergence these has been studied ....

and Applied Analysis 3 R1 F T / ∅; R2 φ p, Tx ≤ φ p, x , for all x ∈ C, p ∈ F T ; R3 F T F̂ T . Definition 1.4. A point p ∈ C is said to be an strong asymptotic fixed point of T if C contains a sequence {xn}n 0 which converges strongly to p and limn→∞‖xn − Txn‖ 0. The set of strong asymptotic fixed points of T is denoted by F̃ T . We say that a mapping T is weak relatively nonexpansive see, e.g.,...

The purpose of this paper is to prove strong convergence theorems for common fixed points of two families of weak relatively nonexpansive mappings and a family of equilibrium problems by a new monotone hybrid method in Banach spaces. Because the hybrid method presented in this paper is monotone, so that the method of the proof is different from the original one. We shall give an example which i...

The aim of this paper is to prove strong and △-convergence theorems of modified S-iterative scheme for asymptotically quasi-nonexpansive mapping in hyperbolic spaces. The results obtained generalize several results of uniformly convex Banach spaces and CAT(0) spaces. KeywordsHyperbolic space, fixed point, asymptotically quasi nonexpansive mapping, strong convergence, △-convergence.

We prove the weak and strong convergence of the implicit iterative process to a common fixed point of an asymptotically quasi-I-nonexpansive mapping T and an asymptotically quasi-nonexpansive mapping I, defined on a nonempty closed convex subset of a Banach space.

We combine a sequence of contractive mappings {fn} and propose a generalized viscosity approximation method. One side, we consider a nonexpansive mapping S with the nonempty fixed point set defined on a nonempty closed convex subset C of a real Hilbert space H and design a new iterative method to approximate some fixed point of S, which is also a unique solution of the variational inequality. O...

The purpose of this article is to prove strong convergence theorems for fixed points of closed hemirelatively nonexpansive mappings. In order to get these convergence theorems, the monotone hybrid iteration method is presented and is used to approximate those fixed points. Note that the hybrid iteration method presented by S. Matsushita and W. Takahashi can be used for relatively nonexpansive m...

Let C be a nonempty closed convex subset of a Hilbert spaceH, T a self-mapping of C. Recall that T is said to be nonexpansive if ‖Tx − Ty‖ ≤ ‖x − y‖, for all x, y ∈ C. Construction of fixed points of nonexpansive mappings via Mann’s iteration 1 has extensively been investigated in literature see, e.g., 2–5 and reference therein . But the convergence about Mann’s iteration and Ishikawa’s iterati...