The influence of fixed point theorems for contractive and nonexpansive mappings see 1, 2 on fixed point theory is so huge that there are many results dealing with fixed points of mappings satisfying various types of contractive and nonexpansive conditions. On the other hand, it is also huge that well-known Brouwer’s and Schauder’s fixed point theorems for set-contractive mappings exert an influ...

We use a hybrid iterative method to find a common element of the set of fixed points of an infinite family of Lipschitzian quasi-nonexpansive mappings, the set of solutions of the general system of the variational inequality and the set of solutions of the generalized mixed equilibrium problem in real Hilbert spaces. We also show that our main strong convergence theorem for finding that common ...

In this article, we considered the class of generalized α , β -nonexpansive (GABN) mappings that properly includes all nonexpansive, Suzuki nonexpansive (SN), id="M2"> (GAN), and Reich–Suzuki (RSN) mappings. We used iterative scheme J...

The purpose of this paper is to study the strong convergence of an implicit iteration process with errors to a common fixed point for a finite family of asymptotically pseudocontractive mappings and nonexpansive mappings in normed linear spaces. The results in this paper improve and extend the corresponding results of Xu and Ori, Zhou and Chang, Sun, Yang and Yu in some aspects.

Let X be a real Banach space and let C be a nonempty closed convex subset of X. A selfmapping T : C → C is said to be nonexpansive if ‖Tx−Ty‖ ≤ ‖x−y‖, for all x, y ∈ C.A point x ∈ C is a fixed point of T provided Tx x. Denote by Fix T the set of fixed points of T ; that is, Fix T {x ∈ C : Tx x}. It is assumed throughout this paper that T is a nonexpansive mapping such that Fix T / ∅. Constructi...

Let K be a nonempty closed convex subset of a 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, 2, · · · , N be a family of nonexpansive mappings which are weakly inward with F = ⋂N i=1 F (Ti) 6= ∅. Let f : K → K be a fixed contractive mapping. For given x0...

in this paper‎, ‎strong convergence theorems of ishikawa type implicit iteration‎ ‎process with errors for a finite family of asymptotically‎ ‎nonexpansive in the intermediate sense and asymptotically‎ ‎quasi-pseudocontractive type mappings in normed linear spaces are‎ ‎established by using a new analytical method‎, ‎which essentially‎ ‎improve and extend some recent results obtained by yang‎ ‎...

This research article introduces a new iterative process called MP iteration and prove some convergence approximation results for the fixed points of $\rho$-nonexpansive mappings in modular function spaces. To demonstrate that converges faster than well-known existing processes mappings, we constructed numerical examples. In end, concept summably almost T-stability is discussed.

We introduce a new projection algorithm for solving the fixed point problem of relatively nonexpansive mappings in the framework of Banach spaces. We also prove the strong convergence theorem for such mappings. Mathematics Subject Classification: 47H09, 47H10

In this paper, we introduce a broad class of nonlinear mappings in a Hilbert space which contains the classes of nonexpansive mappings, nonspreading mappings, hybrid mappings and contractive mappings. Then we prove fixed point theorems for the class of such mappings. Using these results, we prove well-known and new fixed point theorems in a Hilbert space. We finally give an open problem which i...