In this work, we define the notion of an algebraic distance in algebraic cone metric spaces defined by Niknam et al. [A. Niknam, S. Shamsi Gamchi and M. Janfada, Some results on TVS-cone normed spaces and algebraic cone metric spaces, Iranian J. Math. Sci. Infor. 9 (1) (2014), 71--80] and introduce some its elementary properties. Then we prove the existence and uniqueness of fixed point for a B...

In this paper, we establish some existence of fixed-point results for asymptotically regular multivalued mappings satisfying Kannan-type contractive condition without assuming compactness the underlying metric space or continuity mapping.

Let X be a reflexive Banach space which has a weakly sequentially continuous duality mapping. In this paper, we consider the following viscosity approximation sequence x n λ n fx n 1−λ n T n x n , where λ n ∈ 0, 1, {T n } is a uniformly asymptotically regular sequence, and f is a weakly contractive mapping. Strong convergence of the sequence {x n } is proved.

The purpose of this paper is to study the convergence problem of Mann and Ishikawa type iterative schemes of weakly contractive mapping in a complete convex metric space. We establish the results on invariant approximation for the mapping defined on a class of nonconvex sets in a convex metric space. Finally, we obtain the existence of common fixed points of two asymptotically nonexpansive mapp...

Let K be a compact convex subset of a real Hilbert space H and T:K→K a continuous hemicontractive map. Let {an},{bn} and {cn} be real sequences in [0, 1] such that an+bn+cn=1, and {un} and {vn} be sequences in K. In this paper we prove that, if {bn}, {cn} and {vn} satisfy some appropriate conditions, then for arbitrary x0K, the sequence {xn} defined iteratively by xn=anxn−1+bnTvn+cnun;n≥1, conv...

Let A and B be two nonempty subsets of a metric space X. A mapping T : A∪B → A∪B is said to be noncyclic if T (A) ⊆ A and T (B) ⊆ B. For such a mapping, a pair (x, y) ∈ A×B such that Tx = x, Ty = y and d(x, y) = dist(A,B) is called a best proximity pair. In this paper we give some best proximity pair results for noncyclic mappings under certain contractive conditions.