We introduce an explicit iterative scheme for computing a common fixed point of a sequence of nearly nonexpansive mappings defined on a closed convex subset of a real Hilbert space which is also a solution of a variational inequality problem. We prove a strong convergence theorem for a sequence generated by the considered iterative scheme under suitable conditions. Our strong convergence theore...

We study convergences of Mann and Ishikawa iteration processes for mappings of asymptotically quasi-nonexpansive type in Banach spaces. 1. Introduction and preliminaries. Let D be a nonempty subset of a real Banach space X and T : D → D a nonlinear mapping. The mapping T is said to be asymptotically quasi-nonexpansive (see [5]) if F(T) = ∅ and there exists a sequence {k n } in [0, ∞) with lim n...

*Correspondence: [email protected] School of Science, Southwest University of Science and Technology, Mianyang, Sichuan 621010, China Abstract In this paper, we prove the demiclosed principle for total asymptotically nonexpansive nonself mappings in hyperbolic spaces. Then we obtain convergence theorems of the mixed Agarwal-O’Regan-Sahu type iteration for total asymptotically nonexpansive non...

We introduce two modifications of the Mann iteration, by using the hybrid methods, for equilibrium and fixed point problems for an infinite family of asymptotically nonexpansive mappings in a Hilbert space. Then, we prove that such two sequences converge strongly to a common element of the set of solutions of an equilibrium problem and the set of common fixed points of an infinite family of asy...

In this paper we obtain new effective results on the Halpern iterations of nonexpansive mappings using methods from mathematical logic or, more specifically, proof-theoretic techniques. We give effective rates of asymptotic regularity for the Halpern iterations of nonexpansive self-mappings of nonempty convex sets in normed spaces. The paper presents another case study in the project of proof m...

BACKGROUND Sun exposure has positive and negative effects on health, yet little is known about the sun exposure behaviour of UK adolescents, including those more prone or less prone to sunburn. OBJECTIVE To examine sun exposure behaviour of UK white Caucasian adolescents including time spent outdoors, holiday behaviour, use of sunscreen and clothing, with assessment for differences between su...

Photometric Stereo in outdoor illumination remains a challenging, ill-posed problem. Indeed, it has been shown that the scene structure cannot be recovered unambiguously from the photometric cues alone when it is lit by the sun over the course of a single day. In this paper, we present a CNN-based technique for photometric stereo on a single sunny day. We solve the ambiguity issue by combining ...

editorial

Several recent papers have reported standardized incidence ratios (SIRs) for second cancers after diagnosis of cutaneous malignant melanoma. This review divides the types of cancer into five types: (1) those for which UV-B (UVB) irradiance and vitamin D reduces risk; (2) those for which UVB/vitamin D reduces risk and smoking increases risk; (3) smoking related; (4) unknown UVB/vitamin D and smo...