New fixed point theorem under R-contractions

In this manuscript we introduce the notions of R-function and R-contractions, and we show an ad hoc fixed point theorem. We prove that this new kind of contractions properly includes the family of all Meir-Keeler contractions and other well-known classes of contractions that have been given very recently (for instance, those using simulation functions and manageable functions). As a consequence, our approach turns out to be appropriate to unify the treatment of different kinds of contractive nonlinear operators.This article was funded by the Deanship of Scientific Research (DSR), King Abdulaziz University, Jeddah. The second author, therefore, acknowledges with thanks DSR for technical and financial support. The authors are grateful to three anonymous referees for their useful suggestions and comments. AF Roldán López de Hierro is grateful to the Department of Quantitative Methods for Economics and Business of the University of Granada. The same author has been partially supported by Junta de Andalucía by project FQM-268 of the Andalusian CICYE

Fixed point results for set-contractions on metric spaces with a directed graph

In this paper, we establish the existence of fixed points for set-valued mappings satisfying certain graph contractions with set-valued domain endowed with a graph. These results unify, generalize, and complement various known comparable results in the literature.King Fahd University of Petroleum and Minerals project IN 121023.http://link.springer.com/journal/11784hb201

Root Suberin Forms an Extracellular Barrier That Affects Water Relations and Mineral Nutrition in Arabidopsis

Though central to our understanding of how roots perform their vital function of scavenging water and solutes from the soil, no direct genetic evidence currently exists to support the foundational model that suberin acts to form a chemical barrier limiting the extracellular, or apoplastic, transport of water and solutes in plant roots. Using the newly characterized enhanced suberin1 (esb1) mutant, we established a connection in Arabidopsis thaliana between suberin in the root and both water movement through the plant and solute accumulation in the shoot. Esb1 mutants, characterized by increased root suberin, were found to have reduced day time transpiration rates and increased water-use efficiency during their vegetative growth period. Furthermore, these changes in suberin and water transport were associated with decreases in the accumulation of Ca, Mn, and Zn and increases in the accumulation of Na, S, K, As, Se, and Mo in the shoot. Here, we present direct genetic evidence establishing that suberin in the roots plays a critical role in controlling both water and mineral ion uptake and transport to the leaves. The changes observed in the elemental accumulation in leaves are also interpreted as evidence that a significant component of the radial root transport of Ca, Mn, and Zn occurs in the apoplast

On the existence of fixed points that belong to the zero set of a certain function

Let T : X -> X be a given operator and F-T be the set of its fixed points. For a certain function phi : X -> [0,infinity), we say that F-T is phi-admissible if F-T is nonempty and F-T subset of Z(phi), where Z(phi) is the zero set of phi. In this paper, we study the phi-admissibility of a new class of operators. As applications, we establish a new homotopy result and we obtain a partial metric version of the Boyd-Wong fixed point theorem

Targeting Several CAG Expansion Diseases by a Single Antisense Oligonucleotide

To date there are 9 known diseases caused by an expanded polyglutamine repeat, with the most prevalent being Huntington's disease. Huntington's disease is a progressive autosomal dominant neurodegenerative disorder for which currently no therapy is available. It is caused by a CAG repeat expansion in the HTT gene, which results in an expansion of a glutamine stretch at the N-terminal end of the huntingtin protein. This polyglutamine expansion plays a central role in the disease and results in the accumulation of cytoplasmic and nuclear aggregates. Here, we make use of modified 2′-O-methyl phosphorothioate (CUG)n triplet-repeat antisense oligonucleotides to effectively reduce mutant huntingtin transcript and protein levels in patient-derived Huntington's disease fibroblasts and lymphoblasts. The most effective antisense oligonucleotide, (CUG)7, also reduced mutant ataxin-1 and ataxin-3 mRNA levels in spinocerebellar ataxia 1 and 3, respectively, and atrophin-1 in dentatorubral-pallidoluysian atrophy patient derived fibroblasts. This antisense oligonucleotide is not only a promising therapeutic tool to reduce mutant huntingtin levels in Huntington's disease but our results in spinocerebellar ataxia and dentatorubral-pallidoluysian atrophy cells suggest that this could also be applicable to other polyglutamine expansion disorders as well