GENERALIZED WEAKLY CONTRACTIONS IN PARTIALLY ORDERED FUZZY METRIC SPACES

Abstract. In this paper, a concept of generalized weakly contraction mappings in partially ordered fuzzy metric spaces is introduced and coincidence point theorems on partially ordered fuzzy metric spaces are proved. Also, as the corollary of these theorems, some common fixed point theorems on partially ordered fuzzy metric spaces are presented

On Solution and Stability of a Two-Variable Functional Equations

The main purpose of this paper is to investigate the stability of the functional equation f(x+y,y+z)=2f(x/2,y/2)+2f(y/2,z/2) in normed spaces. The solutions of such functional equations are considered

Characterization of Nash Equilibrium Strategy for Heptagonal Fuzzy Games

In this paper, the Nash equilibrium strategy of two-person zero-sum games with heptagonal fuzzy payoffs is considered and the existence of Nash equilibrium strategy is studied. Also, based on the fuzzy max order several models in heptagonal fuzzy environment is constructed and the existence of their equilibrium strategies is proposed. In the sequel, the existence of Pareto Nash equilibrium strategies and weak Pareto Nash equilibrium strategies is investigated for fuzzy matrix games. Finally, the relation between Pareto Nash equilibrium strategy and parametric bi-matrix games is established

A Note to Paper “On the Stability of Cubic Mappings and Quartic Mappings in Random Normed Spaces” (Erratum)

Recently, Baktash et al. (2008) proved the stability of the cubic functional equation f(2x+y)+f(2x−y)=2f(x+y)+2f(x−y)+12f(x) and the quartic functional equation f(2x+y)+f(2x−y)=4f(x+y)+4f(x−y)+24f(x)−6f(y) in random normed spaces. In this note, we correct the proofs

Contractive Mapping in Generalized, Ordered Metric Spaces with Application in Integral Equations

We consider the concept of Ω-distance on a complete, partially ordered -metric space and prove some fixed point theorems. Then, we present some applications in integral equations of our obtained results

A Transcription Factor Map as Revealed by a Genome-Wide Gene Expression Analysis of Whole-Blood mRNA Transcriptome in Multiple Sclerosis

Background: Several lines of evidence suggest that transcription factors are involved in the pathogenesis of Multiple Sclerosis (MS) but complete mapping of the whole network has been elusive. One of the reasons is that there are several clinical subtypes of MS and transcription factors that may be involved in one subtype may not be in others. We investigate the possibility that this network could be mapped using microarray technologies and contemporary bioinformatics methods on a dataset derived from whole blood in 99 untreated MS patients (36 Relapse Remitting MS, 43 Primary Progressive MS, and 20 Secondary Progressive MS) and 45 age-matched healthy controls. Methodology/Principal Findings: We have used two different analytical methodologies: a non-standard differential expression analysis and a differential co-expression analysis, which have converged on a significant number of regulatory motifs that are statistically overrepresented in genes that are either differentially expressed (or differentially co-expressed) in cases and controls (e.g., V$KROX_Q6, p-value ,3.31E-6; V$CREBP1_Q2, p-value ,9.93E-6, V$YY1_02, p-value ,1.65E-5). Conclusions/Significance: Our analysis uncovered a network of transcription factors that potentially dysregulate several genes in MS or one or more of its disease subtypes. The most significant transcription factor motifs were for the Early Growth Response EGR/KROX family, ATF2, YY1 (Yin and Yang 1), E2F-1/DP-1 and E2F-4/DP-2 heterodimers, SOX5, and CREB and ATF families. These transcription factors are involved in early T-lymphocyte specification and commitment as well as in oligodendrocyte dedifferentiation and development, both pathways that have significant biological plausibility in MS causation