Fixed points of dynamic processes of set-valued F-contractions and application to functional equations

The article is a continuation of the investigations concerning F-contractions which have been recently introduced in [Wardowski in Fixed Point Theory Appl. 2012:94,2012]. The authors extend the concept of F-contractive mappings to the case of nonlinear F-contractions and prove a fixed point theorem via the dynamic processes. The paper includes a non-trivial example which shows the motivation for such investigations. The work is summarized by the application of the introduced nonlinear F-contractions to functional equations

Some remarks on fuzzy contractive mappings

Recently a new concept of fuzzy contraction in fuzzy metric spaces in the sense of George and Veeramani (Wardowski, 2013 [5]) has been introduced. Here we provide some comments to this paper.Juan-Jose Minana acknowledges the support of Conselleria de Educacion, Formacion y Empleo (Programa Vali+d para investigadores en formacion) of Generalitat Valenciana, Spain and the support of Universitat Politecnica de Valencia under Grant PAID-06-12 SP20120471.Gregori Gregori, V.; Miñana, J. (2014). Some remarks on fuzzy contractive mappings. Fuzzy Sets and Systems. 251:101-103. https://doi.org/10.1016/j.fss.2014.01.002S10110325

Monotone iterative procedure and systems of a finite number of nonlinear fractional differential equations

The aim of the paper is to present a nontrivial and natural extension of the comparison result and the monotone iterative procedure based on upper and lower solutions, which were recently established in (Wang et al. in Appl. Math. Lett. 25:1019-1024, 2012), to the case of any finite number of nonlinear fractional differential equations.The author is very grateful to the reviewers for the remarks, which improved the final version of the manuscript. This article was financially supported by University of Łódź as a part of donation for the research activities aimed at the development of young scientists, grant no. 545/1117

Polyphenoloxidase activity and total phenolic content as related to browning of minimally processed ‘Jonagored’ apple

Phenolic content, polyphenoloxidase (PPO) activity and browning have been reported by different authors to vary in different ways, depending on cultivar, picking maturity, storage conditions, etc. Numerous authors have attempted to correlate browning results with the phenolic content and/or enzymatic activity of apples, but data published in the literature are divergent as to which of the two factors, ie the enzyme or the substrate, plays the decisive role in the overall phenomenon of enzymatic browning. The aim of this work was to follow the PPO activity and phenolic content of minimally processed apple (cv ‘Jonagored’) during cold storage and to establish a potential relationship with enzymatic browning. Increasing storage time of minimally processed apple seemed to result in an increase in PPO activity. No changes (P > 0.05) in total phenolic content were observed during storage. Colour degradation of apple cubes, as indicated by changes in colour parameters, was found to be highly correlated with PPO activity. Browning of ‘Jonagored’ apple cubes during storage was found to be moderately correlated with PPO activity. No correlation was found between the browning index and the total phenolic content

Some fixed point theorems for generalized contractive mappings in complete metric spaces

We introduce new concepts of generalized contractive and generalized alpha-Suzuki type contractive mappings. Then, we obtain sufficient conditions for the existence of a fixed point of these classes of mappings on complete metric spaces and b-complete b-metric spaces. Our results extend the theorems of Ciric, Chatterjea, Kannan and Reich