9 research outputs found
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
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
The Sehgal’s Fixed Point Result in the Framework of <i>ρ</i>-Space
In this paper, we prove a fixed point theorem of Sehgal type (see Sehgal, V.M., Proc Amer Math Soc 23: 631–634, 1969) in a more general setting of ρ-space (see Secelean, N.A. and Wardowski, D., Results Math, 72: 919–935, 2017). In this way, we can find, as particular cases, some results of Sehgal type in metric, b-metric and rectangular b-metric spaces