Some Results on Fixed Points

Visual Analogue Scale(VAS)による運動習慣継続性の検討

In this manuscript, we propose a solution for Volterra type fractional integral equations by using a hybrid type contraction that unifies both nonlinear and linear type inequalities in the context of metric spaces. Besides this main goal, we also aim to combine and merge several existing fixed point theorems that were formulated by linear and nonlinear contractions.

https://www.mdpi.com/2227-7390/7/8/694/pdf

A Solution for Volterra Fractional Integral Equations by Hybrid Contractions

In this paper, we initiate the concept of interpolative Ciric-Reich-Rus type contractions via the Branciari distance and prove some related fixed points results for such mappings. Moreover, an example is provided to show the useability of our obtained results.

https://www.mdpi.com/2227-7390/7/1/84/pdf

Interpolative Ćirić-Reich-Rus Type Contractions via the Branciari Distance

In this paper, using the concept of ω -admissibility, we prove some fixed point results for interpolate Ciric-Reich-Rus-type contraction mappings. We also present some consequences and a useful example.

https://www.mdpi.com/2227-7390/7/1/57/pdf

ω-Interpolative Ćirić-Reich-Rus-Type Contractions

Introduction with a Brief Historical Survey.- Preliminaries.- G-Metric Spaces.- Basic Fixed Point Results in the Setting of G-Metric Spaces.- Fixed Point Theorems in Partially Ordered G-Metric Spaces.- Further Fixed Point Results on G-Metric Spaces.- Fixed Point Theorems via Admissible Mappings.- New Approaches to Fixed Point Results on G-Metric Spaces.- Expansive Mappings.- Reconstruction of G-Metrics: G*-Metrics.- Multidimensional Fixed Point Theorems on G-Metric Spaces.- Recent Motivating Fixed Point Theory.

Fixed Point Theory in Metric Type Spaces

Regression analysis is a powerful statistical tool that has many applications in different areas. The problem of regression analysis under a fuzzy environment has been treated in the literature from different points of view and considering a variety of input/output data (crisp or fuzzy). However, we realize that, in general, most research papers have a conflict between the solution of the fuzzy regression problem using crisp distances (minimizing a real error function) and the interpretation of fuzzy data as possibility distributions. The main aim of this paper is to develop a methodology to solve this problem introducing a fuzzy partial order and a family of fuzzy distance measures on the whole set of fuzzy numbers. The new approach allows us to obtain linear and nonlinear models that reach the lowest fuzzy error; the estimation process, in general, can be considered easier to apply in practice, and it is not limited to triangular fuzzy numbers. Numerical examples are provided to illustrate the usefulness and applicability of these results, and comparisons with existing methodologies show that the performance of the proposed solution is very satisfactory.

Estimation of a Fuzzy Regression Model Using Fuzzy Distances

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.

/pdf/new-fixed-point-theorem-under-r-contractions-490na7lkug.pdf

Antonio Francisco Roldán López de Hierro

Papers

ω-Interpolative Ćirić-Reich-Rus-Type Contractions

Fixed Point Theory in Metric Type Spaces

Estimation of a Fuzzy Regression Model Using Fuzzy Distances

New fixed point theorem under R-contractions

On a new methodology for ranking fuzzy numbers and its application to real economic data