Multiparametric Contractions and Related Hardy-Roger Type Fixed Point Theorems

The authors acknowledge with thanks DSR for financial support. A.F. Roldán López de Hierro is grateful to Junta de Andalucía by project FQM-365 of the Andalusian CICYE and Project TIN2017-89517-P of the Ministerio de Economía, Industria y Competitividad.In this paper we present some novel fixed point theorems for a family of contractions depending on two functions (that are not defined on t = 0) and on some parameters that we have called multiparametric contractions. We develop our study in the setting of b-metric spaces because they allow to consider some families of functions endowed with b-metrics deriving from similarity measures that are more general than norms. Taking into account that the contractivity condition we will employ is very general (of Hardy-Rogers type), we will discuss the validation and usage of this novel condition. After that, we introduce the main results of this paper and, finally, we deduce some consequences of them which illustrates the wide applicability of the main results.Junta de Andalucia FQM-365Ministerio de Economia, Industria y Competitividad TIN2017-89517-PDS

Extended Proinov X-contractions in metric spaces and fuzzy metric spaces satisfying the property NC by avoiding the monotone condition

In recent years, Fixed Point Theory has achieved great importance within Nonlinear Analysis especially due to its interesting applications in real-world contexts. Its methodology is based on the comparison between the distances between two points and their respective images through a nonlinear operator. This comparison is made through contractive conditions involving auxiliary functions whose role is increasingly decisive, and which are acquiring a prominent role in Functional Analysis. Very recently, Proinov introduced new fixed point results that have very much attracted the researchers’ attention especially due to the extraordinarily weak conditions on the auxiliary functions considered. However, one of them, the nondecreasing character of the main function, has been used for many years without the chance of being replaced by another alternative property. In this way, several researchers have recently raised this question as an open problem in this field of study. In order to face this open problem, in this work we introduce a novel class of auxiliary functions that serve to define contractions, both in metric spaces and in fuzzy metric spaces, which, in addition to generalizing to Proinov contractions, avoid the nondecreasing character of themain auxiliary function. Furthermore, we present these new results in the setting of fuzzy metric spaces that satisfy the conditionNC, which open new possibilities in the metric theory compared to classic non-Archimedean fuzzy metric spaces. Finally, we include some illustrative examples to show how to apply the novel theorems to cases that are not covered by other previous results.Universidad de Granada / CBU

Solving Integral Equations by Means of Fixed Point Theory

The authors thank their respective universities. A.F. Roldan Lopez de Hierro is grateful to Ministerio de Ciencia e Innovacion by Project PID2020-119478GB-I00 and to Program FEDER Andalucia 2014-2020 by Project A-FQM-170-UGR20.One of the most interesting tasks in mathematics is, undoubtedly, to solve any kind of equations. Naturally, this problem has occupied the minds of mathematicians since the dawn of algebra. There are hundreds of techniques for solving many classes of equations, facing the problem of finding solutions and studying whether such solutions are unique or multiple. One of the recent methodologies that is having great success in this field of study is the fixed point theory. Its iterative procedures are applicable to a great variety of contexts in which other algorithms fail. In this paper, we study a very general class of integral equations by means of a novel family of contractions in the setting of metric spaces. The main advantage of this family is the fact that its general contractivity condition can be particularized in a wide range of ways, depending on many parameters. Furthermore, such a contractivity condition involves many distinct terms that can be either adding or multiplying between them. In addition to this, the main contractivity condition makes use of the self-composition of the operator, whose associated theorems used to be more general than the corresponding ones by only using such mapping. In this setting, we demonstrate some fixed point theorems that guarantee the existence and, in some cases, the uniqueness, of fixed points that can be interpreted as solutions of the mentioned integral equations.Instituto de Salud Carlos III Spanish Government European Commission PID2020-119478GB-I00Program FEDER Andalucia 2014-2020 A-FQM-170-UGR2

Extended Simulation Function via Rational Expressions

In this paper, we introduce some common fixed point theorems for two distinct self-mappings in the setting of metric spaces by using the notion of a simulation function introduced in 2015. The contractivity conditions have not to be verified for all pairs of points of the space because it is endowed with an antecedent conditions. They are also of rational type because the involved terms in the contractivity upper bound are expressed, in some cases, as quotients.MINECO BIO2014-56092-R RTI2018-098296-BI00 CTQ2016-76311European Union (EU) BIO2014-56092-R RTI2018-098296-BI00 CTQ2016-76311 P12-CTS-1507Andalusian Government P12-CTS-1507 BIO-267 CTS-107Instituto de Salud Carlos III European Union (EU) PI19/01478Junta de Andalucia PI-0102-201

Ample Spectrum Contractions and Related Fixed Point Theorems

Simulation functions were introduced by Khojasteh et al. as a method to extend several classes of fixed point theorems by a simple condition. After that, many researchers have amplified the knowledge of such kind of contractions in several ways. R-functions, (R, S)-contractions and (A, S)-contractions can be considered as approaches in this direction. A common characteristic of the previous kind of contractive maps is the fact that they are defined by a strict inequality. In this manuscript, we show the advantages of replacing such inequality with a weaker one, involving a family of more general auxiliary functions. As a consequence of our study, we show that not only the above-commented contractions are particular cases, but also another classes of contractive maps correspond to this new point of view.This article was funded by the Deanship of Scientific Research (DSR), King Abdulaziz University, Jeddah

Best Proximity Point Theorems without Fuzzy P-Property for Several (y - phi)-Weak Contractions in Non-Archimedean Fuzzy Metric Spaces

This paper addresses a problem of global optimization in a non-Archimedean fuzzy metric space context without fuzzy P-property. Specifically, it concerns the determination of the fuzzy distance between two subsets of a non-Archimedean fuzzy metric space. Our approach to solving this problem is to find an optimal approximate solution to a fixed point equation. This approach has been well studied within a category of problems called proximity point problems. We explore some new types of (psi-phi)-weak proximal contractions and investigate the existence of the unique best proximity point for such kinds of mappings. Subsequently, some fixed point results for corresponding contractions are proved, and some illustrative examples are presented to support the validity of the main results. Moreover, an interesting application in computer science, particularly in the domain of words has been provided. Our work is a fuzzy generalization of the proximity point problem by means of fuzzy fixed point method

Hipersuperficies y operador de Dirac

Tesis Univ. de Granada. Departamento de Geometría y Topología. Leída el 28 de abril de 200

Using Excel to improve the teaching of the confidence interval for proportion

III Congreso Internacional Virtual de Educación Estadística (CIVEEST), 21-24 febrero de 2019. [www.ugr.es/local/fqm126/civeest.html]En el estudio de la inferencia estadística, el alumnado suele determinar el intervalo de confianza para la proporción de una forma mecánica, empleando la fórmula tradicional, sin realizar actividades de interpretación adecuada de los resultados obtenidos. En esta comunicación proponemos el uso de la simulación mediante una hoja de cálculo para reforzar la interpretación del estudiante. Se añade también una metodología diferente de construcción (propuesta por Wilson) que mejora la aproximación normal de la distribución muestral. Todo ello nos sirve para reflexionar sobre el procedimiento llevado a cabo durante el proceso de cálculo. La potencia del ordenador permite dedicar nuestro tiempo y esfuerzo a la interpretación del coeficiente de confianza y de los intervalos obtenidos. Finalmente, describimos algunas reflexiones didácticas sobre el estudio desarrollado.In the study of statistical inference, students usually determine the confidence interval for the proportion, in a mechanical way, using the traditional formula, without carrying out adequate interpretation of the obtained results. In this communication we propose the use of simulation, using a spreadsheet to reinforce the student's interpretation. An alternative methodology (proposed by Wilson) is also described to improve the normal approximation of the sample distribution. This permit us to reflect on the procedure carried out during the calculation process. The computers power allows us to spend our time and effort on the interpretation of the confidence coefficient and the obtained intervals. Finally, we describe some didactic aspects about the developed study

Tree diagram: a tool for solving probability problems in the baccalaureate

III Congreso Internacional Virtual de Educación Estadística (CIVEEST), 21-24 febrero de 2019. [www.ugr.es/local/fqm126/civeest.html]Los diagramas de árbol permiten representar la estructura de muchos problemas combinatorios y probabilísticos, facilitando su resolución. No obstante, la investigación sobre el tema muestra la existencia de dificultades en la construcción e interpretación de diagramas de árbol por parte de los estudiantes, posiblemente debido a que en la enseñanza no reciben la atención necesaria. En esta comunicación sugerimos su utilidad incluso en la etapa de bachillerato, donde pueden contribuir a resolver con éxito problemas similares a los propuestos en las pruebas de acceso a la Universidad. Como conclusión, sugerimos la necesidad de prestar más atención a este recurso didáctico en la enseñanza.Tree diagrams allow us to represent the structure of many combinatorial and probabilistic problems, in facilitating their resolution. However, research on this subject shows the existence of difficulties in the construction and interpretation of tree diagrams by students, possibly due to the fact that they do not receive the necessary attention in teaching. In this communication we suggest its usefulness even in the Baccalaureate, where they can contribute to successfully solve problems similar to those proposed in the university entrance tests. As a conclusion, we suggest the need to pay more attention to this didactic resource in teaching

Resolución del examen de Selectividad de 'Matemáticas Aplicadas a las Ciencias Sociales II' en Andalucía - Septiembre de 2019

En este documento de muestra una posible resolución del examen de Selectividad de 'Matemáticas Aplicadas a las Ciencias Sociales II' en Andalucía en la convocatoria de septiembre de 2019. De interés para el alumnado de segundo curso de Bachillerato (en la rama de Ciencias Sociales o en cualquier otra rama siempre que se esté cursando la mencionada asignatura) y de primer curso de grado (que esté cursando una asignatura de Estadística o de Matemáticas)