On fuzzy phi-contractive sequences and fixed point theorems

In this paper we give a fixed point theorem in the context of fuzzy metric spaces in the sense of George and Veeramani. As a consequence of our result we obtain a fixed point theorem due to D. Mihet and generalize a fixed point theorem due to D. Wardowski. Also, we answer in a positive way to a question posed by D. Wardowski, and solve partially an open question on Cauchyness and contractivity. (C) 2015 Elsevier B.V. All rights reserved.Juan Jose Minana acknowledges the support of Conselleria de Educacion, Formacion y Empleo of Generalitat Valenciana, Spain, by Programa Vali+d para investigadores en formacion under Grant ACIF/2012/040.Gregori Gregori, V.; Miñana, JJ. (2016). On fuzzy phi-contractive sequences and fixed point theorems. Fuzzy Sets and Systems. 300:93-101. doi:10.1016/j.fss.2015.12.010S9310130

Strong convergence in fuzzy metric spaces

[EN] In this paper we introduce and study the concept of strong convergence in fuzzy metric spaces (X, M,*) in the sense of George and Veeramani. This concept is related with the condition Lambda M-t > 0(x, y, t) > 0, which frequently is required or missing in this context. Among other results we characterize the class of s-fuzzy metrics by the strong convergence defined here and we solve partially the question of finding explicitly a compatible metric with a given fuzzy metric.Valentn Gregori acknowledges the support of the Spanish Ministry of Economy and Competitiveness under Grant MTM2015-64373-P (MINECO/FEDER, UE).Gregori Gregori, V.; Miñana, J. (2017). Strong convergence in fuzzy metric spaces. Filomat. 31(6):1619-1625. https://doi.org/10.2298/FIL1706619GS1619162531

A Banach contraction principle in fuzzy metric spaces defined by means of t-conorms

[EN] Fixed point theory in fuzzy metric spaces has grown to become an intensive field of research. The difficulty of demonstrating a fixed point theorem in such kind of spaces makes the authors to demand extra conditions on the space other than completeness. In this paper, we introduce a new version of the celebrated Banach contracion principle in the context of fuzzy metric spaces. It is defined by means of t-conorms and constitutes an adaptation to the fuzzy context of the mentioned contracion principle more "faithful" than the ones already defined in the literature. In addition, such a notion allows us to prove a fixed point theorem without requiring any additional condition on the space apart from completeness. Our main result (Theorem 1) generalizes another one proved by Castro-Company and Tirado. Besides, the celebrated Banach fixed point theorem is obtained as a corollary of Theorem 1.Juan-José Miñana acknowledges financial support from FEDER/Ministerio de Ciencia, Innovación y Universidades-Agencia Estatal de Investigación/¿Proyecto PGC2018-095709-B-C21. This work is also partially supported by Programa Operatiu FEDER 2014-2020 de les Illes Balears, by project PROCOE/4/2017 (Direcció General d¿Innovació i Recerca, Govern de les Illes Balears) and by projects ROBINS and BUGWRIGHT2. These two latest projects have received funding from the European Union¿s Horizon 2020 research and innovation programme under grant agreements No 779776 and No 871260, respectively. This publication reflects only the authors views and the European Union is not liable for any use that may be made of the information contained therein. Valentín Gregori acknowledges the support of Generalitat Valenciana under grant AICO-2020-136.Gregori Gregori, V.; Miñana, J. (2021). A Banach contraction principle in fuzzy metric spaces defined by means of t-conorms. Revista de la Real Academia de Ciencias Exactas Físicas y Naturales Serie A Matemáticas. 115(3):1-11. https://doi.org/10.1007/s13398-021-01068-6S111115

An overview on transformations on generalized metrics

[EN] We will present an overview on the results appeared in the literature about the study of those functions that preserve or transform a generalized metric.Miñana, JJ. (2017). An overview on transformations on generalized metrics. En Proceedings of the Workshop on Applied Topological Structures. Editorial Universitat Politècnica de València. 95-102. http://hdl.handle.net/10251/128010OCS9510

On completable fuzzy metric spaces

In this paper we construct a non-completable fuzzy metric space in the sense of George and Veeramani which allows to answer an open question related to continuity on the real parameter t. In addition, the constructed space is not strong (non-Archimedean).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.; Morillas, S. (2015). On completable fuzzy metric spaces. Fuzzy Sets and Systems. 267:133-139. https://doi.org/10.1016/j.fss.2014.07.009S13313926

Colour image denoising by eigenvector analysis of neighbourhood colour samples

[EN] Colour image smoothing is a challenging task because it is necessary to appropriately distinguish between noise and original structures, and to smooth noise conveniently. In addition, this processing must take into account the correlation among the image colour channels. In this paper, we introduce a novel colour image denoising method where each image pixel is processed according to an eigenvector analysis of a data matrix built from the pixel neighbourhood colour values. The aim of this eigenvector analysis is threefold: (i) to manage the local correlation among the colour image channels, (ii) to distinguish between flat and edge/textured regions and (iii) to determine the amount of needed smoothing. Comparisons with classical and recent methods show that the proposed approach is competitive and able to provide significative improvements.Latorre-Carmona, P.; Miñana, J.; Morillas, S. (2020). Colour image denoising by eigenvector analysis of neighbourhood colour samples. 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La Orquesta Sinfónica de Valencia (1916-2016) y su aportación a la evolución de la música sinfónica en Valencia

[ES] Con el trabajo de esta tesis doctoral realizamos un estudio de la primera Orquesta Sinfónica que se fundó en Valencia a principios del siglo XX, todo ello, después de varios intentos de formaciones orquestales, más bien de cámara, y de agrupaciones que se dedican solamente a formar parte de la música lírica. La Orquesta Sinfónica de Valencia aparece en los escenarios valencianos como una necesidad del ambiente social y musical que tiene el público valenciano de poder disfrutar, de manera prioritaria, de la música sinfónica, que ya en otras partes del Estado está floreciendo con gran intensidad, sobre todo en Madrid, Barcelona y Bilbao. Analizamos la tipología de los conciertos que se realizan, los compositores que más se interpretan, y la aceptación y valoración del público y de la prensa sobre las audiciones realizadas. El estudio de la Orquesta Sinfónica de Valencia, lo realizamos desde su nacimiento en 1916, hasta su centenario desde su formación, si bien hay periodos o etapas en las que su actividad desaparece temporalmente, debido principalmente a motivos económicos y/o sociales dentro de su gestión. El trabajo de la tesis lo dividimos en cuatro periodos diferentes de su existencia: periodo inicial de constitución de la Orquesta, puesta en funcionamiento y presentación a la sociedad valenciana que abarca desde 1916 hasta 1924 bajo la dirección del maestro Arturo Saco del Valle; un segundo periodo en el cual se produce el máximo esplendor y actividad de la Orquesta Valenciana que va desde 1924 hasta 1951 con el maestro José Manuel Izquierdo; el tercer periodo, en el cual la Orquesta Sinfónica de Valencia posee momentos álgidos y momentos de pura supervivencia en el que las riendas de la Orquesta son llevadas principalmente por los maestros José María Machancoses, Daniel de Nueda y Juan Vicente Mas Quiles que comprende desde 1951 hasta 1979, donde desaparece de los escenarios momentáneamente; y el cuarto periodo que va desde 1991 hasta 2016, en el cual se produce un renacimiento de la Orquesta con actividad diversa con los maestros Manuel Galduf y Joan Cerveró. Estos cuatro periodos son objeto de estudio tanto a la actividad artística, como al repertorio interpretativo de la Orquesta. En ocasiones, la ausencia de documentación directa, nos ha hecho realizar una investigación pormenorizada indagando en fuentes indirectas, aportando satisfactoriamente a la tesis el objeto principal del trabajo: la aportación y la evolución de la música sinfónica de la Orquesta Sinfónica de Valencia a la sociedad valenciana.[CA] Amb el treball d'aquesta tesi doctoral realitzem un estudi de la primera Orquestra Simfònica que es va fundar a València a principis del segle XX, tot això, després de diversos intents de formacions orquestrals, més aviat de cambra, i d'agrupacions que es dediquen només a formar part de la música lírica. L'Orquestra Simfònica de València apareix als escenaris valencians com una necessitat de l'ambient social i musical que té el públic valencià de poder gaudir, de manera prioritària, de la música simfònica, que ja en altres parts de l'Estat està florint amb gran intensitat, sobretot a Madrid, Barcelona i Bilbao. Analitzem la tipologia dels concerts que es realitzen, els compositors que més s'interpreten, i l'acceptació i valoració del públic i de la premsa sobre les audicions realitzades. L'estudi de l'Orquestra Simfònica de València, el realitzem des del seu naixement en 1916, fins a la seva centenari des de la seva formació, si bé hi ha períodes o etapes en les que la seva activitat desapareix temporalment, degut principalment a motius econòmics i/o socials dins de la seua gestió. El treball de la tesi el dividim en quatre períodes diferents de la seva existència: període inicial de constitució de l'Orquestra, posada en funcionament i presentació a la societat valenciana que comprén des de 1916 fins 1924 sota la direcció del mestre Arturo Saco del Valle; un segon període en el qual es produeix el màxim esplendor i activitat de l'Orquestra Valenciana que va des de 1924 fins 1951 amb el mestre José Manuel Izquierdo; el tercer període, en el qual l'Orquestra Simfònica de València posseeix moments àlgids i moments de pura supervivència en què les regnes de l'Orquestra són portades principalment pels mestres José María Machancoses, Daniel de Nueda i Juan Vicente Mas Quiles que comprèn des de 1951 fins a 1979, on desapareix dels escenaris momentàniament; i el quart període que va des de 1991 fins 2016, en el qual es produeix un renaixement de l'Orquestra amb activitat diversa amb els mestres Manuel Galduf i Joan Cerveró. Aquests quatre períodes són objecte d'estudi tant a l'activitat artística, com al repertori interpretatiu de l'Orquestra. De vegades, l'absència de documentació directa, ens ha fet realitzar una investigació detallada indagant en fonts indirectes, aportant satisfactòriament a la tesi l'objecte principal del treball: l'aportació i l'evolució de la música simfònica de l'Orquestra Simfònica de València a la societat valenciana.[EN] With the work of this doctoral thesis we realized a study of the first Symphony Orchestra that was founded in Valencia at the beginning of century XX, all of it, after several attempts of orchestral formations, more of camera and of groupings that are dedicated only to comprise of the lyrical music. The Valencia Symphony Orchestra appears in the Valencian stages as a necessity of the social and musical environment that has the Valencian public to be able to enjoy, as a priority, the symphonic music, which already in other parts of the State is flourishing with great intensity, especially in Madrid, Barcelona and Bilbao. We analyze the typology of the concerts performed, the composers who are most interpreted, and the acceptance and appreciation of the public and the press about the auditions performed. The study of the Symphony Orchestra of Valencia, from its birth in 1916, to its centenary since its formation, although there are periods or stages in which its activity disappears temporarily, mainly due to economic and/or social reasons within its management. The work of the thesis is divided into four different periods of its existence: initial period of constitution of the Orchestra, put into operation and presentation to the Valencian society that it embraced from 1916 to 1924 under the direction of the conductor Arturo Saco del Valle; a second period in which there is the maximum splendor and activity of the Valencian Orchestra that goes from 1924 to 1951 with the conductor José Manuel Izquierdo; the third period, in which the Symphonic Orchestra of Valencia has high moments and moments of pure survival in which the reins of the Orchestra are carried mainly by the conductors José María Machancoses, Daniel de Nueda and Juan Vicente Mas Quiles, which he has since 1951 until 1979, where he disappears from the scenes momentarily; and the fourth period from 1991 to 2016, in which there is a renaissance of the Orchestra with diverse activity with conductors Manuel Galduf and Joan Cerveró. These four periods are the subject of study as much the artistic activity, as the repertoire interpretative of the Orchestra. At times, the absence of direct documentation has led us to carry out a detailed investigation by investigating indirect sources, satisfactorily contributing to the thesis the main object of the work: the contribution and evolution of symphonic music from the Valencia Symphony Orchestra to society Valencian.Miñana Juan, JM. (2019). LA ORQUESTA SINFÓNICA DE VALENCIA (1916-2016) Y SU APORTACIÓN A LA EVOLUCIÓN DE LA MÚSICA SINFÓNICA EN VALENCIA [Tesis doctoral no publicada]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/129877TESI

A Duality Relationship Between Fuzzy Partial Metrics and Fuzzy Quasi-Metrics

[EN] In 1994, Matthews introduced the notion of partial metric and established a duality relationship between partial metrics and quasi-metrics defined on a set X. In this paper, we adapt such a relationship to the fuzzy context, in the sense of George and Veeramani, by establishing a duality relationship between fuzzy quasi-metrics and fuzzy partial metrics on a set X, defined using the residuum operator of a continuous t-norm *. Concretely, we provide a method to construct a fuzzy quasi-metric from a fuzzy partial one. Subsequently, we introduce the notion of fuzzy weighted quasi-metric and obtain a way to construct a fuzzy partial metric from a fuzzy weighted quasi-metric. Such constructions are restricted to the case in which the continuous t-norm * is Archimedean and we show that such a restriction cannot be deleted. Moreover, in both cases, the topology is preserved, i.e., the topology of the fuzzy quasi-metric obtained coincides with the topology of the fuzzy partial metric from which it is constructed and vice versa. Besides, different examples to illustrate the exposed theory are provided, which, in addition, show the consistence of our constructions comparing it with the classical duality relationship.Juan-Jose Minana acknowledges financial support from FEDER/Ministerio de Ciencia, Innovacion y Universidades-Agencia Estatal de Investigacion/Proyecto PGC2018-095709-B-C21, and by Spanish Ministry of Economy and Competitiveness under contract DPI2017-86372-C3-3-R (AEI, FEDER, UE). This work is also partially supported by Programa Operatiu FEDER 2014-2020 de les Illes Balears, by project PROCOE/4/2017 (Direccio General d'Innovacio i Recerca, Govern de les Illes Balears) and by projects ROBINS and BUGWRIGHT2. These two latest projects have received funding from the European Union's Horizon 2020 research and innovation program under grant agreements No 779776 and No 871260, respectively. This publication reflects only the authors views and the European Union is not liable for any use that may be made of the information contained therein.Gregori Gregori, V.; Miñana, J.; Miravet, D. (2020). A Duality Relationship Between Fuzzy Partial Metrics and Fuzzy Quasi-Metrics. Mathematics. 8(9):1-16. https://doi.org/10.3390/math809157511689MATTHEWS, S. G. (1994). Partial Metric Topology. Annals of the New York Academy of Sciences, 728(1 General Topol), 183-197. doi:10.1111/j.1749-6632.1994.tb44144.xGeorge, A., & Veeramani, P. (1994). On some results in fuzzy metric spaces. Fuzzy Sets and Systems, 64(3), 395-399. doi:10.1016/0165-0114(94)90162-7Roldán-López-de-Hierro, A.-F., Karapınar, E., & Manro, S. (2014). Some new fixed point theorems in fuzzy metric spaces. Journal of Intelligent & Fuzzy Systems, 27(5), 2257-2264. doi:10.3233/ifs-141189Gregori, V., & Miñana, J.-J. (2016). On fuzzy ψ -contractive sequences and fixed point theorems. Fuzzy Sets and Systems, 300, 93-101. doi:10.1016/j.fss.2015.12.010Gregori, V., Miñana, J.-J., Morillas, S., & Sapena, A. (2016). Cauchyness and convergence in fuzzy metric spaces. Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas, 111(1), 25-37. doi:10.1007/s13398-015-0272-0Gutiérrez García, J., Rodríguez-López, J., & Romaguera, S. (2018). On fuzzy uniformities induced by a fuzzy metric space. Fuzzy Sets and Systems, 330, 52-78. doi:10.1016/j.fss.2017.05.001Beg, I., Gopal, D., Došenović, T., … Rakić, D. (2018). α-type fuzzy H-contractive mappings in fuzzy metric spaces. Fixed Point Theory, 19(2), 463-474. doi:10.24193/fpt-ro.2018.2.37Gregori, V., Miñana, J.-J., & Miravet, D. (2018). Fuzzy partial metric spaces. 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Fuzzy Partial Metric Spaces

"This is an Accepted Manuscript of an article published by Taylor & Francis in International Journal of General Systems on 01 Dec 2018, available online: https://doi.org/10.1080/03081079.2018.1552687"[EN] In this paper we provide a concept of fuzzy partial metric space (X, P, ¿) as an extension to fuzzy setting in the sense of Kramosil and Michalek, of the concept of partial metric due to Matthews. This extension has been defined using the residuum operator ¿¿ associated to a continuous t-norm ¿ and without any extra condition on ¿. Similarly, it is defined the stronger concept of GV -fuzzy partial metric (fuzzy partial metric in the sense of George and Veeramani). After defining a concept of open ball in (X, P, ¿), a topology TP on X deduced from P is constructed, and it is showed that (X, TP) is a T0-space.Valentin Gregori acknowledges the support of the Ministry of Economy and Competitiveness of Spain under Grant MTM2015-64373-P (MINECO/Feder, UE). Juan Jose Minana acknowledges the partially support of the Ministry of Economy and Competitiveness of Spain under Grant TIN2016-81731-REDT (LODISCO II) and AEI/FEDER, UE funds, by the Programa Operatiu FEDER 2014-2020 de les Illes Balears, by project ref. PROCOE/4/2017 (Direccio General d'Innovacio i Recerca, Govern de les Illes Balears), and by project ROBINS. The latter has received research funding from the European Union framework under GA 779776. This publication reflects only the authors views and the European Union is not liable for any use that may be made of the information contained therein.Gregori Gregori, V.; Miñana, J.; Miravet-Fortuño, D. (2018). Fuzzy Partial Metric Spaces. International Journal of General Systems. https://doi.org/10.1080/03081079.2018.1552687SBukatin, M., Kopperman, R., & Matthews, S. (2014). Some corollaries of the correspondence between partial metrics and multivalued equalities. 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