Common Fixed Point Theorems in Non-archimedean Fuzzy Metric Spaces

The aim of this paper is to define the concept of weakly comparable multi-valued mappings. Also we obtain some common fixed point theorems for pairs of weakly comparable multi-valued mappings in ordered non-Archimedean fuzzy metric space

std-Convergence in fuzzy metric spaces

In this note we answer two recent questions posed by Morillas and Sapena [10] related to standard convergence in fuzzy metric spaces in the sense of George and Veeramani. The obtained results lead us to establish what conditions must satisfy a concept about sequential convergence to be considered compatible with a concept of Cauchyness.Juan Jose Minana acknowledges the support of Conselleria de Educacion, Formacion y Empleo (Programa Vali+d para investigadores en formacion) of Generalitat Valenciana, Spain, ACIF/2012/040, and the support of Universitat Politecnica de Valencia under Grant PAID-06-12 SP20120471.Gregori Gregori, V.; Miñana, JJ. (2015). std-Convergence in fuzzy metric spaces. Fuzzy Sets and Systems. 267:140-143. https://doi.org/10.1016/j.fss.2014.05.007S14014326

COMMON FIXED POINT THEOREM FOR A PAIR OF WEAKLY COMPATIBLE SELF-MAPPINGS IN FUZZY METRIC SPACE USING (CLRG) PROPERTY

In this paper we prove a common fixed point theorem for a pair of weakly compatible self-mappings in fuzzy metric space by using (CLRg) property. The result is extended for two finite families of self-mappings infuzzy metric space by using the concept of pairwise commuting. An example is provided which demonstrates the validity of main theorem

FIXED POINT THEOREM IN FUZZY METRIC SPACE WITH THE PROPERTY

The purpose of this paper is to prove a common fixed point theorem for semi-compatible and occasionally weakly compatible mappings in fuzzy metric space by using the property (E.A.) and implicit relation. Our result generalizes  the result of [14]. Keywords: Fuzzy metric space, property (E.A.), semi-compatible and weakly compatible mappings. 2010 MSC: Primary 54E70; Secondary 54H25

On Yager and Hamacher t-Norms and Fuzzy Metric Spaces

Recently, Gregori et al. have discussed (Fuzzy Sets Syst 2011;161:2193 2205) the so-called strong fuzzy metrics when looking for a class of completable fuzzy metric spaces in the sense of George and Veeramani and state the question of finding a non-strong fuzzy metric space for a continuous t-norm different from the minimum. Later on, Gutíerrez-García and Romaguera solved this question (Fuzzy Sets Syst 2011;162:91 93) by means of two examples for the product and the Lukasiewicz t-norm, respectively. In this direction, they posed to find further examples of nonstrong fuzzy metrics for continuous t-norms that are greater than the product but different from minimum. In this paper, we found an example of this kind. On the other hand, Tirado established (Fixed Point Theory 2012;13:273 283) a fixed-point theorem in fuzzy metric spaces, which was successfully used to prove the existence and uniqueness of solution for the recurrence equation associated with the probabilistic divide and conquer algorithms. Here, we generalize this result by using a class of continuous t-norms known as ω-Yager t-norms.The second author acknowledges the support of the Ministry of Economy and Competitiveness of Spain under grant MTM2012-37894-C02-01 and the support of Universitat Politecnica de Valencia under grant PAID-06-12-SP20120471.Castro Company, F.; Tirado Peláez, P. (2014). On Yager and Hamacher t-Norms and Fuzzy Metric Spaces. International Journal of Intelligent Systems. 29:1173-1180. https://doi.org/10.1002/int.21688S1173118029Sherwood, H. (1966). On the completion of probabilistic metric spaces. Zeitschrift f�r Wahrscheinlichkeitstheorie und Verwandte Gebiete, 6(1), 62-64. doi:10.1007/bf00531809Gregori, V. (2002). On completion of fuzzy metric spaces. Fuzzy Sets and Systems, 130(3), 399-404. doi:10.1016/s0165-0114(02)00115-xGregori, V., Morillas, S., & Sapena, A. (2010). On a class of completable fuzzy metric spaces. Fuzzy Sets and Systems, 161(16), 2193-2205. doi:10.1016/j.fss.2010.03.013Gutiérrez García, J., & Romaguera, S. (2011). Examples of non-strong fuzzy metrics. Fuzzy Sets and Systems, 162(1), 91-93. doi:10.1016/j.fss.2010.09.017Yager, R. R. (1980). On a general class of fuzzy connectives. Fuzzy Sets and Systems, 4(3), 235-242. doi:10.1016/0165-0114(80)90013-5Castro-Company, F., & Tirado, P. (2012). Some classes of t-norms and fuzzy metric spaces. doi:10.1063/1.4756272George, 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)90162-7Hadžić, O., & Pap, E. (2001). Fixed Point Theory in Probabilistic Metric Spaces. doi:10.1007/978-94-017-1560-7Klement, E. P., Mesiar, R., & Pap, E. (2000). Triangular Norms. Trends in Logic. doi:10.1007/978-94-015-9540-

On Pseudo Fuzzy Length Space and Quotient of Fuzzy Length Space

In this paper we recall the definition of fuzzy length space on a fuzzy set after that we recall basic definitions and properties of this space. Then we introduce the notion pseudo fuzzy length space on a fuzzy set to prove that the fuzzy completion of pseudo fuzzy length is a fuzzy length space. Finally we defined the quotient of a fuzzy length space then we defined the fuzzy length to the quotient space

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

Existence and Uniqueness Solutions of Fuzzy Fractional Integral Equation of Volterra-Stieltjes Type

In this paper, we establish the existence and uniqueness results to the Cauchy problem posed for a fuzzy fractional Volterra-Stieltjes integrodifferential equation. The method of successive approximations is used to prove the existence, whereas the contraction theory is applied to prove the uniqueness of the solution to the problem