Unique Fixed-Point Results in Fuzzy Metric Spaces with an Application to Fredholm Integral Equations

Abstract

This paper aims at proving some unique fixed-point results for different contractive-type self-mappings in fuzzy metric spaces by using the “triangular property of the fuzzy metric”. Some illustrative examples are presented to support our results. Moreover, we present an application by resolving a particular case of a Fredholm integral equation of the second kind.

Fixed-Point Theorems for Nonlinear Contraction in Fuzzy-Controlled Bipolar Metric Spaces

“…In order to strengthen the main results, an additive example and supportive application was also presented. In [20], fixed-point theorems without continuity were provied by using triangular property in FMSs by Shamas…”

“…Rakesh Tiwari and Shraddha Rajput [11] introduced the notion of bipolar-controlled fuzzy metric spaces. The above analysis shows that there are several works on fixed-point theory based on the previous two types of complete fuzzy metric space [12][13][14][15][16][17][18][19][20].…”

Some Results in Fuzzy b-Metric Space with b-Triangular Property and Applications to Fredholm Integral Equations and Dynamic Programming

“…In this manuscript, we prove some results of fixed points in the fuzzy b-metric spaces for non-continuous mappings. Motivated by the solutions of Shamas et al [9] and Mani et al [29] we recall the b-triangular property in fuzzy b-metric space, which is crucial for proving the new results here presented. Furthermore, we give some interesting applications of our results, the first result for proving the existence of a unique result of an integral Fredholm equation, and the other in dynamic programming.…”

“…For example, see the generalizations of Sedghi and Shobe [7] and Abbas et al [8]. The notion of the triangular property of the fuzzy metric in fuzzy metric spaces was given by Shamas et al [9] in order to prove fixed point results losing the continuity condition. Moreover, many results on fuzzy metric spaces can be consulted in the following research works [10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26][27][28].…”

Fixed-Point Theorems on Fuzzy Bipolar b-Metric Spaces

“…In 1994, the fuzzy metric space definition was modified by George and Veeramani [6]. Moreover, Shamas, Rehman, Aydi, Mahmood, and Ameer [7] described more results on the fixed-point results. Mutlu and Gurdal [8] introduced the concept of generalized metric space as a bipolar metric space.…”