Restricted accessResearch articleFirst published online 2026
A New Approach to Investigate Fixed Point for the Sequence of Mappings in Intuitionistic Fuzzy Rectangular Triple Controlled Metric Spaces with Applications
This paper introduces and investigates the concept of an intuitionistic fuzzy rectangular triple controlled metric space (IFRTCMS), providing illustrative examples for clarity. Now fixed point theorems are established for sequence of mappings within this framework. Furthermore, a distinct fixed point theorem is proved by proposing an innovative notion of T-intuitionistic fuzzy contraction. To underline the practical significance of the theoretical developments, the obtained results are successfully applied to solve integral equations.
AssadN. A.KirkW. A. (1972). Fixed point theorems for set-valued mappings of contractive type. Pacific Journal of Mathematics, 43(3), 553–562.
3.
AzamA.ArshadM.BegI. (2008). Common fixed points of two maps in cone metric spaces. Rendiconti del Circolo Matematico di Palermo, 57, 433–441.
4.
AzmiF. M. (2023). Exploring fuzzy triple controlled metric spaces: Applications in integral equations. Symmetry, 15(10), 1943.
5.
BanachS. (1922). Sur les opérations dans les ensembles abstraits et leur application aux équations intégrales. Fundamenta mathematicae, 3(1), 133–181.
6.
BegI.ButtA. R. (2009). Fixed point for set valued mappings satisfying an implicit relation in partially ordered metric spaces. Nonlinear Analysis, 71, 3699–3704.
7.
BegI.ButtA. R. (2010). Common fixed point for generalized set valued contractions satisfying an implicit relation in partially ordered metric spaces. Mathematical Communications, 2, 1491–1498.
8.
BhaskarT. G.LaskhmikanthamV. (2006). Fixed point theorems in partially ordered metric spaces and applications. Nonlinear Analysis, 65(7), 1379–1393.
9.
ĆirićL. B. (2006). Common fixed point theorems for multi-valued mappings. Demonstratio Mathematica, 39(2), 419–428.
10.
ĆirićL.SametB.AydiH.VetroC. (2011). Common fixed points of generalized contractions on partial metric spaces and an application. Applied Mathematics and Computing, 218, 2398–2406.
11.
DafferP. Z.KanekoH. (1965). Fixed points of generalized contractive multi-valued mappings. Journal of Mathematics and Applications, 192, 655–666.
12.
FarheenM.AhmedK.JavedK.ParvanehV.DinF. U.IshtiaqU. (2022). Intuitionistic fuzzy double controlled metric spaces and related results. Security and Communication Networks, 2022(1), 6254055.
13.
FengY.LiuS. (2006). Fixed point theorems for multi-valued contractive mappings and multi-valued Caristi-type mappings. Journal of Mathematics and Applications, 317, 103–112.
14.
FurqanS.IsikH.SaleemN. (2021). Fuzzy triple controlled metric spaces and related fixed point results. Journal of Function Spaces, 2021(1), 9936992.
15.
GeorgeA.VeeramaniP. (1994). On some results in fuzzy metric spaces. Fuzzy Sets and Systems, 64, 395–399.
16.
GrabiecM. (1988). Fixed points in fuzzy metric spaces. Fuzzy Sets and Systems, 27, 385–389.
17.
GregoriV.RomagueraS.VeeramaniP. (2006). A note on intuitionistic fuzzy metric spaces. Chaos, Solitons & Fractals, 28(4), 902–905.
18.
HussainA.Al SulamiH.IshtiaqU. (2022). Some new aspects in the intuitionistic fuzzy and neutrosophic fixed point theory. Journal of Function Spaces, 2022(1), 3138740.
19.
HussainN.AbbasM. (2011). Common fixed point results for two new classes of hybrid pairs in symmetric spaces. Applied Mathematics and Computing, 218, 542–547.
20.
JavedK.NazamM.JahangeerF.ArshadM.DeM.SenL. (2023). A new approach to generalized interpolative proximal contractions in non archimedean fuzzy metric spaces. AIMS Mathematics, 8(2), 2891–2909.
21.
KanwalS.AzamA.ShamiF. A. (2022). On coincidence theorem in intuitionistic fuzzy b-metric spaces with application. Journal of Function Spaces, 2022(1), 5616824.
22.
KattanD.AlzanbaqiA. O.IslamS. (2022). Contraction mappings in intuitionistic fuzzy rectangular extended B-metric spaces. Mathematical Problems in Engineering, 2022(1), 1814291.
23.
KonwarN. (2020). Extension of fixed point results in intuitionistic fuzzy b metric space. Journal of Intelligent & Fuzzy Systems, 39(5), 7831–7841.
ManiG.RamaswamyR.GnanaprakasamA. J.AbdelnabyO. A. A.RadojevicS.RadenovićS. (2022). Solution of integral equation with neutrosophic rectangular triple controlled metric spaces. Symmetry, 14(10), 2074.
26.
NazamM.AttiqueS.HussainA.AlsulamiH. H. (2024). Exploring fixed-point theorems in -Fuzzy metric spaces: A comprehensive study. Axioms, 13(8), 558.
RahmatR. S.NooraniS. M. (2006). Fixed point theorem on intuitionistic fuzzy metric spaces. Iranian Journal of Fuzzy Systems, 3(1), 23–29.
29.
ShoaibA.KhaliqK. (2022). Fixed-point results for generalized contraction in K-sequentially complete ordered dislocated fuzzy quasimetric spaces. Fixed Point Theory and Algorithms for Sciences and Engineering, 2022(1), 27.
30.
TurkogluD.AlacaC. İ.ChoY. J.YildizC. (2006). Common fixed point theorems in intuitionistic fuzzy metric spaces. Journal of Applied Mathematics and Computing, 22, 411–424.
