A study of neutrosophic controlled pentagonal metric space with applications
Abstract views: 167
/ 
PDF downloads: 148
Keywords:
Neutrosophic metric space; neutrosophic controlled pentagonal metric space; fixed point theorem; fractional differential equationAbstract
In this manuscript, we present the concept of neutrosophic controlled pentagonal metric space (NCPMS), and prove some new fixed point results. Furthermore, we established many interesting outcomes for contraction maps. At last, we show the uniqueness and existence results for fractional differential and integral equations to illustrate the validity of the main outcomes.
References
Zadeh, L.A. Fuzzy sets. Inf. Control 1965, 8, 338–353.
Schweizer, B.; Sklar, A. Statistical metric spaces. Pac. J. Math. 1960, 10, 314–334.
Kramosil, I.; Michlek, J. Fuzzy metric and statistical metric spaces. Kybernetika 1975, 11, 336–344.
Grabiec, M. Fixed points in fuzzy metric spaces. Fuzzy Sets Syst. 1988, 27, 385–389.
Rehman, S.U.; Jabeen, S.; Khan, S.U.; Jaradat, M.M.M. Some α–φ-Fuzzy cone contraction results with integral type
application. J. Math. 2021, 2021, 1566348. https://doi.org/10.1155/2021/156634.
Park, J.H. Intuitionistic fuzzy metric spaces. Chaos Solitons Fractals 2004, 22, 1039–1046.
Konwar, N. Extension of fixed results in intuitionistic fuzzy b-metric spaces. J. Intell. Fuzzy Syst. 2020, 39, 7831–7841.
Ishtiaq, U.; Saleem, N.; Uddin, F.; Sessa, S.; Ahmad, K.; di Martino, F. Graphical views of intuitionistic fuzzy double-controlled metric-like spaces and certain fixed-point results with application, Symmetry 2022, 14, 2364. https://doi.
org/10.3390/sym14112364
Saleem, N.; Ishtiaq, U.; Guran, L.; Bota, M.-F. On graphical fuzzy metric spaces with application to fractional differential equations, Fractal Fract. 2022, 6, 238. https://doi.org/10.3390/fractalfract6050238
Saleem, N.; Furqan, S.; Abuasbeh, K.; Awadalla, M. Fuzzy triple controlled metric like spaces with applications,
Mathematics 2023, 11, 1390. https://doi.org/10.3390/math11061390.
Saleem, N.; Furqan, S.; Nabwey, H.A.; George, R. Survivability of AIDS patients via fractional differential equations
with fuzzy rectangular and fuzzy b-rectangular metric like spaces, Symmetry 2022, 14, 2450. https://doi.org/10.3390/
sym14112450.
Saleem, N.; Furqan, S.; Jarad, F. On extended -Rectangular and controlled rectangular fuzzy metric-like
spaces with application, Journal of Function Spaces, vol. 2022, Article ID 5614158, 14 pages, 2022. https://doi.
org/10.1155/2022/5614158.
Furqan, S.; Saleem, N.; Sessa, S. Fuzzy -controlled metric space, Int. J. Anal. Appl., 2023, 21, 101.
Hussain, A.; Ishtiaq, U.; Ahmed, K.; Al-Sulami, H. On pentagonal controlled fuzzy metric spaces with an application
to dynamic market equilibrium, Journal of Function Spaces, vol. 2022, Article ID 5301293, 8 pages, 2022. https://doi.
org/10.1155/2022/5301293.
Kirişci, M.; Simsek, N. Neutrosophic metric spaces. Math. Sci. 2020, 14, 241–248.
Simsek, N.; Kirişci, M. Fixed point theorems in Neutrosophic metric spaces. Sigma J. Eng. Nat. Sci. 2019, 10, 221–230.
Sowndrarajan, S.; Jeyarama, M.; Smarandache, F. Fixed point Results for Contraction Theorems in Neutrosophic
Metric Spaces. Neutrosophic Sets Syst. 2020, 36, 23.
Itoh, S. Random fixed point theorems with an application to random differential equations in Banach spaces. J. Math.
Anal. Appl. 1979, 67, 261–273.
Mlaiki, N. Controlled metric type spaces and the related contraction principle. Mathematics 2018, 6, 194.
Sezen, M.S. Controlled fuzzy metric spaces and some related fixed point results. Numer. Methods Partial Differ. Equ.
, 37, 583–593. https://doi.org/10.1002/num.22541.
Saleem, N.; Isik, H.; Furqan, S.; Park, C. Fuzzy double controlled metric spaces. J. Intell. Fuzzy Syst. 2021, 40,
–9985.
Rafi, M.; Noorani, M.S.M. Fixed theorems on intuitionistic fuzzy metric space. Iran. J. Fuzzy Syst. 2006, 3, 23–29.
Sintunavarat, W.; Kumam, P. Fixed Theorems for a Generalized Intuitionistic Fuzzy Contraction in Intuitionistic
Fuzzy Metric Spaces. Thai J. Math. 2012, 10, 123–135.
Alaca, C.; Turkoglu, D.; Yildiz, C. Fixed points in intuitionistic fuzzy metric spaces. Chaos Solitons Fractals 2006, 29,
–1078.
Javed, K.; Uddin, F.; Aydi, H.; Arshad, M.; Ishtiaq, U.; Alsamir, H. On Fuzzy b-Metric-Like Spaces. J. Funct. Spaces
, 2021, 6615976.
Mohamad, A.; Fixed-point theorems in intuitionistic fuzzy metric spaces. Chaos Solitons Fractals 2007, 34, 1689–1695.
Dey, D.; Saha, M. An extension of Banach fixed point theorem in fuzzy metric space. Bol. Soc. Parana. Mat. 2014, 32,
–304.
Uddin, F.; Ishtiaq, U.; Hussain, A.; Javed, K.; Al Sulami, H.; Ahmed, K. Neutrosophic double controlled metric spaces
and related results with application, Fractal and Fractional. 2022; 6(6):318. https://doi.org/10.3390/fractalfract6060318
Gunaseelan, M.; Rajagopalan, R.; Arul Joseph, G.; Ola, A.A, Slobodan, R. and Stojan, R. Solution of integral equation
with neutrosophic rectangular triple controlled metric spaces, Symmetry 14, 2022, no. 10: 2074. https://doi.org/10.3390/
sym14102074.
Gunaseelan, M.; Arul Joseph, G.; Vidhya, V.; Jarad, F. Solving an integral equation vi an orthogonal neutrosophic
rectangular metric space, AIMS Mathematics, 2023, 8(2): 3791-3825. doi: 10.3934/math.2023189.
Saleem, N.; Ahmad, K.; Ishtiaq, U.; De la Sen, M. Multivalued neutrosophic fractals and Hutchinson-Barnsley operator in neutrosophic metric space, Chaos, Solitons Fractals, Volume 172, 2023, 113607, ISSN 0960-0779, https://doi.
org/10.1016/j.chaos.2023.113607.
Uddin, F.; Ishtiaq, U.; Saleem, N.; Ahmad, K.; Jarad, F. Fixed point theorems for controlled neutrosophic metric-like
spaces, AIMS Mathematics, 2022, 7(12): 20711-20739. doi: 10.3934/math.20221135.
Riaz, M.; Ishtiaq, U,; Park, C.; Ahmad, K.; Uddin, F. Some fixed point results for -chainable neutrosophic and generalized neutrosophic cone metric spaces with application, AIMS Mathematics, 2022, 7(8): 14756-14784. doi: 10.3934/
math.2022811.
Ishtiaq, U.; Ahmad, K.; Imran Asjad, Farhan Ali, M.; Jarad, F. Common fixed point, Baire’s and Cantor’s theorems in
neutrosophic 2-metric spaces, AIMS Mathematics, 2023, 8(2): 2532-2555. doi: 10.3934/math.2023131
Gunaseelan, M.; Poornavel, S.; Mitrović, Z. D.; Aloqaily, A.; Mlaiki, N. Solving some integral and fractional differential
equations via neutrosophic pentagonal metric space. Axioms. 2023; 12(8):758. https://doi.org/10.3390/axioms12080758.
Saleem, N.; Ishtiaq, U.; Ahmad, K.; Sessa, S. and Di Martino, F. Fixed point results in neutrosophic rectangular
extended b-metric spaces. Neutrosophic Systems With Applications, 2023, 9, 48-80. https://doi.org/10.61356/j.
nswa.2023.63.
Ishtiaq, U.; Asif, M.; Hussain, A.; Ahmad, K.; Saleem, I.; Al Sulami, H. Extension of a unique solution in generalized
neutrosophic cone metric spaces, Symmetry 2023, 15, 94. https://doi.org/10.3390/sym15010094.
Downloads
Published
How to Cite
Issue
Section
License
Copyright (c) 2024 Results in Nonlinear Analysis
This work is licensed under a Creative Commons Attribution 4.0 International License.
