Fixed point theorems for controlled neutrosophic metric-like spaces

Fahim Uddin; Umar Ishtiaq; Naeem Saleem; Khaleel Ahmad; Fahd Jarad; Fahim Uddin; Umar Ishtiaq; Naeem Saleem; Khaleel Ahmad; Fahd Jarad

doi:10.3934/math.20221135

AIMS Mathematics

2022, Volume 7, Issue 12: 20711-20739. doi: 10.3934/math.20221135

Previous Article Next Article

Research article

Fixed point theorems for controlled neutrosophic metric-like spaces

1.
Abdus Salam School of Mathematical Sciences, Government College University, Lahore, Pakistan
2.
Office of Research, Innovation and Commercialization, University of Management and Technology, Lahore, Pakistan
3.
Department of Mathematics, University of Management and Technology, Lahore, Pakistan
4.
Department of Mathematics and Statistics, International Islamic University Islamabad, Islamabad, Pakistan
5.
Department of Mathematics, Cankaya University, 06790 Etimesgut, Ankara, Turkey
6.
Department of Medical Research, China Medical University Hospital, China Medical University, Taichung, Taiwan

Received: 03 August 2022 Revised: 08 September 2022 Accepted: 14 September 2022 Published: 26 September 2022
MSC : 47H10, 54H25

In this paper, we establish the concept of controlled neutrosophic metric-like spaces as a generalization of neutrosophic metric spaces and provide several non-trivial examples to show the spuriousness of the new concept in the existing literature. Furthermore, we prove several fixed point results for contraction mappings and provide the examples with their graphs to show the validity of the results. At the end of the manuscript, we establish an application to integral equations, in which we use the main result to find the solution of the integral equation.
- fixed point,
- controlled metric space,
- metric-like space,
- controlled neutrosophic metric-like space,
- integral equations,
- unique solution
Citation: Fahim Uddin, Umar Ishtiaq, Naeem Saleem, Khaleel Ahmad, Fahd Jarad. Fixed point theorems for controlled neutrosophic metric-like spaces[J]. AIMS Mathematics, 2022, 7(12): 20711-20739. doi: 10.3934/math.20221135

Related Papers:

Abstract

In this paper, we establish the concept of controlled neutrosophic metric-like spaces as a generalization of neutrosophic metric spaces and provide several non-trivial examples to show the spuriousness of the new concept in the existing literature. Furthermore, we prove several fixed point results for contraction mappings and provide the examples with their graphs to show the validity of the results. At the end of the manuscript, we establish an application to integral equations, in which we use the main result to find the solution of the integral equation.

References

[1]	L. A. Zadeh, Fuzzy sets, Inform. Control, 8 (1965), 338–353. https://doi.org/10.1016/S0019-9958(65)90241-X doi: 10.1016/S0019-9958(65)90241-X
[2]	D. Dey, M. Saha, An extension of banach fixed point theorem in fuzzy metric space, Bol. Soc. Paran. Mat., 32 (2014), 299–304. https://doi.org/10.5269/bspm.v32i1.17260 doi: 10.5269/bspm.v32i1.17260
[3]	S. Nadaban, Fuzzy b-metric spaces, Int. J. Comput. Commun. Control, 11 (2016), 273–281. https://doi.org/10.15837/ijccc.2016.2.2443 doi: 10.15837/ijccc.2016.2.2443
[4]	B. Schweizer, A. Sklar, Statistical metric spaces, Pacific. J. Math., 10 (1960), 314–334. https://doi.org/10.2140/PJM.1960.10.313 doi: 10.2140/PJM.1960.10.313
[5]	V. Gregory, A. Sapena, On fixed point theorems in fuzzy metric spaces, Fuzzy Set. Syst., 125 (2002), 245–253. https://doi.org/10.1016/S0165-0114(00)00088-9 doi: 10.1016/S0165-0114(00)00088-9
[6]	I. Kramosil, J. Michlek, Fuzzy metric and statistical metric spaces, Kybernetika, 11 (1975), 336–344.
[7]	A. George, P. Veeramani, On some results in fuzzy metric spaces, Fuzzy Set. Syst., 64 (1994), 395–399. https://doi.org/10.1016/0165-0114(94)90162-7 doi: 10.1016/0165-0114(94)90162-7
[8]	M. Grabiec, Fixed points in fuzzy metric spaces, Fuzzy Set. Syst., 27 (1988), 385–389. https://doi.org/10.1016/0165-0114(88)90064-4 doi: 10.1016/0165-0114(88)90064-4
[9]	F. Mehmood, R. Ali, C. Ionescu, T. Kamran, Extended fuzzy b-metric spaces, J. Math. Anal., 8 (2017), 124–131.
[10]	A. Harandi, Metric-like paces, partial metric spaces and fixed point, Fixed Point Theory Appl., 2012 (2012), 204. https://doi.org/10.1186/1687-1812-2012-204 doi: 10.1186/1687-1812-2012-204
[11]	N. Mlaiki, H. Aydi, N. Souayah, T. Abdeljawad, Controlled metric type spaces and the related contraction principle, Mathematics, 6 (2018), 194. http://dx.doi.org/10.3390/math6100194 doi: 10.3390/math6100194
[12]	N. Mlaiki, N. Souayah, T. Abdeljawad, H. Aydi, A new extension to the controlled metric type spaces endowed with a graph, Adv. Differ. Equ-Ny., 2021 (2021). https://doi.org/10.1186/s13662-021-03252-9 doi: 10.1186/s13662-021-03252-9
[13]	M. S. Sezen, Controlled fuzzy metric spaces and some related fixed point results, Numer. Meth. Part. D. E., 37 (2021), 583–593. https://doi.org/10.1002/num.22541 doi: 10.1002/num.22541
[14]	S. Shukla, M. Abbas, Fixed point results in fuzzy metric-like spaces, Iran. J. Fuzzy Syst., 11 (2014), 81–92. https://doi.org/10.22111/IJFS.2014.1724 doi: 10.22111/IJFS.2014.1724
[15]	K. Javed, F. Uddin, H. Aydi, M. Arshad, U. Ishtiaq, H. Alsamir, On Fuzzy b-Metric-Like Spaces, J. Funct. Spaces., 2021 (2021), 6615976. https://doi.org/10.1155/2021/6615976 doi: 10.1155/2021/6615976
[16]	J. H. Park, Intuitionistic fuzzy metric spaces, Chaos Soliton. Fract., 22 (2004), 1039–1046. https://doi.org/10.1016/j.chaos.2004.02.051 doi: 10.1016/j.chaos.2004.02.051
[17]	F. Smarandache, Neutrosophy: Neutrosophic probability, set and logic, Rehoboth: American Research Press, 1998. https://doi.org/10.5281/ZENODO.57726
[18]	K. T. Atanassov, Intuitionistic fuzzy sets, Fuzzy Set. Syst., 20 (1986), 87–96. https://doi.org/10.1016/S0165-0114(86)80034-3 doi: 10.1016/S0165-0114(86)80034-3
[19]	M. Şahin, O. Ecemiş, V. Uluçay, A. Kargın, Some new generalized aggregation operators based on centroid single valued triangular neutrosophic numbers and their applications in multi-attribute decision making, Asian J. Math. Comput. Res., 16 (2017), 63–84.
[20]	M. Şahin, A. Kargın, A. Dayan, A. Kılıç, Neutrosophic triplet m-metric space, In: Quadruple neutrosophic theory and applications, 2020,213–223.
[21]	M. Şahin, A. Kargın, Neutrosophic triplet metric topology, Neutrosophic Sets. Sy., 27 (2019), 154–162. https://doi.org/10.5281/zenodo.3275557 doi: 10.5281/zenodo.3275557
[22]	A. Rezaei, F. Smarandache, The neutrosophic triplet of BI-algebras, Neutrosophic Sets. Sy., 33 (2020), 313–321. https://doi.org/10.5281/zenodo.3808944 doi: 10.5281/zenodo.3808944
[23]	C. Aslan, A. Kargın, M. Şahin, Neutrosophic modeling of talcott parsons's action and decision-making applications for it, Symmetry, 12 (2020), 1166. https://doi.org/1166.10.3390/SYM12071166
[24]	A. Kargın, A. Dayan, M. Şahin, Generalized hamming similarity measure based on neutrosophic quadruple numbers and its applications to law sciences, Neutrosophic Sets. Sy., 40 (2021), 45–67. https://doi.org/10.5281/zenodo.4549328 doi: 10.5281/zenodo.4549328
[25]	S. Şahin, A. Kargın, M. Yücel, Hausdorff measures on generalized set valued neutrosophic quadruple numbers and decision making applications for adequacy of online education, Neutrosophic Sets. Sy., 40 (2021), 86–116. https://doi.org/10.5281/zenodo.4549332 doi: 10.5281/zenodo.4549332
[26]	M. Şahin, A. Kargın, M. S. Uz, Neutrosophic triplet partial bipolar metric spaces, Neutrosophic Sets. Sy., 33 (2020), 297–312. https://doi.org/10.5281/zenodo.3808896 doi: 10.5281/zenodo.3808896
[27]	W. F. Al-Omeri, S. Jafari, F. Smarandache, (ϕ, ψ)-Weak contractions in neutrosophic cone metric spaces via fixed point theorems, Math. Probl. Eng., 2020 (2020), 9216805. https://doi.org/10.1155/2020/9216805 doi: 10.1155/2020/9216805
[28]	M. Şahin, A. Kargın, Neutrosophic triplet normed space, Open Phys., 15 (2017), 697–704. https://doi.org/10.1515/phys-2017-0082 doi: 10.1515/phys-2017-0082
[29]	M. Kirişci, N. Simsek, Neutrosophic metric spaces, Math. Sci., 14 (2020), 241–248. https://doi.org/10.1007/s40096-020-00335-8 doi: 10.1007/s40096-020-00335-8
[30]	M. Şahin, A. Kargın, Neutrosophic triplet v-generalized metric space, Axioms, 7 (2018), 67. https://doi.org/10.3390/axioms7030067 doi: 10.3390/axioms7030067
[31]	M. Şahin, A. Kargın, M. S. Uz, A. Kılıç, Neutrosophic triplet bipolar metric space, In: Quadruple neutrosophic theory and applications, 2020,150–164.
[32]	N. Simsek, M. Kirişci, Fixed point theorems in neutrosophic metric spaces, Sigma J. Eng. Nat. Sci., 10 (2019), 221–230. https://doi.org/10.1007/s40096-020-00335-8 doi: 10.1007/s40096-020-00335-8
[33]	M. Şahin, A. Kargın, Neutrosophic triplet b–metric space, In: Neutrosophic triplet structures, 2019, 79–90.
[34]	S. Sowndrarajan, M. Jeyarama, F. Smarandache, Fixed point results for contraction theorems in neutrosophic metric spaces, Neutrosophic Sets. Sy., 36 (2020), 308–318. https://doi.org/10.5281/zenodo.4065458 doi: 10.5281/zenodo.4065458
[35]	N. Saleem, S. Furqan, F. Jarad, On extended-rectangular and controlled rectangular fuzzy metric-like spaces with application, J. Funct. Space., 2022 (2022), 5614158. https://doi.org/10.1155/2022/5614158 doi: 10.1155/2022/5614158
[36]	N. Saleem, K. Javed, F. Uddin, U. Ishtiaq, K. Ahmed, T. Abdeljawad, et al., Unique solution of integral equations via intuitionistic extended fuzzy b-metric-like spaces, Comp. Model. Eng. Sci., 2022. https://doi.org/10.32604/cmes.2022.021031 doi: 10.32604/cmes.2022.021031
[37]	N. Saleem, U. Ishtiaq, L. Guran, M. F. Bota, On graphical fuzzy metric spaces with application to fractional differential equations, Fractal. Fract, 6 (2022), 238. https://doi.org/10.3390/fractalfract6050238 doi: 10.3390/fractalfract6050238
[38]	M. M. A. Khater, Diverse solitary and jacobian solutions in a continually laminated fluid with respect to shear flows through the ostrovsky equation, Mod. Phys. Lett. B., 35 (2021), 2150220. https://doi.org/10.1142/S0217984921502201 doi: 10.1142/S0217984921502201
[39]	M. M. A. Khater, Numerical simulations of zakharov's (ZK) non-dimensional equation arising in langmuir and ion-acoustic waves, Mod. Phys. Lett. B., 35 (2021), 2150480. https://doi.org/10.1142/S0217984921504807 doi: 10.1142/S0217984921504807

Reader Comments

Your name:*

Email:*
© 2022 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)