Common fixed point theorems in intuitionistic menger spaces using CLR property
Downloads
DOI:
https://doi.org/10.26637/mjm304/001Abstract
We use the notion of CLR property to prove some common fixed point theorems for weakly compatible mappings in intuitionistic Menger spaces. Our theorems generalize and improve theorems of [5], [6], [7], [8], [10], [20] and [28].
Keywords:
Common fixed point, intuitionistic Menger space, weakly compatible mappings, CLR property, JCLR propertyMathematics Subject Classification:
47H10, 54H25- Pages: 368-381
- Date Published: 01-10-2015
- Vol. 3 No. 04 (2015): Malaya Journal of Matematik (MJM)
M. Aamri and D. El Moutawakil, some new common fixed point theorems under strict contractive conditions, J. Math. Anal. Appl., 270 (2002), 181-188 . DOI: https://doi.org/10.1016/S0022-247X(02)00059-8
K. Atanassov, Intuitionistic fuzzy sets. In: Sgurev, editor. VII ITKR's Session, Sofia June, 1983 (Central Sci. and Techn. Library, Bulg. Academy of Sciences, 1984).
K. Atanassov, Intuitionistic fuzzy sets, Fuzzy Sets and Syst., 20 (1986), 87-96. DOI: https://doi.org/10.1016/S0165-0114(86)80034-3
S. Chauhan, W. Sintunavarat and P. Kumam, Common fixed point theorems for weakly compatible mappings in fuzzy metric spaces using (JCLR) property, Appl. Math., 3 (2012), 976-982. DOI: https://doi.org/10.4236/am.2012.39145
S. Chauhan, M. A. Khan and W. Sintunavarat, Common Fixed Point Theorems in Fuzzy Metric Spaces Satisfying $phi$-Contractive Condition with Common Limit Range Property, Abstract Appl. Anal., Volume 2013, Article ID 735217, 14 pages. DOI: https://doi.org/10.1155/2013/735217
S. Chauhan, S. Bhatnagar and S. Radenović, Common fixed point theorems for weakly compatible mappings in fuzzy metric spaces, Le Matematiche, Vol. LXVIII (2013) - Fasc. I, pp. 87-98. DOI: https://doi.org/10.1186/1687-1812-2013-220
S. Chauhan, S. Dalal, W. Sintunavarat and J. Vujakovic, Common property (E.A) and existence of fixed points in Menger spaces, J. Inequal. Appl., 2014, Article No. 56. DOI: https://doi.org/10.1186/1029-242X-2014-56
J. -X. Fang and Y. Gao, Common fixed point theorems under strict contractive conditions in Menger spaces, Nonlinear Anal., 70 (2009), 184-193. DOI: https://doi.org/10.1016/j.na.2007.11.045
A. George and P. Veeramani, On some results in fuzzy metric spaces, Fuzzy sets and syst., 64 (1994), 395-399. DOI: https://doi.org/10.1016/0165-0114(94)90162-7
J. Ali, M. Imdad, D. Mihet and M. Tanveer, Common fixed points of strict contractions in Menger spaces, Acta Math. Hung., 132 (4) (2011), 367-386. DOI: https://doi.org/10.1007/s10474-011-0105-3
M. Imdad, J. Ali and M. Tanveer, Coincidence and common fixed point theorems for nonlinear contractions in Menger PM spaces, Chaos Solitons & Fractals 42 (5) (2009) 3121-3129. DOI: https://doi.org/10.1016/j.chaos.2009.04.017
M. Imdad, B. D. Pant and S. Chauhan, Fixed point theorems in Menger spaces using the CLR $_{S T}$ property and applications, J. Nonlinear Anal. Optim., 3 (2) (2012), 225-237.
G. Jungck, Compatible mappings and common fixed points, Inter. J. Math. & Math. Sci., 9 (1986), 771-773. DOI: https://doi.org/10.1155/S0161171286000935
G. Jungck, Common fixed points for non continuous non self-maps on non metric spaces, Far East J. Math. Sci., $4(1996), 199-215$.
O. Kramosil and J. Michalek, Fuzzy metric and statistical spaces, Kybernetica, 11 (1975), $326-334$.
I. Kubiaczyk and S. Sharma, Some common fixed point theorems in Menger space under strict contractive conditions, Southeast Asian Bull. Math., 32 (2008), 117-124.
S. Kutukcu A. Tuna and A. T. Yakut, Generalized contraction mapping principle in intuitionistic Menger spaces and application to differential equations, Appl. Math. & Mech., 28 (6) (2007), 799-809. DOI: https://doi.org/10.1007/s10483-007-0610-z
Y. Liu, J. Wu and Z. Li, Common fixed points of single-valued and multi-valued maps, Internat. J. Math. Math. Sci., 19 (2005), 3045-3055. DOI: https://doi.org/10.1155/IJMMS.2005.3045
R. Lowen, Fuzzy set theory, Dordrecht: Kluwer Academic Publishers, 1996. DOI: https://doi.org/10.1007/978-94-015-8741-9
S. Manro and C. Vetro, Common fixed point theorems in fuzzy metric spaces employing CLR C and JCLR $_{S T}$ properties, Facta Universitatis (NIŜ), Ser. Math. Inform., 29 (1) (2014), 77-90
K. Menger, Statistical metrics, Proc. Nat. acad. Sci. U.S.A, 28 (1942), 535-537. DOI: https://doi.org/10.1073/pnas.28.12.535
S. N. Mishra, Common fixed points of compatible mappings in probabilistic metric spaces, Math. Japon, $36(1991), 283-289$
B. D. Pant, S. Chauhan and V. Pant, Comon fixed point theorems in intuitionistic Menger spaces, J. Advan. Stud. Topology, 1 (2010), 54-62. DOI: https://doi.org/10.20454/jast.2010.206
J. H. Park, Intuitionistic fuzzy metric spaces, Chaos, Solitions & Fractals, 22 (2004), 1039-1046. DOI: https://doi.org/10.1016/j.chaos.2004.02.051
K. P. R. Sastry and I. S. R. Krishna Murthy, Common fixed points of two partially commuting tangential self-maps on a metric Space, J. Math. Anal. Appl., 250 (2000) 731-734. DOI: https://doi.org/10.1006/jmaa.2000.7082
B. Schweizer and A. Sklar, Statistical metric spaces. Pacific J. Math., 10 (1960), 313–334. DOI: https://doi.org/10.2140/pjm.1960.10.313
B. Schweizer and A. Sklar, Probabilistic metric spaces. Elsevier, North-Holland, New York, 1983.
S. Sedghi, N. Shobe and A. Aliouche, A common fixed point theorem for weakly compatible mappings in fuzzy metric spaces. Gen. Math., 18 (3) (2010), 3-12.
V. M. Sehgal and A. T. Bharucha-Reid, Fixed points of contraction mappings in PM-spaces, Math. System Theory, $6(1972), 97-102$. DOI: https://doi.org/10.1007/BF01706080
B. Singh and S. Jain, A fixed point theorem in Menger space through weak compatibility, J. Math. Anal. Appl. $301(2005)$, 439-448. DOI: https://doi.org/10.1016/j.jmaa.2004.07.036
W. Sintunavarat and P. Kumam, Common fixed point theorems for a pair of weakly compatible mappings in Fuzzy Metric Spaces, J. Appl. Math., Vol. 2011, Article ID 637958, pp. 14, DOI: 10.1155/2011/637958. DOI: https://doi.org/10.1155/2011/637958
L. A. Zadeh, Fuzzy sets, Inform. Control, 8 (1965), 338-353. DOI: https://doi.org/10.1016/S0019-9958(65)90241-X
- NA
Similar Articles
- Ilknur Yesilce, Gabil Adilov, Hermite-Hadamard inequalities for L(j)-convex functions and S(j)-convex functions , Malaya Journal of Matematik: Vol. 3 No. 03 (2015): Malaya Journal of Matematik (MJM)
- Sercan Turhan, ˙Imdat ˙Is¸can, Mehmet Kunt, Improvement of conformable fractional Hermite-Hadamard type inequality for convex functions and some new conformable fractional midpoint type inequalities , Malaya Journal of Matematik: Vol. 8 No. 03 (2020): Malaya Journal of Matematik (MJM)
- Sümeyye ERMEYDAN, Hüseyin YILDIRIM, Riemann-Liouville fractional Hermite-Hadamard inequalities for differentiable \(\lambda\phi\)-preinvex functions , Malaya Journal of Matematik: Vol. 4 No. 03 (2016): Malaya Journal of Matematik (MJM)
- Abdullah AKKURT, Hüseyin YILDIRIM , Hermite-Hadamard type inequalities for \(\left(n, m, h_1, h_2, \varphi\right)\)-convex functions via fractional integrals , Malaya Journal of Matematik: Vol. 4 No. 02 (2016): Malaya Journal of Matematik (MJM)
- Shahid Qaisar, Sabir Hussain, Generalization of integral inequalities of the type of Hermite-Hadamard through invexity , Malaya Journal of Matematik: Vol. 3 No. 01 (2015): Malaya Journal of Matematik (MJM)
- Badreddine Meftah, Fractional Hermite-Hadamard type inequalities for co-ordinated convex functions , Malaya Journal of Matematik: Vol. 12 No. 04 (2024): Malaya Journal of Matematik (MJM)
- Erhan SET, İmdat İşcan, Seda Paça, Hermite Hadamard-Fejer type inequalities for quasi convex functions via fractional integrals , Malaya Journal of Matematik: Vol. 3 No. 03 (2015): Malaya Journal of Matematik (MJM)
- Mehmet Zeki SARIKAYA, Hakan Bozkurt , Mehmet Eyüp KIRIS, On Hermite-Hadamard type integral inequalities for functions whose second derivative are nonconvex , Malaya Journal of Matematik: Vol. 2 No. 03 (2014): Malaya Journal of Matematik (MJM)
You may also start an advanced similarity search for this article.
Metrics
Published
How to Cite
Issue
Section
License
Copyright (c) 2015 MJM

This work is licensed under a Creative Commons Attribution 4.0 International License.