Prevalent fixed point theorems on MIFM-Spaces using the (\(CLR_{SR}\)) property and implicit function
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Authors
P. K. Sharma
- Department of Mathematics, SVIS, Shri Vaishnav Vidyapeeth Vishwavidyalaya, Indore-453111, MP, India.
Sh. Sharma
- Department of Mathematics , Govt. P. G. College, Guna-473001, MP, India.
Abstract
The main goal of this study is to use an implicit function to demonstrate the existence of a common fixed point on modified intuitionistic fuzzy metric spaces by using the concept of common limit range property with regard to two self-mappings \(S\) and \(R\), i.e., (\(CLR_{SR}\)) property. Our primary result is supported by an example that validates the hypotheses of our result. Our findings improve and generalize the findings of Tanveer et al. [M. Tanveer, M. Imdad, D. Gopal, D. K. Patel, Fixed Point Theory Appl., \(\bf 2012\) (2012), 1--12], and other existing results related to this study.
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ISRP Style
P. K. Sharma, Sh. Sharma, Prevalent fixed point theorems on MIFM-Spaces using the (\(CLR_{SR}\)) property and implicit function, Journal of Mathematics and Computer Science, 25 (2022), no. 4, 341--350
AMA Style
Sharma P. K., Sharma Sh., Prevalent fixed point theorems on MIFM-Spaces using the (\(CLR_{SR}\)) property and implicit function. J Math Comput SCI-JM. (2022); 25(4):341--350
Chicago/Turabian Style
Sharma, P. K., Sharma, Sh.. "Prevalent fixed point theorems on MIFM-Spaces using the (\(CLR_{SR}\)) property and implicit function." Journal of Mathematics and Computer Science, 25, no. 4 (2022): 341--350
Keywords
- Common fixed point
- common property (E-A)
- common limit in range property (CLR property)
- implicit function
MSC
References
-
[1]
M. Aamri, D. El Moutawakil, Some new common fixed point theorems under strict contractive conditions, J. Math. Anal. Appl., 270 (2002), 181--188
-
[2]
H. M. Abu-Donia, A. A. Nasef, Common fixed point theorems in intuitionistic fuzzy metric spaces, Fuzzy Syst. Math., 22 (2008), 100-106
-
[3]
C. Alaca, D. Turkoglu, C. Yildiz, Fixed points in intuitionistic fuzzy metric spaces, Chaos Solitons Fractals, 29 (2006), 1073--1078
-
[4]
K. T. Atanassov, Intuitionistic fuzzy sets, Fuzzy Sets and Systems, 20 (1986), 87--96
-
[5]
G. V. R. Babu, P. Subhashini, Coupled common fixed point theorems of Cir´ic type g-weak contractions with CLRg property, Journal of Nonlinear Analysis and Optimization, 4 (2013), 133--145
-
[6]
L. B. Ciric, S. N. Jesic, J. S. Ume, The existence theorems for fixed and periodic points of nonexpansive mappings in intuitionistic fuzzy metric spaces, Chaos Solitons Fractals, 37 (2008), 781--791
-
[7]
S. Chauhan, M. Imdad, B. Samet, Coincidence and common fixed point theorems in modified intuitionistic fuzzy metric spaces, Math. Comput. Model., 58 (2013), 898--906
-
[8]
S. Chauhan, M. Imdad, C. Vetro, Unified metrical common fixed point theorems in 2-metric spaces via an implicit relation, Journal of Operators, 2013 (2013), 11 pages
-
[9]
S. Chauhan, M. A. Khan, S. Kumar, Unified fixed point theorems in fuzzy metric spaces via common limit range property, J. Inequal. Appl., 2013 (2013), 17 pages
-
[10]
S. Chauhan, M. A. Khan, W. Sintunavarat, Common fixed point theorems in fuzzy metric spaces satisfying φ-contractive condition with common limit range property, Abstract and Applied Analysis, 2013 (2013), 14 pages
-
[11]
S. Chauhan, B. D. Pant, S. Radenovic, Common fixed point theorems for R-weakly commuting mappings with a common limit in the range property, J. Indian Math. Soc., 81 (2014), 13--14
-
[12]
D. Coker, An introduction to intuitionistic fuzzy topological spaces, Fuzzy Sets and Systems, 88 (1997), 81--89
-
[13]
G. Deschrijver, C. Cornelis, E. E. Kerre, On the representation of intuitionistic fuzzy t-norm and t-conorm, IEEE Transactions on Fuzzy Systems, 12 (2004), 45--61
-
[14]
G. Deschrijver, E. E. Kerre, On the relationship between some extensions of fuzzy set theory, Fuzzy Sets and Systems, 133 (2003), 227--235
-
[15]
A. George, P. Veeramani, On some results in fuzzy metric spaces, Fuzzy Sets and Systems, 64 (1994), 395--399
-
[16]
V. Gregori, S. Romaguera, P. Veeramani, A note on intuitionistic fuzzy metric spaces, Chaos Solitons Fractals, 28 (2006), 902--905
-
[17]
U. Gul, E. Karapınar, On almost contractions in partially ordered metric spaces via implicit relations, J. Inequal. Appl., 2012 (2012), 11 pages
-
[18]
S. Gulyaz, E. Karapınar, I S. Yuce, A coupled coincidence point theorem in partially ordered metric spaces with an implicit relation, Fixed Point Theory Appl., 2013 (2013), 11 pages
-
[19]
V. Gupta, R. K. Saini, A. Kanwar, Some coupled fixed point results on modified intuitionistic fuzzy metric spaces and application to integral type contraction, Iran. J. Fuzzy Syst., 14 (2017), 123--137
-
[20]
X. Huang, C. Zhu, X. Wen, Common fixed point theorems for families of compatible mappings in intuitionistic fuzzy metric spaces, Ann. Univ. Ferrara Sez. VII Sci. Mat., 56 (2010), 305--326
-
[21]
N. M. Hung, E. Karapınar, N. V. Luong, Coupled coincidence point theorem in partially ordered metric spaces via implicit relation, Abstr. Appl. Anal., 2012 (2012), 14 pages
-
[22]
M. Imdad, J. Ali, M. Hasan, Common fixed point theorems in modified intuitionistic fuzzy metric spaces, Iran. J. Fuzzy Syst., 9 (2012), 77--92
-
[23]
M. Imdad, J. Ali, M. Tanveer, Coincidence and common fixed point theorems for nonlinear contractions in Menger PM spaces, Chaos Solitons Fractals, (),
-
[24]
M. Imdad, S. Chauhan, Employing common limit range property to prove unified metrical common fixed point theorems, Int. J. Anal.,, 2013 (2013), 10 pages
-
[25]
M. Imdad, B. D. Pant, S. Chauhan, Fixed point theorems in Menger spaces using the (CLRST) property and applications, J. Nonlinear Anal. Optim., 3 (2012), 225--237
-
[26]
S. Jain, S. Jain, L. Bahadur Jain, Compatibility of type (P) in modified intuitionistic fuzzy metric space, J. Nonlinear Sci. Appl., 3 (2010), 96--109
-
[27]
M. Jain, K. Tas, S. Kumar, N. Gupta, Coupled fixed point theorems for a pair of weakly compatible maps along with CLRg property in fuzzy metric spaces, J. Appl. Math., 2012 (2012), 13 pages
-
[28]
G. Jungck, Compatible mappings and common fixed points, Internat. J. Math. Math. Sci., 9 (1986),
-
[29]
G. Jungck, B. E. Rhoades, Fixed points for set-valued functions without continuity, Indian J. Pure Appl. Math., 29 (1998), 227--238
-
[30]
M. Kumar, P. Kumar, S. Kumar, Some common fixed point theorems using (CLRg) property in cone metric spaces, Adv. Fixed Point Theory, 2 (2012), 340--356
-
[31]
Y. Liu, J. Wu, Z. Li, Common fixed points of single-valued and multivalued maps, Int. J. Math. Math. Sci., 19 (2005), 3045--3055
-
[32]
T. K. Mondal, S. K. Samanta, On intuitionistic gradation of openness, Fuzzy Sets and Systems, 131 (2002), 323--336
-
[33]
R. P. Pant, Common fixed point theorems for contractive maps, J. Math. Anal. Appl., 226 (1998), 251--258
-
[34]
B. D. Pant, S. Kumar, S. Chauhan, Common fixed point of weakly compatible maps on intuitionistic fuzzy metric spaces, J. Adv. Stud. Topol., 1 (2010), 41--49
-
[35]
J. H. Park, Intuitionistic fuzzy metric spaces, Chaos Solitons Fractals, 22 (2004), 1039--1046
-
[36]
R. Saadati, S. Sedghi, N. Shobe, Modified intuitionistic fuzzy metric spaces and some fixed point theorems, Chaos Solitons Fractals, 38 (2008), 36--47
-
[37]
S. Sedghi, N. Shobe, A. Aliouche, Common fixed point theorems in intuitionistic fuzzy metric spaces through conditions of integral type, Appl. Math. Inf. Sci., 2 (2008), 61--82
-
[38]
P. K. Sharma, Some common fixed point theorems for a sequence of self mappings in fuzzy metric space with property (CLRg), J. Math. Comput. Sci., 10 (2020), 1499--1509
-
[39]
S. Sharma, B. Deshpande, Common fixed point theorems for a finite number of mappings without continuity and compatibility on intuitionistic fuzzy metric spaces, Chaos Solitons Fractals, 40 (2009), 2242--2256
-
[40]
W. Shatanawi, V. Gupta, A. Kanwar, New results on modified intuitionistic generalized fuzzy metric spaces by employing E.A property and common E.A property for coupled maps, Journal of Intelligent and Fuzzy Systems, 38 (2020), 3003--3010
-
[41]
W. Sintunavarat, S. Chauhan, P. Kumam, Some fixed point results in modified intuitionistic fuzzy metric spaces, Afr. Mat., 25 (2014), 461--473
-
[42]
W. Sintunavarat, P. Kumam, Common fixed point theorems for a pair of weakly compatible mappings in fuzzy metric spaces, J. Appl. Math., 2011 (2011), 14 pages
-
[43]
W. Sintunavarat, P. Kumam, Fixed point theorems for a generalized intuitionistic fuzzy contraction in intuitionistic fuzzy metric spaces, Thai J. Math., 10 (2012), 123--135
-
[44]
W. Sintunavarat, P. Kumam, Common fixed points for R-weakly commuting in fuzzy metric spaces, Ann. Univ. Ferrara Sez. VII Sci. Mat., 58 (2012), 389--406
-
[45]
M. Tanveer, M. Imdad, D. Gopal, D. K. Patel, Common fixed point theorems in modified intuitionistic fuzzy metric spaces with common property (E.A.), Fixed Point Theory Appl., 2012 (2012), 1--12
-
[46]
R. K. Verma, H. K. Pathak, Common fixed point theorems using property (E.A) in complex-valued metric spaces, Thai J. Math., 11 (2013), 347--355
-
[47]
L. A. Zadeh, Fuzzy sets, Inform. Control, 8 (1965), 338--353