×

zbMATH — the first resource for mathematics

Fixed point and (DS)-weak commutativity condition in intuitionistic fuzzy metric spaces. (English) Zbl 1198.54009
Summary: The aim of this paper is to show that a common fixed point theorem can be proved for nonlinear contractive condition in intuitionistic fuzzy metric spaces without assuming continuity of any mappings. To prove the result we use new commutativity condition for mappings weaker than compatibility of mappings.
Editorial remark: There are doubts about a proper peer-reviewing procedure of this journal. The editor-in-chief has retired, but, according to a statement of the publisher, articles accepted under his guidance are published without additional control.

MSC:
54A40 Fuzzy topology
54H25 Fixed-point and coincidence theorems (topological aspects)
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Alaca, C.; Turkoglu, D.; Yildiz, C., Fixed points in intuitionistic fuzzy metric spaces, Chaos, solitons and fractals, 29, 1073-1078, (2006) · Zbl 1142.54362
[2] Atanassov, K., Intuitionistic fuzzy sets, Fuzzy sets syst, 20, 87-96, (1986) · Zbl 0631.03040
[3] Banach S. Theoriles operations. Linearies Manograie Mathematyezne, Warsaw, Poland.
[4] Boyd, D.W.; Wong, J.S.W., On nonlinear contractions, Proc am math soc, 20, 458-464, (1969) · Zbl 0175.44903
[5] Dubois D, Prade H. Fuzzy sets: theory and applications to policy analysis and informations systems. New York: Plenum Press; 1980. · Zbl 0444.94049
[6] Edelstein, M., On fixed and periodic points under contractive mappings, J lond math soc, 37, 74-79, (1962) · Zbl 0113.16503
[7] El Naschie, M.S., On the uncertainty of Cantorian geometry and two-slit experiment, Chaos, solitons and fractals, 9, 517-529, (1998) · Zbl 0935.81009
[8] El Naschie, M.S., On the verification of heterotic strings theory and \(e^{(\infty)}\) theory, Chaos, solitons and fractals, 11, 2397-2408, (2000) · Zbl 1008.81511
[9] El Naschie, M.S., Wild, topology hyperbolic geometry and fusion algebra of high energy particle, Chaos, solitons and fractals, 13, 1935-1945, (2002) · Zbl 1024.81055
[10] El Naschie, M.S., Transfinite electrical networks, sponoral varieties and gravity Q bits, Int J nonlinear sci numer simul, 5, 3, 191-197, (2004)
[11] El Naschie, M.S., Non Euclidean spacetime structure and the two slit experiment, Chaos, solitons and fractals, 26, 1-6, (2000) · Zbl 1122.81338
[12] El Naschie, M.S., From experimental quantum optics gravity via a fuzzy kahler manifold, Chaos, solitons and fractals, 25, 969-977, (2005) · Zbl 1070.81118
[13] El Naschie, M.S., The two slit experiment as the foundation of E-infinity of high energy physics, Chaos, solitons and fractals, 25, 509-514, (2005) · Zbl 1069.81069
[14] El Naschie, M.S., ‘thooft ultimate building blocks and space – time an infinite dimensional set of transfinite discrete points, Chaos, solitons and fractals, 25, 521-524, (2005) · Zbl 1077.53509
[15] George, A.; Veeramani, P., On some results in fuzzy metric spaces, Fuzzy sets syst, 64, 395-399, (1994) · Zbl 0843.54014
[16] Grabiec, M., Fixed points in fuzzy metric spaces, Fuzzy sets syst, 27, 385-389, (1988) · Zbl 0664.54032
[17] Gregory, V.; Romaguera, S.; Veeramani, P., A note on intuitionistic fuzzy metric spaces, Chaos, solitons and fractals, 28, 902-905, (2006) · Zbl 1096.54003
[18] Hadzic O. Fixed point theory in probabilistic metric spaces, Novi Sad: Serbian Academy of Science and Arts; 1995.
[19] Hadzic O. Fixed point theory in topological vector space, Novi Sad: University of Novi Sad, Institute of Mathematics; 1984. · Zbl 0576.47030
[20] Jesic, S.N.; Babacev, N.A., Common fixed point theorems in intuitionistic fuzzy metric spaces and £-fuzzy metric spaces with nonlinear contractive condition, Chaos, solitons and fractals, 37, 675-687, (2008) · Zbl 1137.54328
[21] Jungck, G., Compatible mappings and common fixed points, Int J math math sci, 9, 771-779, (1986) · Zbl 0613.54029
[22] Klement, E.P., Operations on fuzzy sets an axiomatic approach, Inform sci, 27, 221-232, (1984) · Zbl 0515.03036
[23] Klement, E.P.; Mesiar, R.; Pap, E., Triangular norm: trends in logic 8, (2000), Kluwer Academic Publishers Dordrecht
[24] Kramosil, O.; Michalek, J., Fuzzy metric and statistical metric spaces, Kybernetica, 11, 326-334, (1975)
[25] Rodriguez-Lopez, J.; Ramagurea, S., The Hausdorff fuzzy metric on compact sets, Fuzzy set syst, 147, 273-283, (2004) · Zbl 1069.54009
[26] Lowen, R., Fuzzy set theory, (1996), Kluwer Academic Publishers Dordrecht
[27] Menger, K., Statistical metric, Proc natl acad sci USA, 28, 535-537, (1942) · Zbl 0063.03886
[28] Mishra, S.N.; Sharma, N.; Singh, S.L., Common fixed points of maps on fuzzy metric spaces, Int J math math sci, 17, 253-288, (1994) · Zbl 0798.54014
[29] Pant, R.P., Common fixed points of noncommuting mappings, J math anal appl, 188, 436-440, (1994) · Zbl 0830.54031
[30] Pant, R.P., Common fixed point theorems for contractive maps, J math anal appl, 226, 251-258, (1998) · Zbl 0916.54027
[31] Pant, R.P., Common fixed points of Lipschitz type mappings pair, J math anal appl, 240, 280-283, (1999) · Zbl 0933.54031
[32] Pant, R.P., Discontinuity and fixed points, J math anal appl, 240, 284-289, (1999) · Zbl 0938.54040
[33] Park, J.H., Intuitionistic fuzzy metric spaces, Chaos, solitons and fractals, 22, 1039-1046, (2004) · Zbl 1060.54010
[34] Pathak, H.K.; Cho, Y.J.; Kang, S.M., Remarks on R-weakly commuting mappings and common fixed point theorems, Bull Korean math soc, 34, 247-257, (1997) · Zbl 0878.54032
[35] Sadati, R.; Park, J.H., On the intuitionistic topological spaces, Chaos, solitons and fractals, 27, 331-344, (2006) · Zbl 1083.54514
[36] Schweizer, B.; Sklar, A., Statistical metric spaces, Pacific J math, 10, 314-334, (1960) · Zbl 0091.29801
[37] Sessa, S., On a weak commutativity condition of mappings in fixed point consideration, Publ inst math (beogad), 27, 46, 149-153, (1982) · Zbl 0523.54030
[38] Sharma, S.; Deshpande, B., Common fixed point theorems for non-compatible mappings and meir – keeler type contractive condition in fuzzy metric spaces, Int rev fuzzy math, 1, 2, 147-159, (2006) · Zbl 1191.54044
[39] Sharma, S.; Deshpande, B., Common fixed point theorems for finite number of mappings without continuity and compatibility on intuitionistic fuzzy metric spaces, Chaos, solitons and fractals, 40, 5, 2242-2256, (2007) · Zbl 1198.54089
[40] Sharma, S.; Deshpande, B., Compatible mappings of type (I) and (II) on intuitionistic fuzzy metric spaces in consideration of common fixed point, Commun Korean math soc, 24, 2, 197-214, (2009) · Zbl 1168.54333
[41] Sharma S, Deshpande B. A fixed point theorem in intuitionistic fuzzy metric spaces by using new commutativity condition, submitted for publication. · Zbl 1332.54093
[42] Turkoglu, D.; Alaca, C.; Cho, Y.J.; Yildiz, C., Common fixed point theorems in intuitionistic fuzzy metric spaces, J appl math comput, 22, 1-2, 411-424, (2006) · Zbl 1106.54020
[43] Turkoglu, D.; Alaca, C.; Yildiz, C., Compatible maps and compatible maps of type (\(\alpha\)) and (\(\beta\)) in intuitionistic fuzzy metric spaces, Demonstrat math, 39, 3, 671-684, (2006) · Zbl 1112.54014
[44] Vasuki, R., A common fixed point theorem in fuzzy metric space, Fuzzy sets syst, 97, 395-397, (1998) · Zbl 0926.54005
[45] Yager, R.R., On a class of weak triangular norm operators, Inform sci, 96, 1-2, 47-78, (1997) · Zbl 0916.93040
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.