Some Fixed Point Theorems in intuitionistic fuzzy metric spaces

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Published: Dec 31, 2011
DOI: https://doi.org/10.5556/j.tkjm.42.2011.683
Keywords:
Intuitionistic fuzzy metric space (S-B) property R-weak commutativity of type (sp) Common fixed point.

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Sushil Sharma
Department of Mathematics, Madhav Science College, Vikram University, Ujjain-456010, India.
Prashant Tilwankar
Department of Mathematics, Shri Vaishnav Institute of Management, Indore-452009, India.

Abstract

The aim of this paper is to prove some common fixed point theorems by using the property ($S$-$B$) and the notion of R-weak commutativity of type $(S_p)$ in intuitionistic fuzzy metric spaces. We first formulate the definition of R-weakly commuting mappings of type $(S_p)$ in intuitionistic fuzzy metric spaces and prove the intuitionistic fuzzy version of Pant's theorem.

Article Details

How to Cite
Sharma, S., & Tilwankar, P. (2011). Some Fixed Point Theorems in intuitionistic fuzzy metric spaces. Tamkang Journal of Mathematics, 42(4), 405–414. https://doi.org/10.5556/j.tkjm.42.2011.683
Issue
Vol. 42 No. 4 (2011)
Section
Papers

References

C. Alaca, D.Turkoglu and C. Yildiz, Fixed points in intuitionistic fuzzy metric spaces, Choas, Solitons & Fractals, 29 (2006),1073--1078.

C. Alaca, I. Altun and D. Turkoglu, On compatible mappings of type (I) and (II) in intuitionistic fuzzy metric spaces, Commun.Korean Math. Soc., 23 (2008), 427--446.

C. Alaca, D. Turkoglu and C. Yildiz, Common fixed points of compatible maps in intuitionistic fuzzy metric spaces, Southeast Asian Bull. Math., 32(2008), 21--33.

M. Aamri and D. EI Moutawakil, Some new common fixed point theorems under strict contractive conditions, J.Math. Anal. Appl.,270 (2002), 181--188.

S. Banach, Theoriles operations Linearies Manograie Mathematyezne, Warsaw, Poland, 1932.

L. Ciric, S. Jesic and J. Ume, The existence theorems for fixed and periodic points of nonexpansive mappings in intuitionistic fuzzy metric spaces, Choas, Solitons & Fractals,37 (2008), 781--791.

M. Edelstein, On fixed and periodic points under contractive mappings, J. London Math. Soc., 37 (1962), 74--79.

M. Grabiec, Fixed points in fuzzy metric spaces, Fuzzy Sets and Systems, 27 (1988), 385--389.

V. Gregory, S. Romaguera and P. Veeramani, A note on intuitionistic fuzzy metric spaces, Chaos, Solitons & Fractals, 28 (2006), 902--905.

S. Jesic, Convex structure, normal structure and a fixed point theorem in intuitionistic fuzzy metric paces, Chaos, Solitons & Fractals, 41 (2009), 292--301.

O. Karmosil and J. Michalek, Fuzzy metric and statistical metric spaces, Kybernetica, 11 (1975), 326--334.

E. P. Klement, R. Mesiar and E. Pap, Triangular Norms, Kluwer Academic Pub. Trends in Logic 8, Dordrecht 2000.

S. Kutukcu, Weak Compatibility and common coincidence points in intuitionistic fuzzy metric spaces, Southeast Asian Bulletin of Mathematics, 32(2008), 1081--1089.

S. Kutukcu, C. Yildiz and D. Turkoglu, Fixed points of contractive mappings in intuitionistic fuzzy metric spaces, J. Comput. Anal. Appl., 9 (2007), 181--193.

K. Menger, Statistical metrices, Proc. Nat. Acad. Sci., 28 (1942), 535--537.

S. N. Mishra, N. Sharma and S. L. Singh, Common fixed points of maps on fuzzy metric spaces, Internat. J. Math. Math. Sci.,17 (1994), 253--258.

J. H. Park, Intuitionistic fuzzy metric spaces, Choas, Solitons & Fractals, 22 (2004), 1039--1046.

R. P. Pant, Common fixed points of contractive maps, J. Math. Anal. Appl., 226 (1998), 251--258.

R. P. Pant, Noncompatible mappings and common fixed points, Soochow J. Math., 26 (2000), 29--35.

R. P. Pant, Common fixed points of noncommuting mappings, J. Math. Anal. Appl., 188 (1994), 436--440.

R. P. Pant, Common fixed points of Lipschitz type mapping Pairs, J. Math. Anal. Appl., 240 (1999), 280--283.

V. Pant, Some fixed point theorems in fuzzy metric space,Tamkang J. Math., 40 (2009), 59--66.

H. K. Pathak, Y. J. Cho and S. M. Kang, Remarks on R-weakly commuting mappings and common fixed point theorems, Bull. Korean Math. Soc., 34 (1997), 247--257.

LDJ Sigalotti and A. Mejias, On El Naschie's conjugate complex time, fractal $E(infty )$ space-time and faster-than-light particles, Int. J. Nonlinear Sci. Number Simul., 7, (2006), 467--472.

R. Saadati, S. Sedghi and N. Shobe, Modified intuitionistic fuzzy metric spaces and some fixed point theorems, Chaos, Solitons & Fractals, 38 (2008), 36--47.

B. Schweizer and A. Sklar, Statistical metric spaces, Pacific Journal Math., 10 (1960), 314--334.

Sushil Sharma and B. Deshpande, Common fixed point theorems for finite number of mappings without continuity and compatibility on intuitionistic fuzzy metric spaces, Choas, Solitons & Fractals,40 (2009), 2242--2256.

Sushil Sharma and B. Deshpande, Compatible mappings of type (I) and (II) on intuitionistic in consideration of common fixed point, Comm. Korean Math. Soc., 24 (2009), 197--214.

Sushil Sharma and B. Deshpande, Discontinuity and weak compatibility in fixed point consideration on non-complete fuzzy metric spaces, J. Fuzzy Math., 11 (2003), 671--686.

Sushil Sharma, S. Kutukcu and A. Pathak, Common fixed point theorems for weakly compatible mappings in intuitionistic fuzzy metric spaces, J. Fuzzy Math., 17(2009), 225--240.

D. Turkoglu, C. Alaca and C. Yildiz, Compatible maps and compatible maps of types $(alpha)$ and $(beta)$ in intuitionistic fuzzy metric spaces, Demonstratio Math., 39 (2006),671--684.

D. Turkoglu, C. Alaca, Y. J. Cho and C. Yildiz, Common fixed point theorems in intuitionistic fuzzy metric spaces, J. Appl. Math. and Computing, 22 (2006), 411--424.

R. Vasuki, Common fixed point for R-weakly commuting maps in fuzzy metric spaces, Indian J. Pure Appl. Math., 30 (1999), 419--423.

R. R. Yager, On a class of weak triangular norm operators, Information Sciences, 96 (1997), 47--78.