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Research Article

Common fixed point theorems in intuitionistic Menger space using property E.A. and an application to Fredholm integral equations

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Pages 2187-2207 | Received 01 Nov 2020, Published online: 04 May 2022

References

  • M., Aamri, D., El Moutawakil, some new common fixed point theorems under strict contractive conditions, J. Math. Anal. Appl., 270, 181–188 (2002). doi: 10.1016/S0022-247X(02)00059-8
  • A., George, P., Veeramani, On some results in fuzzy metric spaces, Fuzzy set. sys., 64, 395–399, 1994. doi: 10.1016/0165-0114(94)90162-7
  • O., Hadzic, E., Pap V., Radu, Generalized contraction mapping principles in probabilistic metric spaces J. Acta. Math. Hungar., 101, 131–148 (2003). doi: 10.1023/B:AMHU.0000003897.39440.d8
  • Hadzic O, Pap E. Fixed point theory in probabilistic metric spaces[M], Dordrecht: Kluwer Acad Pub, 2001.
  • J. H., He, Nonlinear dynamics and the Nobel prize in physics, Inter. J. of Nonl. Sci. Num. Simul. 8(1), 1–4 (2007). doi: 10.1515/IJNSNS.2007.8.1.1
  • A., Jain, V. K., Gupta, R., Bhinde, Fixed points in intutionistic Menger space, Italian J. Pure Appl. Math, 35, 557-568 (2015)
  • G., Jungck, Compatible mappings and common fixed points, Inter. J. Math. & Math. Sci., 9, 771–773, (1986). doi: 10.1155/S0161171286000935
  • G., Jungck, B. E., Rhoades, Fixed points for set valued functions without continuity Indian. J. pure. appl. math., 29, 227–238 (1998).
  • E. P., Klement, R., Mesiar, E., Pap, Triangular norms[M]. Dordrecht: Kluwer Acad Pub Trends in Logic 8, 2000.
  • O., Kramosil, J., Michalek, Fuzzy metric and statistical spaces. Kybernetica, 11, 326–334, (1975).
  • M. A., Krasnoselskii, Topological Methods in the Theory of Nonlinear Integral Equations, Pergamon. Press., New York, (1964)
  • S., Kutukcu, A., Tuna, A. T., Yakut, Generalized contraction mapping principle in intuitionistic menger spaces and application to differential equations, Appl. Math. & Mech., 28,799–809, (2007). doi: 10.1007/s10483-007-0610-z
  • K., Menger, Statistical metric, Proc. Nat. acad. Sci. U.S.A, 28,535–537, (1942). doi: 10.1073/pnas.28.12.535
  • S. N., Mishra, Common fixed points of compatible mappings in probabilistic metric spaces Math. Japon., 36, 283–289 (1991).
  • B. D., Pant, S., Chauhan, V.,Pant, Common fixed point theorems in intuitionistic Menger spaces, Journal of Advanced Studies in Topology, 1(1), 54-62 (2010) doi: 10.20454/jast.2010.206
  • J. H., Park, Intuitionistic fuzzy metric spaces, Chaos. Soli. & Fract., 22, 1039–1046, (2004). doi: 10.1016/j.chaos.2004.02.051
  • Radu V. Some remarks on the probabilistic contractions on fuzzy Menger spaces[J]. Automat Comput Appl Math, 11(1): 125-131 (2002)
  • M. R. S., Rahmat, M. S. M., Noorani, Approximate fixed point theorems in probabilistic normed (metric) spaces, Proc. the2nd. IMT-GT Reg. Conf. Math., Stat. and Appl., Uni. Sains. Malaysia., Penang, June 13–15 (2006)
  • R., Saadati, S. M., Vaezpour, Some results on fuzzy Banach spaces, J. Appl. Math. Comput, 17, 475–484 (2005) doi: 10.1007/BF02936069
  • R., Saadati, S., Sedghi, N., Shobe, Modified intuitionistic fuzzy metric spaces and some fixed point theorems Chaos. Soli. Fract. 38(1), 36–47 (2008) doi: 10.1016/j.chaos.2006.11.008
  • N., Sarkar, M., Sen, D., Saha, Solution of non linear Fredholm integral equation involving constant delay by BEM with piecewise linear approximation. J. Interdisciplinary Maths, 23(2), 537-544. (2020). doi: 10.1080/09720502.2020.1731965
  • B., Schweizer, A., Sklar, Statistical metric spaces, Paci. J. Math., 10, 313–334 (1960). doi: 10.2140/pjm.1960.10.313
  • B., Schweizer, A., Sklar, Probabilistic metric spaces, Elsevier, North-Holland, New York, (1983).
  • V., Sharma, A Common Fixed-Point Theorem in Ituitionistic Menger Spaces, International Journal on Recent and Innovation Trends in Computing and Communication, 4(4), 536-541.
  • S., Zhang, Y., Chen, J., Guo, Ekeland’s variational principle and Caristi’s fixed point theorem in probabilistic metric space, Acta Mathematicae Applicatae Sinica, 7(3), 217–228 (1991). doi: 10.1007/BF02005971
  • Zhang, S. S., Goudarzi, M., Saadati, R., Vaezpour, S. M. Intuitionistic Menger inner product spaces and applications to integral equations. Applied Mathematics and Mechanics, 31(4), 415-424. (2010). doi: 10.1007/s10483-010-0402-z

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