Fixed Point Results by Altering Distances in Fuzzy Metric Spaces

Affiliation(s)

^{1}
College of Science, Jazan University, Jazan, kingdom of Saudi Arabia.

^{2}
Allama Iqbal Open University, Islamabad, Pakistan.

ABSTRACT

We establish fixed point theorems in complete fuzzy metric space by using
notion of altering distance, initiated by Khan *et al*. [Bull. Austral. Math. Soc. 30 (1984), 1-9]. Also, we find an
affirmative answer in fuzzy metric space to the problem of Sastry [TamkangJ. Math.,
31(3) (2000), 243-250].

Cite this paper

Masmali, I. , Dalal, S. and Rehman, N. (2015) Fixed Point Results by Altering Distances in Fuzzy Metric Spaces.*Advances in Pure Mathematics*, **5**, 377-382. doi: 10.4236/apm.2015.56036.

Masmali, I. , Dalal, S. and Rehman, N. (2015) Fixed Point Results by Altering Distances in Fuzzy Metric Spaces.

References

[1] Kramosil, I. and Michalek, J. (1975) Fuzzy Metric and Statistical Metric Spaces. Kybernetika, 11, 326-334.

[2] Grabiec, M. (1988) Fixed Points in Fuzzy Metric Spaces. Fuzzy Sets and Systems, 27, 385-389.

http://dx.doi.org/10.1016/0165-0114(88)90064-4

[3] George, A. and Veeramani, P. (1994) On Some Results in Fuzzy Metric Space. Fuzzy Sets and Systems, 64, 395-399.

http://dx.doi.org/10.1016/0165-0114(94)90162-7

[4] Boyd, W. and Wong, S.W. (1969) On Nonlinear Contractions. Proceedings of the American Mathematical Society, 20, 458-464.

http://dx.doi.org/10.1090/S0002-9939-1969-0239559-9

[5] Alber, Y.I. and Guerre-Delabriere, S. (1997) Principle of Weakly Contractive Maps in Hilbert Spaces. In: Gohberg, I. and Lyubich, Y., Eds., New Results in Operator Theory and Its Applications, Vol. 98 of Operator Theory, Advances and Applications, Birkhauser, Basel, 7-22.

[6] Khan, M.S., Swaleh, M. and Sessa, S. (1984) Fixed Point Theorems by Altering Distances between the Points. Bulletin of the Australian Mathematical Society, 30, 1-9.

http://dx.doi.org/10.1017/S0004972700001659

[7] Pant, R.P., Jha, K. and Lohani, A.B. (2003) A Note on Common Fixed Points by Altering Distances. Tamkang Journal of Mathematics, 34, 59-62.

[8] Pant, R.P., Jha, K. and Pande, V.P. (2003) Common Fixed Point for by Altering Distances between Points. Bulletin of Calcutta Mathematical Society, 95, 421-428.

[9] Pant, R.P., Jha, K. and Padaliya, S. (2003) On Common Fixed Point by Altering Distances between the Points. Tamkang Journal of Mathematics, 34, 239-243.

[10] Sumitra, Chauhan, S. and Kadelburg, Z. (2013) A Common Fixed Point Theorem in Metric Space under General Contractive Condition. Journal of Applied Mathematics, 2013, Article ID: 510691, 7 p.

http://dx.doi.org/10.1155/2013/510691

[11] Sumitra, Imdad, M. and Chauhan, S. (2013) Unified Fixed Point Theorems via Common Limit Range Property in Modified Intuitionistic Fuzzy Metric Spaces. Hindawi Publishing Corporation, Abstract and Applied Analysis, 2013, Article ID: 413473, 11 p.

[12] Sumitra, Manro, S., Bhatia, S.S., Kumar, S. and Kumum, P. (2013) Weakly Compatibly Mapping with CLRS Mapping in Fuzzy-Metric Spaces. Journal Nonlinear Analysis and Applications, 2013, 1-12.

[13] Sastry, K.P.R., Naidu, S.V.R., Babu, G.V.R. and Naidu, G.A. (2000) Generalization of Common Fixed Point Theorems for Weakly Commuting Maps by Altering Distances. Tamkang Journal of Mathematics, 31, 243-250.

[14] Vasuki, R. (1999) Common Fixed Points for R-Weakly Commuting Mappings in Fuzzy Metric Spaces. Indian Journal of Pure and Applied Mathematics, 30, 419-423.

[15] Abbas, M., Imdad, M. and Gopal, D. (2011) ψ-Weak Contractions in Fuzzy Metric Spaces. Iranian Journal of Fuzzy Systems, 8, 141-148.

[16] Vetro, C. and Vetro, P. (2008) Common Fixed Points for Discontinuous Mappings in Fuzzy Metric Spaces. Rendiconti del Circolo Matematico di Palermo, 57, 295-303.

[17] Jha, K., Abbas, M., Beg, I., Pant, R.P. and Imdad, M. (2011) Common Fixed Point Theorem for (?, ψ)-Weak Contractions in Fuzzy Metric Spaces. Bulletin of Mathematical Analysis and Applications, 3, 149-158.

[18] Sharma, P. and Chandel, R.S. (2013) Reciprocally Continuous Maps in a Fuzzy Metric Space Involving Implicit Relations. Journal of Advanced Studies in Topology, 4, 32-39.

[1] Kramosil, I. and Michalek, J. (1975) Fuzzy Metric and Statistical Metric Spaces. Kybernetika, 11, 326-334.

[2] Grabiec, M. (1988) Fixed Points in Fuzzy Metric Spaces. Fuzzy Sets and Systems, 27, 385-389.

http://dx.doi.org/10.1016/0165-0114(88)90064-4

[3] George, A. and Veeramani, P. (1994) On Some Results in Fuzzy Metric Space. Fuzzy Sets and Systems, 64, 395-399.

http://dx.doi.org/10.1016/0165-0114(94)90162-7

[4] Boyd, W. and Wong, S.W. (1969) On Nonlinear Contractions. Proceedings of the American Mathematical Society, 20, 458-464.

http://dx.doi.org/10.1090/S0002-9939-1969-0239559-9

[5] Alber, Y.I. and Guerre-Delabriere, S. (1997) Principle of Weakly Contractive Maps in Hilbert Spaces. In: Gohberg, I. and Lyubich, Y., Eds., New Results in Operator Theory and Its Applications, Vol. 98 of Operator Theory, Advances and Applications, Birkhauser, Basel, 7-22.

[6] Khan, M.S., Swaleh, M. and Sessa, S. (1984) Fixed Point Theorems by Altering Distances between the Points. Bulletin of the Australian Mathematical Society, 30, 1-9.

http://dx.doi.org/10.1017/S0004972700001659

[7] Pant, R.P., Jha, K. and Lohani, A.B. (2003) A Note on Common Fixed Points by Altering Distances. Tamkang Journal of Mathematics, 34, 59-62.

[8] Pant, R.P., Jha, K. and Pande, V.P. (2003) Common Fixed Point for by Altering Distances between Points. Bulletin of Calcutta Mathematical Society, 95, 421-428.

[9] Pant, R.P., Jha, K. and Padaliya, S. (2003) On Common Fixed Point by Altering Distances between the Points. Tamkang Journal of Mathematics, 34, 239-243.

[10] Sumitra, Chauhan, S. and Kadelburg, Z. (2013) A Common Fixed Point Theorem in Metric Space under General Contractive Condition. Journal of Applied Mathematics, 2013, Article ID: 510691, 7 p.

http://dx.doi.org/10.1155/2013/510691

[11] Sumitra, Imdad, M. and Chauhan, S. (2013) Unified Fixed Point Theorems via Common Limit Range Property in Modified Intuitionistic Fuzzy Metric Spaces. Hindawi Publishing Corporation, Abstract and Applied Analysis, 2013, Article ID: 413473, 11 p.

[12] Sumitra, Manro, S., Bhatia, S.S., Kumar, S. and Kumum, P. (2013) Weakly Compatibly Mapping with CLRS Mapping in Fuzzy-Metric Spaces. Journal Nonlinear Analysis and Applications, 2013, 1-12.

[13] Sastry, K.P.R., Naidu, S.V.R., Babu, G.V.R. and Naidu, G.A. (2000) Generalization of Common Fixed Point Theorems for Weakly Commuting Maps by Altering Distances. Tamkang Journal of Mathematics, 31, 243-250.

[14] Vasuki, R. (1999) Common Fixed Points for R-Weakly Commuting Mappings in Fuzzy Metric Spaces. Indian Journal of Pure and Applied Mathematics, 30, 419-423.

[15] Abbas, M., Imdad, M. and Gopal, D. (2011) ψ-Weak Contractions in Fuzzy Metric Spaces. Iranian Journal of Fuzzy Systems, 8, 141-148.

[16] Vetro, C. and Vetro, P. (2008) Common Fixed Points for Discontinuous Mappings in Fuzzy Metric Spaces. Rendiconti del Circolo Matematico di Palermo, 57, 295-303.

[17] Jha, K., Abbas, M., Beg, I., Pant, R.P. and Imdad, M. (2011) Common Fixed Point Theorem for (?, ψ)-Weak Contractions in Fuzzy Metric Spaces. Bulletin of Mathematical Analysis and Applications, 3, 149-158.

[18] Sharma, P. and Chandel, R.S. (2013) Reciprocally Continuous Maps in a Fuzzy Metric Space Involving Implicit Relations. Journal of Advanced Studies in Topology, 4, 32-39.