Year 2013,
Volume: 26 Issue: 1, 47 - 50, 31.03.2013
Sunny Chauhan
,
Suneel Kumar
References
- [1] S. Banach, “Sur les operations dans les ensembles abstraits et leur application aux equations integrals”, Fund. Math., 3:133-181 (1922).
- [2] R. C. Dimri, B. D. Pant and S. Kumar, “Fixed point of a pair of non-surjective expansion mappings in Menger spaces”, Stud. Cerc. Sţ. Ser. Matematica Universitatea Bacău, 18:55- 62(2008).
- [3] M. Frechet, “Sur quelques points du calculfonctionnel”, Rendic. Circ. Mat. Palermo, 22:1-74(1906).
- [4] R. K. Gujetiya, V. K. Gupta, M. S. Chauhan and O. Sikhwal, “Common fixed point theorem for expansive maps in Menger spaces through compatibility”, Int. Math. Forum, 5(63):3147- 3158(2010).
- [5] G. Jungck, “Compatible mappings and common fixed points”, Int. J. Math. Math. Sci., 9(4):771-779(1986).
- [6] I. Kubiaczyk and S. Sharma, “Some common fixed point theorems in Menger space under strict contractive conditions”, Southeast Asian Bull. Math., 32:117- 124(2008).
- [7] S. Kumar, “Some fixed point theorems in Menger spaces and applications”, Ph.D. Dissertation, Kumaun Univ., Nainital (India), (2008).
- [8] S. Kumar, R. Chugh and R. K. Vats, “Fixed point theorems for expansion mappings theorems in various spaces”, Stud. Cerc. Sţ. Ser. Matematica Universitatea Bacău, 16:47- 68(2006).
- [9] S. Kumar and B. D. Pant, A common fixed point theorem for expansion mappings in probabilistic metric spaces, Ganita, 57(1):89- 95(2006).
- [10] K. Menger, “Statistical metrics”, Proc. Nat. Acad. Sci. U.S.A., 28:535-537(1942).
- [11] S. N. Mishra, “Common fixed points of compatible mappings in PM-spaces”, Math. Japon., 36 283-289(1991).
- [12] B. D. Pant, R. C. Dimri and S. L. Singh, “Fixed point theorems for expansion mapping on probabilistic metric spaces”, Honam Math. J., 9(1):77-81(1987).
- [13] B. Schweizer and A. Sklar, “Probabilistic Metric Spaces”, North-Holland Series in Probability and Applied MathematicsNorthHolland Publishing Co., New York, (1983).
- [14] V. M. Sehgal, “Some fixed point theorems in functional analysis and probability”, Ph.D. Dissertation, Wayne State Univ., (1966).
- [15] B. Singh and S. Jain, A fixed point theorem in Menger Space through weak compatibility, J. Math. Anal. Appl., 301:439-448(2005).
- [16] S. L. Singh and B. D. Pant, “Common fixed point theorems in probabilistic metric spaces and extension to uniform spaces”, Honam Math. J., 6:1-12 (1984).
- [17] R. Vasuki, “Fixed point and common fixed point theorems for expansive maps in Menger spaces”, Bull. Cal. Math. Soc., 83:565- 570(1991).
- [18] S. Z.Wang, B. Y. Li, Z. M. Gao and K. Iseki, “Some fixed point theorems on expansion mappings,”Math. Japon., 29:631-636(1984
Fixed Points of Expansion Mappings in Menger Spaces With Property (E.A.)
Year 2013,
Volume: 26 Issue: 1, 47 - 50, 31.03.2013
Sunny Chauhan
,
Suneel Kumar
Abstract
The aim of this paper is to prove a common fixed point theorem for non-surjective expansion mappings in Menger space employing the property (E.A). We also furnish an illustrative example to support our result. Our results improve and generalize a host of previously known fixed point theorems.
References
- [1] S. Banach, “Sur les operations dans les ensembles abstraits et leur application aux equations integrals”, Fund. Math., 3:133-181 (1922).
- [2] R. C. Dimri, B. D. Pant and S. Kumar, “Fixed point of a pair of non-surjective expansion mappings in Menger spaces”, Stud. Cerc. Sţ. Ser. Matematica Universitatea Bacău, 18:55- 62(2008).
- [3] M. Frechet, “Sur quelques points du calculfonctionnel”, Rendic. Circ. Mat. Palermo, 22:1-74(1906).
- [4] R. K. Gujetiya, V. K. Gupta, M. S. Chauhan and O. Sikhwal, “Common fixed point theorem for expansive maps in Menger spaces through compatibility”, Int. Math. Forum, 5(63):3147- 3158(2010).
- [5] G. Jungck, “Compatible mappings and common fixed points”, Int. J. Math. Math. Sci., 9(4):771-779(1986).
- [6] I. Kubiaczyk and S. Sharma, “Some common fixed point theorems in Menger space under strict contractive conditions”, Southeast Asian Bull. Math., 32:117- 124(2008).
- [7] S. Kumar, “Some fixed point theorems in Menger spaces and applications”, Ph.D. Dissertation, Kumaun Univ., Nainital (India), (2008).
- [8] S. Kumar, R. Chugh and R. K. Vats, “Fixed point theorems for expansion mappings theorems in various spaces”, Stud. Cerc. Sţ. Ser. Matematica Universitatea Bacău, 16:47- 68(2006).
- [9] S. Kumar and B. D. Pant, A common fixed point theorem for expansion mappings in probabilistic metric spaces, Ganita, 57(1):89- 95(2006).
- [10] K. Menger, “Statistical metrics”, Proc. Nat. Acad. Sci. U.S.A., 28:535-537(1942).
- [11] S. N. Mishra, “Common fixed points of compatible mappings in PM-spaces”, Math. Japon., 36 283-289(1991).
- [12] B. D. Pant, R. C. Dimri and S. L. Singh, “Fixed point theorems for expansion mapping on probabilistic metric spaces”, Honam Math. J., 9(1):77-81(1987).
- [13] B. Schweizer and A. Sklar, “Probabilistic Metric Spaces”, North-Holland Series in Probability and Applied MathematicsNorthHolland Publishing Co., New York, (1983).
- [14] V. M. Sehgal, “Some fixed point theorems in functional analysis and probability”, Ph.D. Dissertation, Wayne State Univ., (1966).
- [15] B. Singh and S. Jain, A fixed point theorem in Menger Space through weak compatibility, J. Math. Anal. Appl., 301:439-448(2005).
- [16] S. L. Singh and B. D. Pant, “Common fixed point theorems in probabilistic metric spaces and extension to uniform spaces”, Honam Math. J., 6:1-12 (1984).
- [17] R. Vasuki, “Fixed point and common fixed point theorems for expansive maps in Menger spaces”, Bull. Cal. Math. Soc., 83:565- 570(1991).
- [18] S. Z.Wang, B. Y. Li, Z. M. Gao and K. Iseki, “Some fixed point theorems on expansion mappings,”Math. Japon., 29:631-636(1984