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Year 2013, Volume: 26 Issue: 1, 47 - 50, 31.03.2013

Abstract

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

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
There are 18 citations in total.

Details

Primary Language English
Subjects Engineering
Journal Section Mathematics
Authors

Sunny Chauhan

Suneel Kumar This is me

Publication Date March 31, 2013
Published in Issue Year 2013 Volume: 26 Issue: 1

Cite

APA Chauhan, S., & Kumar, S. (2013). Fixed Points of Expansion Mappings in Menger Spaces With Property (E.A.). Gazi University Journal of Science, 26(1), 47-50.
AMA Chauhan S, Kumar S. Fixed Points of Expansion Mappings in Menger Spaces With Property (E.A.). Gazi University Journal of Science. March 2013;26(1):47-50.
Chicago Chauhan, Sunny, and Suneel Kumar. “Fixed Points of Expansion Mappings in Menger Spaces With Property (E.A.)”. Gazi University Journal of Science 26, no. 1 (March 2013): 47-50.
EndNote Chauhan S, Kumar S (March 1, 2013) Fixed Points of Expansion Mappings in Menger Spaces With Property (E.A.). Gazi University Journal of Science 26 1 47–50.
IEEE S. Chauhan and S. Kumar, “Fixed Points of Expansion Mappings in Menger Spaces With Property (E.A.)”, Gazi University Journal of Science, vol. 26, no. 1, pp. 47–50, 2013.
ISNAD Chauhan, Sunny - Kumar, Suneel. “Fixed Points of Expansion Mappings in Menger Spaces With Property (E.A.)”. Gazi University Journal of Science 26/1 (March 2013), 47-50.
JAMA Chauhan S, Kumar S. Fixed Points of Expansion Mappings in Menger Spaces With Property (E.A.). Gazi University Journal of Science. 2013;26:47–50.
MLA Chauhan, Sunny and Suneel Kumar. “Fixed Points of Expansion Mappings in Menger Spaces With Property (E.A.)”. Gazi University Journal of Science, vol. 26, no. 1, 2013, pp. 47-50.
Vancouver Chauhan S, Kumar S. Fixed Points of Expansion Mappings in Menger Spaces With Property (E.A.). Gazi University Journal of Science. 2013;26(1):47-50.