Surveys in Mathematics and its Applications

ISSN 1842-6298 (electronic), 1843-7265 (print)
 Volume 5 (2010), 83 -- 88

FIXED POINTS OF MAPPINGS WITH DIMINISHING PROBABILISTIC ORBITAL DIAMETERS

Irshad Aalam, Naresh Kumar and B. D. Pant

Abstract. In this paper we prove a fixed point theorem for a pair of mappings with probabilistic diminishing orbital diameters on Menger spaces and introduce the notion of generalized joint diminishing probabilistic orbital diameters (gjdpod) for a quadruplet of mappings.

2010 Mathematics Subject Classification: 47H10; 54H25.
Keywords: PM Space; Diameter; Orbit.

Full text

References

  1. L. P. Belluce and W. A. Kirk, Fixed Point Theorems For Certain Classes Of Non Expansive Mappings, Proc. Amer. Math. Soc. 20 (1969), 141-146. MR0233341. Zbl 0165.16801.

  2. R. J. Egbert, Products And Quotients Of Probabilistic Metric Spaces, 24 (1968), 437-455. MR0226690. Zbl 0175.46601.

  3. B. Fisher, A Common Fixed Point Theorem For Four Mappings On a Compact Metric Space, Bull. Inst. Math. Acad. Sinica,  12 (1984), 249-252. MR764955. Zbl0544.54037.

  4. Y. Y. Huang, J. J. Huang, J. C. Jeng and Jyh-Chung, On Common Fixed Points Of Semi Group In Compact Metric Spaces, Indian J. Pure Appl. Math.,  27(1996)1073-1076. MR1420097. Zbl 0865.47043.

  5. V. I. Istrăţescu and I. Săcuiu, Fixed Point Theorems For Contraction Mappings On Probabilistic Metric Space, Rev. Roumaine Math. Pures Appl. 18 (1973), 1375-1380. MR0331356. Zbl 0293.60014.

  6. W. A. Kirk, On Mappings With Diminishing Orbital Diameters, J. Lond. Math. Soc. 44 (1969), 107-111. MR0233342. Zbl 0162.54902.

  7. Z. Liu and S. M. Kang, On Mappings With Diminishing Orbital Diameters, IJMMS 27, 6 (2001), 341-346. MR1870035. Zbl 1010.54048.

  8. B. D. Pant, R. C. Dimri and V. B. Chandola, Some Results On Fixed Points Of Probabilistic Densifying Mappings, Bull. Cal. Math. Soc. 96 (3) (2004), 189-194. MR2090229. Zbl 1072.47052.

  9. S. Ranganathan, P. Srivastva and V. K. Gupta, Joint Sequence Of Iterates And Common Fixed Points, Nanta Math. 9 (I) (1976), 92-94. MR0445480. Zbl0355.540388.

  10. S. L. Singh, Generalized Diminishing Orbital Diameteral Sum, Math. Sem. Notes Kobe Uni. 5(1977), 295-312. MR0478125. Zbl0374.54040.

  11. S. L. Singh and B. D. Pant, Fixed Points Of Mappings With Diminishing Probabilistic Orbital Diameters, Punjab Univ.J. Math. 19 (1986), 99-105. MR893390. Zbl 0622.54032.

  12. C. S. Wong, Fixed Point Theorems For Generalized Non-Expansive Mappings, J. Aust. Math. Soc. 18 (1974), 265-276. MR0358753. Zbl 0292.47052.



Irshad Aalam Naresh Kumar
Department of Mathematics, Department of Mathematics,
R. H. G. P. G. College Kashipur, R. H. G. P. G. College Kashipur,
U. S. Nagar, Uttarakhand, India. U. S. Nagar, Uttarakhand, India.
e-mail: aalam_math @ rediffmail.com e-mail: knaresh.math @ gmail.com
B. D. Pant
G. P. G. College Champavat,
Uttarakhand, India.
e-mail: bd_math@rediffmail.com


http://www.utgjiu.ro/math/sma