A Related Fixed Point Theorem in Two Menger Spaces

Abstract

In this paper, we prove a related fixed point theorem for single-valued mappings in two Menger spaces.

Keywords

• t-norm
• Menger space
• fixed point.

References

1. C. Alaca, “A related fixed point theorem on two metric spaces satisfying a general contractive condition of integral type”, J. Comput. Anal. Appl., 11(2):263-270 (2009).
2. A. Aliouche and B. Fisher, “Fixed point theorems for mappings satisfying implicit relation on two complete and compact metric spaces”, Applied Math. Mech. (English Ed.), 27(9):1217-1222 (2006).
3. A. Aliouche, F. Merghadi and A. Djoudi, “A related fixed point theorem in two fuzzy metric spaces”, J. Nonlinear Sci. Appl., 2(1):19-24 (2009).
4. I. Beg and S. Chauhan, “Related fixed point of set-valued mappings in three Menger spaces”,Int. J. Anal.,Art. ID 736451, 6 pages (2013).
5. A. T. Bharucha-Reid, “Fixed point theorems in probabilistic analysis”, Bull. Amer. Math. Soc., 82(5):641-657 (1976).
6. V. K. Chourasia and Brian Fisher, “Related fixed points for two pairs of set valued mappings on two metric spaces”, Hacet. J. Math. Stat., 32:27- 32 (2003).
7. B. Fisher, “Fixed point on two metric spaces”, Glasnik Mat.,16(36):333-337 (1981).
8. B. Fisher, “Related fixed point on two metric spaces”, Math. Sem. Notes Kobe Univ., 10(1):17- 26 (1982).

9. B. Fisher and P. P. Murthy, “Related fixed point theorems for two pairs of mappings on two metric spaces”, Kyungpook Math. J.,37(2):343-347 (1997).
10. B. Fisher and D. Türkoğlu, “Related fixed points for mappings on complete and compact metric spaces”, Nonlinear Anal. Forum, 6:113-118 (2001).
11. B. Fisher and D. Türkoğlu, “Related fixed points for two pairs of set valued mappings on two metric spaces”, Fixed Point Theory and Appl., 3:63-70 (2002).
12. S. N. Mishra, “Common fixed points of compatible mappings in PM-spaces”, Math. Japon.,36(2):283-289 (1991).
13. K. Menger, “Statistical metrics”, Proc. Nat. Acad. Sci. U.S.A.,28:535-537 (1942).
14. R. K. Namdeo, S. Jain and B. Fisher, “A related fixed point theorem for two pairs of mappings on two complete metric spaces”, Hacet. J. Math. Stat.,32:7-11 (2003).
15. B.D. Pant, “Relation between fixed points in Menger Math.,24(1):135-142 (2002). Indian Acad.
16. B. D. Pant and S. Kumar, “A related fixed point theorem for two pairs of mappings in two Menger spaces”, Varāhmihir J. Math. Sci.,6(2):471-476 (2006).
17. B. Schweizer and A. Sklar, “Probabilistic Metric Spaces”, North-Holland Series in Probability and Publishing Co., New York, (1983).
18. V. M. Sehgal and A. T. Bharucha-Reid, “Fixed points of contraction mappings on probabilistic metric spaces”, Math. Systems Theory, 6:97-102 (1972).
19. D. Türkoğlu and B. Fisher, “A generalization of afixed point theorem of Ćirić”, Novi Sad J. Math., 29(1):117-121 (1999).