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g- reciprocal Continuity in Probabilistic Metric Spaces

Year 2015, Volume: 28 Issue: 4, 645 - 649, 16.12.2015

Abstract

In the present paper we obtain a common fixed point theorem by
employing the notion of g- reciprocal continuity in probabilistic metric space.
We demonstrate that g- reciprocal continuity ensures the existence of common
xed point under strict contractive conditions, which otherwise do not ensure
the existence of fixed points.

References

  • [1] Menger, K. Statistical metrices, Nat. Acad.Sci.USA. 28(1942) 535-537.
  • [2] Schweizer, B. and Skalar, A. Probabilistic metric spaces, Pacific J. of Math.10 (1960) 313 - 324.
  • [3] Sehgal, V.M. Some fixed point theorems in functional analysis and probability Ph.D.Dissertation, Wayne State Univ. Michigan (1966).
  • [4] Kannan, R. Some results on fixed points, Bull. Calcutta Math. Soc. 60 (1968) 71-76.
  • [5] Egbert, R.J. Products and quotients of probabilistic metric spaces, Pacific J.Math., 24(1968) 437-455.
  • [6] Sehgal, V.M. and Bharucha-Reid, A.T. Fixed points of contraction mappings on Probabilistic metric spaces, Math. Systems Theo. 06(1972) 97-102.
  • [7] Bharucha-Reid, A.T. Fixed point theorems in Probabilistic analysis, Bull.Amer. Math. Soc. 82(1976) 641-657.
  • [8] Jungck, G. Commuting mappings and fixed points, Amer. Math. Month. 73(1976) 261-263. [9] Sessa, S. On a weak commutativity condition of mappings in fixed point considerations, Publ. Inst. Math. 32(1982) 149-153.
  • [10] Schweizer, B. and Sklar, A. Statistical metric spaces, North Holland Amsterdam, (1983). [11] Jungck, G. Compatible mappings and common fixed points, Int.J.Math.andMath.Sci. 09 (1986) 771-779.
  • [12] Jungck, G. Commuting mappings and fixed points, Amer.Math.Monthly, 83(1976)261-263.
  • [13] Mishra, S.N. Common fixed points of compatible mappings in PM-spaces, Math. Japon. 36(1991) 283-289.
  • [14] Jungck, G. and Pathak, H.K., Fixed points via biased maps, Proc. Amer. Math. Soc. 123(1995) 2049-2060.
  • [15] Jungck, G., Common fixed points for noncontinuousnonself maps on nonmetric spaces, Far East J. Math. Sci. 04(1996) 199- 215.
  • [16] Pathak, H.K. and Khan, M.S., A comparison of various types of compatible maps and common fixed points, Indian J. Pure Appl. Math. 28 no. 4,(1997), 477-485.
  • [17] Pant, R.P., Common fixed points of four maps, Bull. Calcutta Math.Soc. 90(1998) 281-286.
  • [18] Naschie, MS.EL., On the uncertainty of Cantorian geometry and two-slit experiment, Chaos Solitons and Frac. 09(03)(1998) 517- 529.
  • [19]Pant, R.P., Discontinuity and fixed points, J. Math. Anal. Appl. 240 (1999), 284-289.
  • [20] Naschie, MS.EL., On the verifications of heterotic string theory and 𝜖 ∞, Chaos, Solitons and Frac. 232(2000) 397-407.
  • [21] Pant, R.P.and Pant, V., Common fixed points under strict contractive conditions, J.Math.Anal.Appl.248(2000) 327-332.
  • [22] Hadzic, O. and Pap, E.,Fixed Point Theory in Probabilistic Metric Spaces, Kluwer Academic Publishers, 2001.
  • [23] Aamri, M. and Moutawakil, D. El., Some new common fixed point theorems under strict contractive conditions, J. Math. Anal. Appl. 270(2002) 181-188.
  • [24] Chandra, H. and Bhatt, A., Fixed point theorems for occasionally weakly compatible maps in probabilistic semi-metric space, International Journal of Mathematical anal.03(2009) 563-570.
  • [25] Pant, R.P. and Bisht, R.KCommon fixed points of pseudo compatible mappings, Revista de la Real Academia de Ciencias Exactas, Fsicas y Naturales. Serie A. Matemticas,DOI 10.1007/s 13398-013-0119-5. Chaos Solitons and Frac. 09(03)(1998) 517- 529.

MetricSpaces

Year 2015, Volume: 28 Issue: 4, 645 - 649, 16.12.2015

Abstract

References

  • [1] Menger, K. Statistical metrices, Nat. Acad.Sci.USA. 28(1942) 535-537.
  • [2] Schweizer, B. and Skalar, A. Probabilistic metric spaces, Pacific J. of Math.10 (1960) 313 - 324.
  • [3] Sehgal, V.M. Some fixed point theorems in functional analysis and probability Ph.D.Dissertation, Wayne State Univ. Michigan (1966).
  • [4] Kannan, R. Some results on fixed points, Bull. Calcutta Math. Soc. 60 (1968) 71-76.
  • [5] Egbert, R.J. Products and quotients of probabilistic metric spaces, Pacific J.Math., 24(1968) 437-455.
  • [6] Sehgal, V.M. and Bharucha-Reid, A.T. Fixed points of contraction mappings on Probabilistic metric spaces, Math. Systems Theo. 06(1972) 97-102.
  • [7] Bharucha-Reid, A.T. Fixed point theorems in Probabilistic analysis, Bull.Amer. Math. Soc. 82(1976) 641-657.
  • [8] Jungck, G. Commuting mappings and fixed points, Amer. Math. Month. 73(1976) 261-263. [9] Sessa, S. On a weak commutativity condition of mappings in fixed point considerations, Publ. Inst. Math. 32(1982) 149-153.
  • [10] Schweizer, B. and Sklar, A. Statistical metric spaces, North Holland Amsterdam, (1983). [11] Jungck, G. Compatible mappings and common fixed points, Int.J.Math.andMath.Sci. 09 (1986) 771-779.
  • [12] Jungck, G. Commuting mappings and fixed points, Amer.Math.Monthly, 83(1976)261-263.
  • [13] Mishra, S.N. Common fixed points of compatible mappings in PM-spaces, Math. Japon. 36(1991) 283-289.
  • [14] Jungck, G. and Pathak, H.K., Fixed points via biased maps, Proc. Amer. Math. Soc. 123(1995) 2049-2060.
  • [15] Jungck, G., Common fixed points for noncontinuousnonself maps on nonmetric spaces, Far East J. Math. Sci. 04(1996) 199- 215.
  • [16] Pathak, H.K. and Khan, M.S., A comparison of various types of compatible maps and common fixed points, Indian J. Pure Appl. Math. 28 no. 4,(1997), 477-485.
  • [17] Pant, R.P., Common fixed points of four maps, Bull. Calcutta Math.Soc. 90(1998) 281-286.
  • [18] Naschie, MS.EL., On the uncertainty of Cantorian geometry and two-slit experiment, Chaos Solitons and Frac. 09(03)(1998) 517- 529.
  • [19]Pant, R.P., Discontinuity and fixed points, J. Math. Anal. Appl. 240 (1999), 284-289.
  • [20] Naschie, MS.EL., On the verifications of heterotic string theory and 𝜖 ∞, Chaos, Solitons and Frac. 232(2000) 397-407.
  • [21] Pant, R.P.and Pant, V., Common fixed points under strict contractive conditions, J.Math.Anal.Appl.248(2000) 327-332.
  • [22] Hadzic, O. and Pap, E.,Fixed Point Theory in Probabilistic Metric Spaces, Kluwer Academic Publishers, 2001.
  • [23] Aamri, M. and Moutawakil, D. El., Some new common fixed point theorems under strict contractive conditions, J. Math. Anal. Appl. 270(2002) 181-188.
  • [24] Chandra, H. and Bhatt, A., Fixed point theorems for occasionally weakly compatible maps in probabilistic semi-metric space, International Journal of Mathematical anal.03(2009) 563-570.
  • [25] Pant, R.P. and Bisht, R.KCommon fixed points of pseudo compatible mappings, Revista de la Real Academia de Ciencias Exactas, Fsicas y Naturales. Serie A. Matemticas,DOI 10.1007/s 13398-013-0119-5. Chaos Solitons and Frac. 09(03)(1998) 517- 529.
There are 23 citations in total.

Details

Journal Section Mathematics
Authors

Arvind Bhatt

Publication Date December 16, 2015
Published in Issue Year 2015 Volume: 28 Issue: 4

Cite

APA Bhatt, A. (2015). g- reciprocal Continuity in Probabilistic Metric Spaces. Gazi University Journal of Science, 28(4), 645-649.
AMA Bhatt A. g- reciprocal Continuity in Probabilistic Metric Spaces. Gazi University Journal of Science. December 2015;28(4):645-649.
Chicago Bhatt, Arvind. “G- Reciprocal Continuity in Probabilistic Metric Spaces”. Gazi University Journal of Science 28, no. 4 (December 2015): 645-49.
EndNote Bhatt A (December 1, 2015) g- reciprocal Continuity in Probabilistic Metric Spaces. Gazi University Journal of Science 28 4 645–649.
IEEE A. Bhatt, “g- reciprocal Continuity in Probabilistic Metric Spaces”, Gazi University Journal of Science, vol. 28, no. 4, pp. 645–649, 2015.
ISNAD Bhatt, Arvind. “G- Reciprocal Continuity in Probabilistic Metric Spaces”. Gazi University Journal of Science 28/4 (December 2015), 645-649.
JAMA Bhatt A. g- reciprocal Continuity in Probabilistic Metric Spaces. Gazi University Journal of Science. 2015;28:645–649.
MLA Bhatt, Arvind. “G- Reciprocal Continuity in Probabilistic Metric Spaces”. Gazi University Journal of Science, vol. 28, no. 4, 2015, pp. 645-9.
Vancouver Bhatt A. g- reciprocal Continuity in Probabilistic Metric Spaces. Gazi University Journal of Science. 2015;28(4):645-9.