References

[1] M. Abbas and B. E. Rhoades, “Common fixed point theorems for occasionally weakly compatible mappings satisfying a generalized contractive condition,” Mathematica Communications, vol. 13, no. 2, pp. 295–301, 2008.

[2] M. Abbas and B. E. Rhoades, “Common fixed point theorems for hybrid pairs of occasionally weakly compatible mappings satisfying generalized contractive condition of integral type,” Fixed Point Theory and Applications, vol. 2007, Art. no. 54101, 2007.

[3] M. A. Al-Thagafi and N. Shahzad, “Generalized I-nonexpansiveselfmaps and invariant approximations,” Acta Mathematica Sinica, English Series, vol. 24, no. 5, pp. 867–876, 2008.

[4] J. Ali, M. Imdad, D. Miheţ, and M. Tanveer, “Common fixed points of strict contractions in Menger spaces,” Acta Mathematica Hungarica, vol. 132, no. 4, pp. 367–386, 2011.

[5] H. Bouhadjera, A. Djoudi, and B. Fisher, “A unique common fixed point theorem for occasionally weakly compatible maps,” Seminar on Mathematical Analysis, vol. 3, pp. 177–182, 2008.

[6] S. Chauhan and B. D. Pant, “Some common fixed point theorems in Menger spaces,” Acta Universitatis PalackianaeOlomucensis. Facultas Rerum Naturalium. Mathematica, vol. 52, no. 1, pp. 57–69, 2013.

[7] A. K. Chaudhary, “Occasionally weakly compatible mappings and common fixed points in Menger space,” Results in Nonlinear Analysis.

[8] D. Dorić, Z. Kadelburg, and S. Radenović, “A note on occasionally weakly compatible mappings and common fixed points,” Fixed Point Theory, 2012.

[9] J.-X. Fang and Y. Gao, “Common fixed point theorems under strict contractive conditions in Menger spaces,” Nonlinear Analysis: Theory, Methods & Applications, vol. 70, no. 1, pp. 184–193, 2009.

[10] O. Hadžić and E. Pap, Fixed Point Theory in Probabilistic Metric Spaces. Dordrecht, The Netherlands: Kluwer Academic Publishers, 2001.

[11] G. Jungck, “Compatible mappings and common fixed points,” International Journal of Mathematics and Mathematical Sciences, vol. 9, no. 4, pp. 771–779, 1986.

[12] G. Jungck and B. E. Rhoades, “Fixed point theorems for occasionally weakly compatible mappings,” Fixed Point Theory, vol. 7, no. 2, pp. 287–296, 2006.

[13] G. Jungck and B. E. Rhoades, “Fixed point theorems for occasionally weakly compatible mappings,” Fixed Point Theory, vol. 9, pp. 383–384, 2008 (Erratum).

[14] K. Menger, “Probabilistic geometry,” Proceedings of the National Academy of Sciences of the United States of America, vol. 37, no. 4, pp. 226–229, 1951.

[15] K. Menger, “Statistical metrics,” Proceedings of the National Academy of Sciences of the United States of America, vol. 28, no. 12, pp. 535–537, 1942.

[16] M. Imdad, M. Tanveer, and M. Hasan, “Some common fixed point theorems in Menger PM spaces,” Fixed Point Theory and Applications, vol. 2010, Art. no. 819269, 2010.

[17] B. Schweizer and A. Sklar, Probabilistic Metric Spaces. New York, NY, USA: North-Holland, 1983.

[18] S. Sedghi, T. Žikić-Došenović, and N. Shobe, “Common fixed point theorems in Menger probabilistic quasimetric spaces,” Fixed Point Theory and Applications, vol. 2009, Art. no. 546273, 2009.

[19] R. Shrivastava, A. Jain, and A. K. Gupta, “Occasionally weak compatible mappings and common fixed point theorem in intuitionistic fuzzy metric space,” International Journal of Mathematics Trends and Technology, vol. 58, no. 2, pp. 120–126, 2017.

[20] S. Sharma, M. Rawal, and K. Devdhare, “Common fixed point of weakly compatible maps without continuity in Menger spaces,” East Asian Mathematical Journal, vol. 27, no. 5, pp. 565–572, 2011.

Cite this paper as : Uma .M & M. Vijaya K (2017). “New Common Fixed-Point Theorems for Occasionally Weakly Compatible Mappings in Menger Spaces”, International Journal of Advances in Engineering & Scientific Research, Volume 4,(Issue 5, Jull- Aug-2017), pp 56-66. ISSN: 2349 –3607 (Online) ,  ISSN: 2349 –4824 (Print),   DOI URL:  http://doi.org/10.5281/zenodo.22095239

References

[1] M. Abbas and B. E. Rhoades, “Common fixed point theorems for occasionally weakly compatible mappings satisfying a generalized contractive condition,” Mathematica Communications, vol. 13, no. 2, pp. 295–301, 2008.

[2] M. Abbas and B. E. Rhoades, “Common fixed point theorems for hybrid pairs of occasionally weakly compatible mappings satisfying generalized contractive condition of integral type,” Fixed Point Theory and Applications, vol. 2007, Art. no. 54101, 2007.

[3] M. A. Al-Thagafi and N. Shahzad, “Generalized I-nonexpansiveselfmaps and invariant approximations,” Acta Mathematica Sinica, English Series, vol. 24, no. 5, pp. 867–876, 2008.

[4] J. Ali, M. Imdad, D. Miheţ, and M. Tanveer, “Common fixed points of strict contractions in Menger spaces,” Acta Mathematica Hungarica, vol. 132, no. 4, pp. 367–386, 2011.

[5] H. Bouhadjera, A. Djoudi, and B. Fisher, “A unique common fixed point theorem for occasionally weakly compatible maps,” Seminar on Mathematical Analysis, vol. 3, pp. 177–182, 2008.

[6] S. Chauhan and B. D. Pant, “Some common fixed point theorems in Menger spaces,” Acta Universitatis PalackianaeOlomucensis. Facultas Rerum Naturalium. Mathematica, vol. 52, no. 1, pp. 57–69, 2013.

[7] A. K. Chaudhary, “Occasionally weakly compatible mappings and common fixed points in Menger space,” Results in Nonlinear Analysis.

[8] D. Dorić, Z. Kadelburg, and S. Radenović, “A note on occasionally weakly compatible mappings and common fixed points,” Fixed Point Theory, 2012.

[9] J.-X. Fang and Y. Gao, “Common fixed point theorems under strict contractive conditions in Menger spaces,” Nonlinear Analysis: Theory, Methods & Applications, vol. 70, no. 1, pp. 184–193, 2009.

[10] O. Hadžić and E. Pap, Fixed Point Theory in Probabilistic Metric Spaces. Dordrecht, The Netherlands: Kluwer Academic Publishers, 2001.

[11] G. Jungck, “Compatible mappings and common fixed points,” International Journal of Mathematics and Mathematical Sciences, vol. 9, no. 4, pp. 771–779, 1986.

[12] G. Jungck and B. E. Rhoades, “Fixed point theorems for occasionally weakly compatible mappings,” Fixed Point Theory, vol. 7, no. 2, pp. 287–296, 2006.

[13] G. Jungck and B. E. Rhoades, “Fixed point theorems for occasionally weakly compatible mappings,” Fixed Point Theory, vol. 9, pp. 383–384, 2008 (Erratum).

[14] K. Menger, “Probabilistic geometry,” Proceedings of the National Academy of Sciences of the United States of America, vol. 37, no. 4, pp. 226–229, 1951.

[15] K. Menger, “Statistical metrics,” Proceedings of the National Academy of Sciences of the United States of America, vol. 28, no. 12, pp. 535–537, 1942.

[16] M. Imdad, M. Tanveer, and M. Hasan, “Some common fixed point theorems in Menger PM spaces,” Fixed Point Theory and Applications, vol. 2010, Art. no. 819269, 2010.

[17] B. Schweizer and A. Sklar, Probabilistic Metric Spaces. New York, NY, USA: North-Holland, 1983.

[18] S. Sedghi, T. Žikić-Došenović, and N. Shobe, “Common fixed point theorems in Menger probabilistic quasimetric spaces,” Fixed Point Theory and Applications, vol. 2009, Art. no. 546273, 2009.

[19] R. Shrivastava, A. Jain, and A. K. Gupta, “Occasionally weak compatible mappings and common fixed point theorem in intuitionistic fuzzy metric space,” International Journal of Mathematics Trends and Technology, vol. 58, no. 2, pp. 120–126, 2017.

[20] S. Sharma, M. Rawal, and K. Devdhare, “Common fixed point of weakly compatible maps without continuity in Menger spaces,” East Asian Mathematical Journal, vol. 27, no. 5, pp. 565–572, 2011.