Common Fixed Point Results for Compatible Map in Digital Metric Spaces
DOI:
https://doi.org/10.24297/jam.v13i5.6458Keywords:
Compatible maps, fixed point results, digital metric space, metric spaceAbstract
The aim of this paper is to define the concept of compatible maps and its variants in the setting of digital metric spaces and establish some common fixed point results for these maps. Also, an application of the proposed results is quoted in this note.
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References
[1] Rani A, Jyoti K and Rani A, Common fixed point theorems in digital metric spaces, International Journal of Scientific & Engineering Research, Volume 7, Issue 12, December-2016 ISSN 2229-5518
[2] Boxer L, Digitally Continuous Functions, Pattern Recognition Letters, 15 (1994), 833-839.
[3] Boxer L, Properties of Digital Homotopy, J. Math. Imaging V is., 22(2005), 19-26.
[4] Boxer L, A Classical Constructions for The Digital Fundamental Group, J. Math. Imaging Vis., 10(1999), 51-62
[5] Boxer L, Continuous Maps on Digital Simple Closed Curves, Appl. Math., 1(2010), 377-386.
[6] Das KM, Naik KV, Common fixed-point theorems for commuting maps on a metric space, Proc. Amer. Math. Soc. 1979, 77, 369-373.
[7] Ege O, Karaca I, Banach Fixed Point Theorem for Digital Images, J. Nonlinear Sci. Appl., 8(2015), 237-245.
[8] Ege O, Karaca I, Lefschetz Fixed Point Theorem for Digital Images, Fixed Point Theory Appl., 2013(2013), 13 pages.
[9] Ege O, Karaca I, Applications of The Lefschetz Number to Digital Images, Bull. Belg. Math. Soc. Simon Stevin, 21(2014), 823-839.
[ 10] Jain D, and Upadhaya A.C, Weakly commuting Mappings in Digital Metric Spces, International Advanced Research Journal in Science, Engineering and Technology, Vol 4, Issue 8, August 2017
[11] Jungck G, Commuting mappings and fixed point, Amer. Math. Monthly 1976, 83, 261-263.
[12] Jungck G, Compatible mappings and common fixed points, International J. Math. Math. Sci. 1986, 9(4), 771-779.
[13] Jungck G, Murthy PP, Cho, YJ, Compatible mappings of type (A) and common fixed points, Math. Japon. 1993, 38, 381 – 390.
[14] Rani A, Kumar S, Kumar N, Garg SK, Common Fixed Point Theorems for Compatible and Weakly Compatible Maps in G-Metic Spaces, Applied Math. 2012, 3, 1128-1134.
[15] Rosenfeld A, Digital Topology, Amer. Math. Monthly, 86(1979), 76-87.
[16] Sessa S and Fisher B, ON COMMON FIXED POINTS OF WEAKLY COMMUTING MAPPINGS AND SET-VALUED MAPPINGS, internat. J. Math. & Math. Sci. Vol. 9 No. 2 (1986) 323-329
[17] Sumitra, COUPLED FIXED POINT THEOREMS FOR COMPATIBLE MAPS AND ITS VARIANTS IN FUZZY METRIC SPACES, Jordan Journal of Mathematics and Statistics (JJMS) 6(2), 2013, pp. 141-155
[18] Sumitra Coupled Fixed Point Theorem for Weakly Compatible Mappings in Intuitionistic Fuzzy Metric Spaces, International Journal of Computer Applications (0975 – 8887) Volume 50– No.23, July 2012
[19] Z-Dos`enovic` T, A common fixed point theorem for compatible mappings in fuzzy metric spaces using implicit relation, Acta Math. Hang. 2009, 125(4), 357-368.
[2] Boxer L, Digitally Continuous Functions, Pattern Recognition Letters, 15 (1994), 833-839.
[3] Boxer L, Properties of Digital Homotopy, J. Math. Imaging V is., 22(2005), 19-26.
[4] Boxer L, A Classical Constructions for The Digital Fundamental Group, J. Math. Imaging Vis., 10(1999), 51-62
[5] Boxer L, Continuous Maps on Digital Simple Closed Curves, Appl. Math., 1(2010), 377-386.
[6] Das KM, Naik KV, Common fixed-point theorems for commuting maps on a metric space, Proc. Amer. Math. Soc. 1979, 77, 369-373.
[7] Ege O, Karaca I, Banach Fixed Point Theorem for Digital Images, J. Nonlinear Sci. Appl., 8(2015), 237-245.
[8] Ege O, Karaca I, Lefschetz Fixed Point Theorem for Digital Images, Fixed Point Theory Appl., 2013(2013), 13 pages.
[9] Ege O, Karaca I, Applications of The Lefschetz Number to Digital Images, Bull. Belg. Math. Soc. Simon Stevin, 21(2014), 823-839.
[ 10] Jain D, and Upadhaya A.C, Weakly commuting Mappings in Digital Metric Spces, International Advanced Research Journal in Science, Engineering and Technology, Vol 4, Issue 8, August 2017
[11] Jungck G, Commuting mappings and fixed point, Amer. Math. Monthly 1976, 83, 261-263.
[12] Jungck G, Compatible mappings and common fixed points, International J. Math. Math. Sci. 1986, 9(4), 771-779.
[13] Jungck G, Murthy PP, Cho, YJ, Compatible mappings of type (A) and common fixed points, Math. Japon. 1993, 38, 381 – 390.
[14] Rani A, Kumar S, Kumar N, Garg SK, Common Fixed Point Theorems for Compatible and Weakly Compatible Maps in G-Metic Spaces, Applied Math. 2012, 3, 1128-1134.
[15] Rosenfeld A, Digital Topology, Amer. Math. Monthly, 86(1979), 76-87.
[16] Sessa S and Fisher B, ON COMMON FIXED POINTS OF WEAKLY COMMUTING MAPPINGS AND SET-VALUED MAPPINGS, internat. J. Math. & Math. Sci. Vol. 9 No. 2 (1986) 323-329
[17] Sumitra, COUPLED FIXED POINT THEOREMS FOR COMPATIBLE MAPS AND ITS VARIANTS IN FUZZY METRIC SPACES, Jordan Journal of Mathematics and Statistics (JJMS) 6(2), 2013, pp. 141-155
[18] Sumitra Coupled Fixed Point Theorem for Weakly Compatible Mappings in Intuitionistic Fuzzy Metric Spaces, International Journal of Computer Applications (0975 – 8887) Volume 50– No.23, July 2012
[19] Z-Dos`enovic` T, A common fixed point theorem for compatible mappings in fuzzy metric spaces using implicit relation, Acta Math. Hang. 2009, 125(4), 357-368.
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Published
2017-12-11
How to Cite
Dalal, S. (2017). Common Fixed Point Results for Compatible Map in Digital Metric Spaces. JOURNAL OF ADVANCES IN MATHEMATICS, 13(5), 7387–7392. https://doi.org/10.24297/jam.v13i5.6458
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