Common Fixed Point Theorems for Complete Multiplicative Metric Space Employing Compatible Mapping of Type (P-1)
Keywords:
Common fixed point, Compatible mapping, Compatible mapping of (P-1) type, Complete MMS, Fixed pointAbstract
The aspiration of this paper is to incorporate the existence and uniqueness of common fixed point results for eight self-mappings on a complete multiplicative metric space, in which the pair of maps satisfy compatible mapping of (P-1) type, which is equivalent to compatible mapping under certain conditions. The notion of multiplicative metric space, introduced recently, generalizes the concept of metric space and is useful in various branches of mathematics and computer sciences. Our results generalize and improve several existing results in the literature, including those for metric spaces and partially ordered metric spaces. Our results have applications in various fields, including computer science, engineering, and economics. They can be used to model and analyze complex systems and phenomena and to develop new algorithms and techniques for solving problems in these fields. We also provide examples to illustrate the applicability of our results.
References
M. Özavşar, “Fixed points of multiplicative contraction mappings on multiplicative metric spaces,” Journal of Engineering Technology and Applied Sciences, vol. 2, no. 2, pp. 65–79, Oct. 2017, doi: https://doi.org/10.30931/jetas.338608
N. Sharma, J. Dudeja and A. Mishra, “Related fixed point theorems for commuting and weakly Compatible maps in complete multiplicative metric space”, International Journal of computational and applied Mathematics, vol. 12, no. 1, pp. 105-113, 2017, https://www.ripublication.com/ijcam17/ijcamv12n1_10.pdf
K.P.R. Sastry, K.K.M. Sharma and S. L. Rao, “A Fixed Point Theorem for Four Self Maps on a Multiplicative Metric Space and Consequences”, International Journal of Mathematics and its Applications, vol. 6(1-B), 215-221, 2018, https://www.gdctekkali.ac.in/userfiles/IJMAA_(PAPER-5).pdf.
B. Vijayabaskererreddy and V. Srinivas, “Some results in multiplicative metric space using absorbing mapping”, Indian Journal of Science and Technology, vol. 13, no. 39, pp. 4161-4167, Oct. 2020, doi: https://doi.org/10.17485/IJST/V13i39.1629.
V. Srinvas, K. Mallaiah, “A results on multiplicative metric space”, Journal of Mathematical and Computational Science, vol. 10, no. 5, pp. 1384-1398, May 2020, https://scik.org/index.php/jmcs/article/view/4628.
M. Katta and Srinivas Veladi, “A Fixed Point Theorem in Multiplicative Metric Space Based on Common EA-Like Property,” Communications in Mathematics and Applications, vol. 13, no. 5, pp. 1363–1372, Dec. 2022, doi: https://doi.org/10.26713/cma.v13i5.2246.
X. He, M. Song, and D. Chen, “Common fixed points for weak commutative mappings on a multiplicative metric space,” Fixed Point Theory and Applications, vol. 2014, no. 1, Feb. 2014, doi: https://doi.org/10.1186/1687-1812-2014-48.
A. Ansar and N. Muh., “Some Fixed Point Results on Multiplicative Metric Spaces,” Journal of Mathematics Theory and Application, pp. 15–20, Aug. 2022, doi: https://doi.org/10.31605/jomta.v4i1.1845.
B. Vijayabaskererreddy and V. Srinivas, “Fixed point results on multiplicative semi-metric space”, Journal of Scientific Research, vol. 10, no. 5, pp. 341-348, May 2020, doi: https://dx.doi.org/10.3329/jsrv12i3.44754.
A.A.N. Abdou, “Common fixed point results for compatible type mapping in multiplicative metric space”, Journal of Nonlinear Science and Applications, 9, pp. 2244-2257, 2016, https://www.emis.de/journals/TJNSA/includes/files/articles/Vol9_Iss5_2244--2257_Common_fixed_point_results_for_comp.pdf
R. P. Agarwal, Erdal Karapınar, and B. Samet, “An essential remark on fixed point results on multiplicative metric spaces,” Fixed point theory and applications, vol. 2016, no. 1, Mar. 2016, doi: https://doi.org/10.1186/s13663-016-0506-7.
P. Nagpal, “Several Fixed Point Theorems for Expansive Mappings in Multiplicative Metric Spaces,” International Journal of Pure and Apllied Mathematics, vol. 107, no. 2, pp. 357-369, 2016, Jan. 30, 2022. https://www.academia.edu/70085266/Several_Fixed_Point_Theorems_for_Expansive_Mappings_in_Multiplicative_Metric_Spaces
