Based on Dominate Function Common Coupled Invariant Point Theorems for Weakly Compatible Mappings in Parametric Metric Spaces
Keywords:
Contractive conditions, Coupled–invariant point, Dominates function, Parametric space, Weakly compatible mappingAbstract
In this research, they develop various common and common coupled – invariant point (CIP) theorems for weakly compatible mappings using the dominate function for rational contractive constraints in the context of a complete parametric measuring space. This framework provides a flexible setting for studying nonlinear issues in fixed-point theory. Derive the existence and distinctiveness of coupled invariant points (CIP) for a mapping by introducing rational contractive using maximum and nonlinear terms, which greatly expands the range of classical contraction principles. With this novel condition, they are able to demonstrate that there are unique coupled invariant points for a different mapping. Results pertaining to the fixed–point concept in parametric measurement (metric) spaces have been presented in academia. To ensure the accuracy of the stated theorems, a demonstration is also included. Furthermore, they present an appropriate example that validates the established theorems and illustrates their prospective use in associated mathematical concerns in order to show how the results can be utilized.
References
N. Hussain, S. Khaleghizadeh, P. Salimi, et al., “A new approach to fixed point results in triangular intuitionistic fuzzy metric spaces,” Abstract and Applied Analysis, 2014.K. P. R.
Rao, D. V. Babu, and E. T. Ramudu, “Some unique common fixed-point theorems in parametric S-metric space,” International Journal of Innovative Research in Science, Engineering and Technology, vol. 3, no. 7, pp. 14375–14387, 2014.
N. Hussain, P. Salimi, and V. Parvaneh, “Fixed point results for various contractions in parametric and fuzzy b-metric spaces,” Journal of Nonlinear Sciences and Applications, vol. 8, pp. 719–739, 2015.
R. Krishnakumar and N. P. Sanaatammappa, “Fixed point theorem in parametric metric space,” International Journal of Mathematics Research, vol. 8, pp. 213–220, 2016.
R. D. Daheriya, R. Jain, and M. Ughade, “Fixed point, coincidence point and common fixed point theorems under various expansive conditions in parametric metric space and parametric b-metric spaces,” Gazi University Journal of Science, vol. 29, no. 1, pp. 95–107, 2016.
R. D. Daheriya, S. Shrivastva, and M. Ughade, “Parametric metric space, parametric b-metric space and expansive type mapping,” International Journal of Mathematics and Its Applications, vol. 4, pp. 107–117, 2016.
N. Priyobarta, Y. Rohen, and R. Stojan, “Fixed point theorems on parametric A-metric spaces,” American Journal of Applied Mathematics and Statistics, vol. 6, pp. 1–5, 2018.
N. Tas and N. Y. Ozgur, “On parametric S-metric spaces and fixed point type theorems for expansive mapping,” Journal of Mathematics, 2016.
N. Tas and N. Y. Ozgur, “Some fixed point results on parametric Nb-metric space,” Communications of the Korean Mathematical Society, vol. 33, pp. 943–960, 2018.
E. Ozgur and M. De la Sen, “A new perspective on parametric metric spaces,” Mathematics, vol. 7, no. 11, p. 1008, 2019.
U. Singh and N. Singh, “A new presumptive on parametric metric space via C-class function,” Sambodhi (UGC Care Scopus Journal), vol. 43, no. 4, 2020.
A. K. Garg et al., “Parametric metric space and fixed point theorems,” International Journal of Research in Applied, Natural and Social Sciences, vol. 10, no. 8, 2022.
Bharathi, M. V. R. Kameswari, and B. Padmavathi, “Coupled fixed points in bicomplex partial metric space and an application,” European Chemical Bulletin, vol. 12, no—10, pp. 5510–5520, 2023.
A. H. Ansari, J. Kumar, and S. Vashistha, “C-class function on common fixed point theorem of weakly compatible maps in partial metric space,” International Journal of Advances in Mathematics, vol. 3, pp. 15–23, 2019.
H. Ansari, “Note on Φ-Φ-contractive type mapping and related fixed point theorem,” in Proceedings of the 2nd Regional Conference on Mathematics and Applications, Payame Noor University, Tehran, Iran, pp. 377–380, 2014.
B. S. Choudhary and P. Maity, “Coupled fixed point theorem in generalized metric spaces,” Mathematical and Computer Modelling, vol. 54, pp. 73–79, 2011.
R. Choudhary and A. K. Garg, “Fixed point results in parametric metric space,” International Journal on Emerging Technologies, vol. 10, no. 2b, pp. 100–104, 2019.
D. Venkatesh and V. Nagaraju, “Some fixed point results in bicomplex valued metric spaces,” Mathematics and Statistics, vol. 10, no. 6, pp. 1334–1339, 2022.
E. Ozgur and I. Karaca, “Fixed point theorems and an application in parametric metric space,” Azerbaijan Journal of Mathematics, vol. 7, no. 1, pp. 27–39, 2017.
G. S. Saluja, “Coupled fixed point results based on control function in complex partial metric spaces,” Functional Analysis, Approximation and Computation, vol. 15, no. 2, pp. 1–15, 2023.
R. Krishnakumar and N. P. Sanaatammappa, “Some fixed point theorem in parametric b-metric space,” International Journal of Mathematical Sciences and Engineering Applications, vol. 10, pp. 99–106, 2016.
S. Likhitkar, R. D. Daheriya, and M. Ughade, “Common fixed point theorems in parametric metric space under nonlinear type contractions,” International Journal of Mathematical Archive, vol. 7, pp. 105–109, 2016.
M. Gunaseelan, G. Arul Joseph, J. Khalil, et al., “Solving a Fredholm integral equation via coupled fixed point on bicomplex partial metric space,” AIMS Mathematics, vol. 7, no. 8, pp. 15402–15416, 2022.
M. Mohammod et al., “Coupled fixed point theorem and dislocated quasi-metric space,” International Journal of Pure and Applied Mathematics, vol. 119, no. 10, pp. 1249–1260, 2018.
R. Namdev, R. Tiwari, U. Singh, and R. Bhardwaj, “Coupled invariant point theorems in bicomplex parametric partial metric space amongst dominate function,” Communications in Mathematics and Applications, vol. 15, no. 2, p. 511, 2024.
H. Posul and S. Kukukcu, “On parametric spaces,” Bulletin of Mathematics and Statistics Research, vol. 5, pp. 17–20, 2017.
S. Poornavel, N. Balamurugan, and H. A. Hammad, “Some common fixed point theorems on tricomplex valued parametric metric space,” Annals of Mathematics and Computer Science, vol. 20, pp. 120–134, 2024.
W. Shatanawi, M. Abbas, and T. Nazir, “Common coupled coincidence and coupled fixed point results in two generalized metric spaces,” Fixed Point Theory and Applications, vol. 2011, article 80, 2011.
W. Shatanawi, “Coupled fixed point theorem in generalized metric spaces,” Hacettepe Journal of Mathematics and Statistics, vol. 40, pp. 441–447, 2011.
U. Singh et al., “Fixed point theorems on parametric metric space and b-parametric metric spaces,” International Journal of Engineering Research in Current Trends, vol. 2, no. 5, 2020.
T. G. Bhaskar and V. Lakshmikantham, “Fixed point theorems in partially ordered metric spaces and applications,” Nonlinear Analysis: Theory, Methods and Applications, vol. 65, no. 7, pp. 1379–1393, 2005.
