Multivalued (θ; г)-generalized contraction in strong b-metric spaces with order structure
Sandeep Kaursandeepkaursandiii@gmail.comDepartment of MathematicsUniversity Institute of Sciences (UIS)Chandigarh UniversityMohali, Punjab, 140413, IndiaView full profile → , Naveen Maninaveenmani81@gmail.comDepartment of MathematicsUniversity Institute of Sciences (UIS)Chandigarh UniversityMohali, Punjab, 140413, IndiaView full profile → , *Amit SharmaCorresponding authordba.amitsharma@gmail.comDepartment of MathematicsAmity University HaryanaGurugram, Haryana, 122413, IndiaView full profile →
* Corresponding author · click or hover a name for details
- Received:
- 01 Feb 2026
- Published Online:
- 25 Aug 2026
- Article type:
- Research Article
- Language:
- EN
- Article no.:
- JIM-2643
- Pages:
- 2573–2581
Abstract
This paper establishes fixed-point theorems for multivalued mappings in the setting of complete partially ordered strong b-metric spaces. By employing appropriate rational contractive conditions together with suitable auxiliary functions, the obtained results extend and unify some well-known fixed-point theorems of literature. An illustrative example is presented to demonstrate and validated the applicability of the proposed result in theoretical framework.
Keywords
Subject Classifications
References
[1] Y. I. Alber and S. Guerre-Delabriere, “Principle of weakly contractive maps in Hilbert spaces,” in New Results in Operator Theory and Its Applications, vol. 98, pp. 7-22 (1997).
[2] B. E. Rhoades, “Some theorems on weakly contractive maps,” Nonlinear Analysis: Theory, Methods & Applications, vol. 47, no. 4, pp. 2683-2693 (2001).
[3] V. Bhardwaj, V. Gupta, and N. Mani, “Common fixed point theorems without continuity and compatible property of maps,” Bol. Soc. Parana. Mat., vol. 35, no. 3, pp. 67-77 (2017).
[4] N. Mani, A. Sharma, and R. Shukla, “Fixed point results via real valued function satisfying integral type rational contraction,” Abstract and Applied Analysis, vol. 2023, Art. no. 2592507 (2023).
[5] M. S. Khan, M. Swaleh, and S. Sessa, “Fixed point theorems by altering distances between the points,” Bull. Aust. Math. Soc., vol. 30, no. 1, pp. 1-9 (1984).
[6] W. A. Kirk and N. Shahzad, Fixed Point Theory in Distance Spaces. Cham, Switzerland: Springer (2014).
[7] B. S. Choudhury and N. Metiya, “Multivalued and singlevalued fixed point results in partially ordered metric spaces,” Arab. J. Math. Sci., vol. 17, no. 2, pp. 135-151 (2011).
[8] N. Mani, V. Gupta, A. Kanwar, and R. Bhardwaj, “Generalized Fδ-contractions and multivalued common fixed point theorems,” Proc. Jangjeon Math. Soc., vol. 21, no. 4, pp. 703-708 (2018).
[9] I. A. Bakhtin, “The contraction mapping principle in quasi-metric spaces,” Functional Analysis, vol. 30, pp. 26-37 (1989).
[10] S. Czerwik, “Contraction mappings in b-metric spaces,” Acta Math. Inform. Univ. Ostraviensis, vol. 1, pp. 5-11 (1993).
[11] H. Doan, “A new type of Kannan’s fixed point theorem in strong b-metric spaces,” AIMS Mathematics, vol. 6, no. 8, pp. 7895-7908 (2021).
[12] N. Kumari, S. Rathee, and P. Mor, “Fixed point theorems in strong partial b-metric spaces,” Bull. Math. Anal. Appl., vol. 15, no. 1, pp. 14-31 (2023).
[13] Anjana, N. Mani, A. Sharma, and M. S. Pingale, “Fixed points theorems for generalized Cβψ-rational contraction mapping in relational metric space,” J. Interdiscip. Math., vol. 27, no. 8, pp. 1787-1795 (2024).
[14] S. S. Chauhan, P. Tyagi, and N. Mani, “Rational contraction mapping in F-modular b-metric spaces,” J. Interdiscip. Math., vol. 27, no. 8, pp. 1781-1786 (2024).
[15] I. Beg and A. R. Butt, “Common fixed point for generalized set valued contractions satisfying an implicit relation in partially ordered metric spaces,” Math. Commun., vol. 15, no. 1, pp. 65-76 (2010).




