i-manager Publications

A Common Fixed-Point Theorem for Semi-Compatible Mappings in a Complete Metric Space of an Implicit Relation via Inverse C-Class Functions

T. Rakesh Singh*

Department of Mathematics, Aurora Higher Education and Research Academy, Hyderabad, Telangana, India.

Periodicity:July - December'2025

Abstract

The aim of the paper is to obtain a common fixed-point theorem in a complete metric space through inverse C-class functions for six self-maps in. The result extends previous work by incorporating semi-compatible and reciprocally continuous pairs of mappings, along with commutatively conditions. A generalized contraction condition involving an implicit relation ensures convergence to a unique common fixed point. The results generalizes and improves upon the main results, contributing to the broader framework of fixed-point theory.

Keywords

Common Fixed-point, Metric Space, Inverse C-Class Function.

How to Cite this Article?

Singh, T. R. (2025). A Common Fixed-Point Theorem for Semi-Compatible Mappings in a Complete Metric Space of an Implicit Relation via Inverse C-Class Functions. i-manager’s Journal on Mathematics, 14(2), 14-20.

References

[1]. Abbas, M., Gopal, D., & Radenovic, S. (2013). A note on recently introduced commutative conditions. Indian Journal of Mathematics, 55(2), 195-201.

[2]. Alghamdi, M. A., Radenović, S., & Shahzad, N. (2012). On some generalizations of commuting mappings. In Abstract and Applied Analysis, 1, 952052. Hindawi Publishing Corporation.

[3]. Al-Thagafi, M. A., & Shahzad, N. (2008). Generalized I-nonexpansive selfmaps and invariant approximations. Acta Mathematica Sinica, English Series, 24(5), 867-876.

[4]. Ansari, A. H. (2014). Note on ϕ-ψ-contractive type mappings and related fixed point. In The 2nd Regional Conference on Mathematics and Applications, Payame Noor University, 11, 377-380.

[5]. Ansari, A. H., Popa, V., Singh, Y. M., & Khan, M. S. (2020). Fixed point theorems of an implicit relation via C-class function in metric spaces. Journal of Advanced Mathematical Studies, 13(1), 1-10.

[6]. Banach, S. (1922). Sur les opérations dans les ensembles abstraits et leur application aux équations intégrales. Fundamenta Mathematicae, 3(1), 133-181.

[7]. Djoudi, A. (2003). A unique common fixed point for compatible mappings of type (B) satisfying an implicit relation. Demonstratio Mathematica, 36(3), 763-770.

[8]. Hussain, N., Shah, M. H., & Radenović, S. (2011). Fixed points of weakly contractions through occasionally weak compatibility. Journal of Computational Analysis & Applications, 13(3), 532.

[9]. Ivković, S. (2020). On various generalizations of semi-A-Fredholm operators. Complex Analysis and Operator Theory, 14(3), 41.

[10]. Jungck, G. (1986). Compatible mappings and common fixed points. International Journal of Mathematics and Mathematical Sciences, 9(4), 771-779.

[11]. Jungck, G., & Rhoades, B. E. (1998). Fixed points for set valued functions without continuity. Indian Journal of Pure and Applied Mathematics, 29, 227-238.

[12]. Jungck, G., Murthy, P. P., & Cho, Y. J. (1993). Compatible mappings of type (A) and common fixed points. Mathematica Japonica, 38(2), 381-390.

[13]. Pathak, H. K., & Khan, M. S. (1995). Compatible mappings of type (B) and common fixed point theorems of Greguš type. Czechoslovak Mathematical Journal, 45(4), 685-698.

[14]. Pathak, H. K., Chang, S. S., & Cho, Y. J. (1994). Fixed point theorems for compatible mappings of type (P). Indian Journal of Mathematics, 36(2), 151-166.

[15]. Pathak, H. K., Cho, Y. J., & Kang, S. M. (1998). Compatible mappings of type (C) and common fixed point theorems of Gregus type. Demonstratio Mathematica, 31(3), 499-518.

[16]. Saleem, N., Ansari, A. H., & Jain, M. K. (2018). Some fixed point theorems of inverse C-class function under weak semi compatibility. J. Fixed Point Theory, 9, 1-23.

[17]. Saluja, A. S., & Jain, M. K. (2013). Fixed point theorems under conditional semicompatibility with control function. Adv. Fixed Point Theory, 3(4), 648-666.

[18]. Saluja, A. S., Jain, M. K., & Jhade, P. K. (2012). Weak semi compatibility and fixed point theorems. Bulletin of International Mathematical Virtual Institute, 2, 205-217.

[19]. Sessa, S. (1982). On a weak commutativity condition of mappings in fixed point considerations. Publications de l'Institut Mathématique, 32(46), 149-153.

[20]. Singh, B., & Jain, S. (2005). Semi-compatibility, compatibility and fixed point theorems in fuzzy metric space. Journal of the Chungcheong Mathematical Society, 18(1), 1-1.

[21]. Singh, M. R., & Singh, Y. M. (2007). Compatible mappings of type (E) and common fixed point theorems of Meir-Keeler type. International Journal of Mathematical Sciences and Engineering Applications, 1(2), 299-315.

[22]. Zhou, M., Jain, M. K., Khan, M. S., Secelean, N. A., & Muscat, O. (2021). Semi-compatible mappings and common fixed point theorems of an implicit relation via inverse C− class functions. AIMS Mathematics, 6(3), 2636-2652.

	North Americas,UK, Middle East,Europe		India	Rest of world
	USD	EUR	INR	USD-ROW
Pdf	35	35	200	20
Online	15	15	200	15
Pdf & Online	35	35	400	25

A Common Fixed-Point Theorem for Semi-Compatible Mappings in a Complete Metric Space of an Implicit Relation via Inverse C-Class Functions

Abstract

Keywords

How to Cite this Article?

References

If you have access to this article please login to view the article or kindly login to purchase the article

Purchase Instant Access

Options for accessing this content: