---

Discontinuity, Nonlinearity, and Complexity 14(4) (2025) 647--658 | DOI:10.5890/DNC.2025.12.003

Smita Sonker$^{1,2}$, Sonia$^{1}$

$^{1}$ Department of Mathematics, National Institute of Technology Kurukshetra-136119, India $^{2}$ School of Physical Sciences, Jawaharlal Nehru University, New Delhi-110067, India

Download Full Text PDF

 

Abstract

In this study, we employ rational expression techniques via $\mathcal{F}$-contractions to establish fixed point theorems within the context of an orthogonal complete metric space. We extend and generalize several established results from prior literature. Additionally, we provide illustrative examples to validate the robustness of our findings. Moreover, our results facilitate the determination of unique solutions for both differential and integral equations.

References

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

2. [2]	Reich, S. (1971), Some remarks concerning contraction mappings, Canadian Mathematical Bulletin, 14(1), 121-124.

3. [3]	Shatanawi, W., Rajic, V. C., Radenovic, S., and Al-Rawashdeh, A. (2012), Mizoguchi-Takahashi-type theorems in tvs-cone metric spaces, Fixed Point Theory and Applications, 2012, 1-7.

4. [4]	Shatanawi, W. and Al-Rawashdeh, A. (2012), Common fıxed points of almost generalized $(\phi,\psi)$-contractive mappings in ordered metric spaces, Fixed Point Theory and Applications, 2012, 1-14.

5. [5]	Shatanawi, W., Al-Rawashdeh, A., Aydi, H., and Nashine, H.K. (2012), On a fixed point for generalized contractions in generalized metric spaces, In Abstract and Applied Analysis 2012(1), 246085.

6. [6]	Bianchini, R.T. (1972), Su un problema di S. Reich riguardonte la teoria dei punti fissi, Bollettino dell'Unione Matematica Italiana, 5, 103-108.

7. [7]	Ćirić, L.B. (1974), A generalization of Banach's contraction principle, Proceedings of the American Mathematical Society, 45(2), 267-273.

8. [8]	Acar, O. and Altun, I. (2014), A fixed point theorem for multivalued mappings with-distance, Abstract and Applied Analysis, 1-5.

9. [9]	Ahmad, J., Al-Rawashdeh, A.S., and Azam, A. (2014), Fixed point results for ($\alpha,\xi$)-expansive locally contractive mappings, Journal of Inequalities and Applications, 2014(1), 1-10.

10. [10]	Shukla, A., Sukavanam, N., and Pandey, D.N. (2016), Complete controllability of semilinear stochastic systems with delay in both state and control, Mathematical Reports, 18(2), 247-259.

11. [11]	Shukla, A., Sukavanam, N., and Pandey, D.N. (2015), Complete controllability of semi-linear stochastic system with delay, Rendiconti del Circolo Matematico di Palermo (1952-), 64, 209-220.

12. [12]	Patel, R., Shukla, A., and Jadon, S.S. (2020), Existence and optimal control problem for semilinear fractional order $(1, 2]$ control system, Mathematical Methods in the Applied Sciences, 47(13), 10940-10951.

13. [13]	Shukla, A., Sukavanam, N., Pandey, D.N., and Arora, U. (2016), Approximate controllability of second-order semilinear control system, Circuits, Systems, and Signal Processing, 35, 3339-3354.

14. [14]	Wardowski, D. (2012), Fixed points of a new type of contractive mappings in complete metric spaces, Fixed point theory and applications, 2012(1), 1-6.

15. [15]	Wardowski, D. and Dung, N.V. (2014), Fixed points of $F$-weak contractions on complete metric spaces, Demonstratio Mathematica, 47(1), 146-155.

16. [16]	Abbas, M., Ali, B., and Romaguera, S. (2013), Fixed and periodic points of generalized contractions in metric spaces, Fixed Point Theory and Applications, 2013(1), 1-11.

17. [17]	Hussain, N. and Salimi Salimi, P. (2014), Suzuki-Wardowski type fixed point theorems for $\alpha-GF$-contractions, 1879-1895.

18. [18]	Batra, R. and Vashistha, S. (2014), Fixed points of an $F$-contraction on metric spaces with a graph, International Journal of Computer Mathematics, 91(12), 2483-2490.

19. [19]	Batra, R., Vashistha, S., and Kumar, R. (2014), A coincidence point therem for F-contractions on metric spaces equipped with an altered distance, Journal of Mathematics and Computer Science, 4(5), 826-833.

20. [20]	Dung, N.V. and Hang, V.T.L. (2015), A fixed point theorem for generalized $F$-contractions on complete metric spaces, Vietnam Journal of Mathematics, 43, 743-753.

21. [21]	Klim, D. and Wardowski, D. (2015), Fixed points of dynamic processes of set-valued F-contractions and application to functional equations, Fixed Point Theory and Applications, 2015(1), 1-9.

22. [22]	Secelean, N.A. (2013), Iterated function systems consisting of F-contractions, Fixed Point Theory and Applications, 2013(1), 1-13.

23. [23]	Cosentino, M. and Vetro, P. (2014), Fixed point results for $F$-contractive mappings of Hardy-Rogers-type, Filomat, 28(4), 715-722.

24. [24]	Gordji, M.E., Ramezani, M., De La Sen, M., and Cho, Y.J. (2017), On orthogonal sets and Banach fixed point theorem, Fixed Point Theory, 18(2), 569-578.

25. [25]	Sawangsup, K., Sintunavarat, W., and Cho, Y.J. (2020), Fixed point theorems for orthogonal F-contraction mappings on O-complete metric spaces, Journal of Fixed Point Theory and Applications, 22, 1-14.