New common fixed point theorems for quartet mappings on orthogonal \(\mathcal{S}\)-metric spaces with applications

Volume 38, Issue 1, pp 80--97 https://dx.doi.org/10.22436/jmcs.038.01.06

Publication Date: November 21, 2024 Submission Date: June 29, 2024 Revision Date: September 02, 2024 Accteptance Date: September 17, 2024

Download PDF

Download XML

• Export citations
  • CITATIONS & REFERENCES
  • EndNote (.ENW)
  • Mendeley, JabRef (.BIB)
  • Papers, Zotero, Reference Manager, RefWorks (.RIS)
  • ARTICLE CITATION
  • EndNote (.ENW)
  • Mendeley, JabRef (.BIB)
  • Papers, Zotero, Reference Manager, RefWorks (.RIS)
  • REFERENCES
  • EndNote (.ENW)
  • Mendeley, JabRef (.BIB)
  • Papers, Zotero, Reference Manager, RefWorks (.RIS)

• 60 Downloads
• 316 Views

Authors

B. W. Samuel - Department of Mathematics, Saveetha School of Engineering, Saveetha Institute of Medical and Technical Sciences, Saveetha University, Chennai, 602105, Tamilnadu, India. G. Mani - Department of Mathematics, Saveetha School of Engineering, Saveetha Institute of Medical and Technical Sciences, Saveetha University, Chennai, 602105, Tamilnadu, India. P. Ganesh - Department of Mathematics, St. Joseph's College of Engineering, Chennai-119, Tamil Nadu, India. S. T. M. Thabet - Department of Mathematics, Saveetha School of Engineering, Saveetha Institute of Medical and Technical Sciences, Saveetha University, Chennai, 602105, Tamilnadu, India. - Department of Mathematics, Radfan University College, University of Lahej, Lahej, Yemen. - Department of Mathematics, College of Science, Korea University, 145 Anam-ro, Seongbuk-gu, Seoul 02814, Republic of Korea. I. Kedim - Department of Mathematics, College of Science and Humanities in Al-Kharj, Prince Sattam Bin Abdulaziz University, Al-Kharj 11942, Saudi Arabia. M. Vivas-Cortez - Faculty of Exact and Natural Sciences, School of Physical Sciences and Mathematics, Pontifical Catholic University of Ecuador, Av. 12 de octubre 1076 y Roca, Apartado Postal 17-01-2184, Sede Quito, Ecuador.

Abstract

In this article, we extend the scope of fixed point theory by proving a common fixed point theorem applicable to quartet mappings defined on orthogonal \(\mathcal{S}\)-metric spaces. Our theorems establish conditions under which the quartet mappings \(\Phi, \Psi, \mathcal{H}\), and \(\mathcal{K}\) are orthogonal preserving, orthogonal continuous, and pairwise compatible mappings, possess a unique common fixed point. To elucidate the practical implications of our theoretical result, we present a concrete example illustrating its application. Finally, we demonstrate the versatility of our theorem by applying it to establish the existence and uniqueness of solutions for Volterra-type integral system, production-consumption equilibrium and fractional differential equations.

Share and Cite

Keywords

• Compatible mappings
• \(\mathcal{S}\)-metric space
• orthogonal metric spaces
• orthogonal \(\mathcal{S}\)-metric space
• common fixed point

MSC

•  47H10
•  45D05

References

• [1] T. Abdeljawad, S. T. M. Thabet, I. Kedim, M. I. Ayari, A. Khan, A higher-order extension of Atangana-Baleanu fractional operators with respect to another function and a Gronwall-type inequality, Bound. Value Probl., 2023 (2023), 16 pages
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [2] O. K. Adewale, C. Iluno, Fixed point theorems on rectangular S-metric spaces, Sci. Afr., 16 (2022), 10 pages
  • View Article
  • Google Scholar


• [3] J. M. Afra, Double contraction in S-metric spaces, Int. J. Math. Anal., 9 (2015), 117–125
  • View Article
  • Google Scholar


• [4] P. Amiri, M. E. Samei, Existence of Urysohn and Atangana-Baleanu fractional integral inclusion systems solutions via common fixed point of multi-valued operators, Chaos Solitons Fractals, 165 (2022), 17 pages
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [5] S. Banach, Sur les opérations dans les ensembles abstraits et leur application aux équations intégrales, Fund. Math., 3 (1922), 133–181
  • View Article
  • MathSciNet
  • Google Scholar


• [6] I. Beg, G. Mani, J. Arul, Fixed point of orthogonal F-Suzuki contraction mapping on O-complete b-metric spaces with applications, J. Funct. Spaces, 2021 (2021), 12 pages
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [7] P. Chouchan, N. Malviya, A common unique fixed point theorem for expansive type mappings in S-metric spaces, Int. Math. Forum, 8 (2013), 1287–1293
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [8] N. V. Dung, N. T. Hieua, S. Radojevi´, Fixed point theorems for g-monotone maps on partially ordered S-metric spaces, Filomat, 28 (2014), 1885–1898
  • View Article
  • MathSciNet
  • Google Scholar


• [9] Z. Eivazi Damirchi Darsi Olia, M. Eshaghi, D. Ebrahimi Bagha, Banach fixed point theorem on incomplete orthogonal S-metric spaces, Int. J. Nonlinear Anal. Appl., 14 (2021), 151–157
  • View Article
  • Google Scholar


• [10] M. Eshaghi Gordji, H. Habibi, Fixed Point theory in generalized orthogonal metric space, J. Linear Topol. Algebra, 6 (2017), 251–260
  • View Article
  • Google Scholar
  • MATH


• [11] A. Gholidahneh, S. Sedghi, T. Doˇsenovi´c, S. Radenovi´c, Ordered S-metric spaces and coupled common fixed point theorems of integral type contraction, Math. Interdiscip. Res., 2 (2017), 71–84
  • View Article
  • Google Scholar


• [12] A. J. Gnanaprakasam, G. Mani, O. Ege, A. Aloqaily, N. Mlaiki, New fixed point results in orthogonal b-metric spaces with related applications, Mathematics, 11 (2023), 18 pages
  • View Article
  • Google Scholar


• [13] A. J. Gnanaprakasam, G. Mani, V. Parvaneh, H. Aydi, Solving a nonlinear Fredholm integral equation via an orthogonal metric, Adv. Math. Phys., 2021 (2021), 8 pages
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [14] M. E. Gordji, M. Rameani, M. De La Sen, Y. J. Cho, On orthogonal sets and Banach fixed point theorem, Fixed Point Theory, 18 (2017), 569–578
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [15] A. Gupta, Cyclic contraction on S-metric spaces, Int. J. Anal., Appl., 3 (2013), 119–130
  • View Article
  • Google Scholar
  • MATH


• [16] H. A. Hammad, R. A. Rashwan, A. Nafea, M. E. Samei, S. Noeiaghdam, Stability analysis for a tripled system of fractional pantograph differential equations with nonlocal conditions, J. Vib. Control, 30 (2024), 632–647
  • View Article
  • MathSciNet
  • Google Scholar


• [17] M. Houas, M. E. Samei, Existence and stability of solutions for linear and nonlinear damping of q-fractional Duffing- Rayleigh problem, Mediterr. J. Math., 20 (2023), 28 pages
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [18] S. A. Khandait, R. Bhardwaj, C. Singh, Common Fixed Point Theorems in Soft S-Metric Spaces, Anusandhan– Rabindranath Tagore Univ. J., 10 (2021), 2400–2405
  • View Article
  • Google Scholar


• [19] T. Kherraz, M. Benbachir, M. Lakrib, M. E. Samei, M. K. A. Kaabar, S. A. Bhanotar, Existence and uniqueness results for fractional boundary value problems with multiple orders of fractional derivatives and integrals, Chaos Solitons Fractals, 166 (2023), 10 pages
  • View Article
  • MathSciNet
  • Google Scholar


• [20] J. K. Kim, S. Sedghi, A. Gholidahneh, M. Mahdi Rezaee, Fixed point theorems in S-metric spaces, East Asian Math. J., 32 (2016), 677–684
  • View Article
  • Google Scholar


• [21] J. U. Maheswari, K. Dillibabu, G. Mani, S. T. M. Thabet, I. Kedim, M. Vivas-Cortez, On new common fixed point theorems via bipolar fuzzy b-metric space with their applications, PLoS ONE, 19 (2024), 17 pages
  • View Article
  • Google Scholar


• [22] G. Mani, S. Chinnachamy, S. Palanisamy, S. T. M. Thabet, I. Kedim, M. Vivas-Cortez, Efficient techniques on bipolar parametric v-metric space with application, J. King Saud Univ. Sci., 36 (2024), 7 pages
  • View Article
  • Google Scholar


• [23] G. Mani, A. J. Gnanaprakasam, K. Javed, S. Kumar, On Orthogonal Coupled Fixed Point Results with an Application, J. Funct. Spaces, 2022 (2022), 7 pages
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [24] G. Mani, A. J. Gnanaprakasam, C. Park, S. Yun, Orthogonal F-contractions on O-complete b-metric space, AIMS Math., 6 (2021), 8315–8330
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [25] G. Mani, S. Haque, A. J. Gnanaprakasam, O. Ege, N. Mlaiki, The Study of bicomplex-valued controlled metric spaces with applications to fractional differential equations, Mathematics, 11 (2023), 19 pages
  • View Article
  • Google Scholar


• [26] G. Mani, P. Subbarayan, Z. D. Mitrovi´c, A. Aloqaily, N. Mlaiki, Solving some integral and fractional differential equations via neutrosophic pentagonal metric space, Axioms, 12 (2023), 30 pages
  • View Article
  • Google Scholar


• [27] M. M. Matar, M. E. Samei, S. Etemad, A. Amara, S. Rezapour, J. Alzabut, Stability analysis and existence criteria with numerical illustrations to fractional jerk differential system involving generalized Caputo derivative, Qual. Theory Dyn. Syst., 23 (2024), 36 pages
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [28] N. Mlaiki, N. Y. Özgür, N. Ta¸, New Fixed-Point Theorems on an S-metric Space via Simulation Functions, Mathematics, 7 (2019), 13 pages
  • View Article
  • Google Scholar


• [29] K. Muthuvel, K. Kaliraj, K. S. Nisar, V. Vijayakumar, Relative controllability for ψ-Caputo fractional delay control system, Results Control Optim., 16 (2024), 16 pages
  • View Article
  • Google Scholar


• [30] G. Nallaselli, A. J. Gnanaprakasam, G. Mani, Z. D. Mitrovi´c, A. Aloqaily, N. Mlaiki, Integral equation via fixed point theorems on a new type of convex contraction in b-metric and 2-metric spaces, Mathematics, 11 (2023), 18 pages
  • View Article
  • Google Scholar


• [31] K. S. Nisar, A constructive numerical approach to solve the Fractional Modified Camassa–Holm equation, Alex. Eng. J., 106 (2024), 19–24
  • View Article
  • Google Scholar


• [32] S. S. Santra, P. Mondal, M. E. Samei, H. Alotaibi, M. Altanji, T. Botmart, Study on the oscillation of solution to second-order impulsive systems, AIMS Math., 8 (2023), 22237–22255
  • View Article
  • MathSciNet
  • Google Scholar


• [33] S. Sedghi, I. Altun, N. Shobe, M. A. Salahshour, Some properties of S-metric spaces and fixed point results, Kyungpook Math. J., 54 (2014), 113–122
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [34] S. Sedghi, N. V. Dung, Fixed point theorems on S-metric spaces, Mat. Vesnik, 66 (2014), 113–124
  • View Article
  • Google Scholar


• [35] S. Sedghi, A. Gholidahneh, T. Došenovi´c, J. Esfahani, S. Radenovi´, Common fixed point of four maps in Sb-metric spaces, J. Linear Topol. Algebra, 5 (2016), 93–104
  • View Article
  • Google Scholar


• [36] S. Sedghi, N. Shobe, Common fixed point theorems for four mappings in complete metric spaces, Bull. Iranian Math. Soc., 33 (2007), 37–47
  • View Article
  • Google Scholar
  • MATH


• [37] S. Sedghi, N. Shobe, A. Aliouche, A generalization of fixed point theorems in S-metric spaces, Mat. Vesnik, 64 (2012), 258–266
  • View Article
  • Google Scholar
  • MATH


• [38] S. Sedghi, N. Shobe, T. Doˇsenovi´c, Fixed point results in S-metric spaces, Nonlinear Funct. Anal. Appl., 20 (2015), 55–67
  • View Article
  • Google Scholar
  • MATH


• [39] S. Sedghi, N. Shobkolaei, M. Shahraki, T. Doˇsenovi´c, Common fixed point of four maps in S-metric spaces, Math. Sci. (Springer), 12 (2018), 137–143
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [40] M. Shabibi, M. E. Samei, M. Ghaderi, S. Rezapour, Some analytical and numerical results for a fractional q-differential inclusion problem with double integral boundary conditions, Adv. Difference Equ., 2021 (2021), 17 pages
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [41] S. T. M. Thabet, S. Al-S ´ adi, I. Kedim, A. S. Rafeeq, S. Rezapour, Analysis study on multi-order ρ-Hilfer fractional pan-tograph implicit differential equation on unbounded domains, AIMS Math., 8 (2023), 18455–18473
  • View Article
  • Google Scholar


• [42] A. A. Thirthar, H. Abboubakar, A. L. Alaoui, K. S. Nisar, Dynamical behavior of a fractional-order epidemic model for investigating two fear effect functions, Results Control Optim., 16 (2024), 21 pages
  • View Article
  • Google Scholar


• [43] S. K. Tiwari, S. K. Mishra, A Common fixed point theorem in S-metric space, Wesley. J. Res., 14 (2021), 170–174
  • View Article
  • Google Scholar