GRAPHICAL VIEWS OF ORTHOGONAL $\mathfrak{M} $-METRIC SPACES WITH AN APPLICATION

Arul Joseph Gnanaprakasam; Haitham Qawaqneh; Senthil Kumar Prakasam; Gunaseelan Mani; Khalil Javed; Hassen Aydi

doi:10.11948/20260033

2026 Volume 16 Issue 6

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Arul Joseph Gnanaprakasam, Haitham Qawaqneh, Senthil Kumar Prakasam, Gunaseelan Mani, Khalil Javed, Hassen Aydi. GRAPHICAL VIEWS OF ORTHOGONAL $\mathfrak{M} $-METRIC SPACES WITH AN APPLICATION[J]. Journal of Applied Analysis & Computation, 2026, 16(6): 2962-2980. doi: 10.11948/20260033

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Arul Joseph Gnanaprakasam, Haitham Qawaqneh, Senthil Kumar Prakasam, Gunaseelan Mani, Khalil Javed, Hassen Aydi. GRAPHICAL VIEWS OF ORTHOGONAL $\mathfrak{M} $-METRIC SPACES WITH AN APPLICATION[J]. Journal of Applied Analysis & Computation, 2026, 16(6): 2962-2980. doi: 10.11948/20260033

GRAPHICAL VIEWS OF ORTHOGONAL $\mathfrak{M} $-METRIC SPACES WITH AN APPLICATION

1.
Department of Mathematics, College of Engineering and Technology, Faculty of Engineering and Technology, SRM Institute of Science and Technology, SRM Nagar, Kattankulathur 603203, Tamil Nadu, India
2.
Department of Basic Sciences, Al-Zaytoonah University of Jordan, Amman 11733, Jordan
3.
Department of Mathematics, Asan Memorial College of Engineering and Technology, Asan nagar, Chengalpattu-603105, Tamil Nadu, India
4.
Department of Mathematics, Vel Tech Rangarajan Dr. Sagunthala R&D Institute of Science and Technology, Chennai-600062, Tamil Nadu, India
5.
Department of Mathematics and Statistics, International Islamic University Islamabad, Islamabad 04436, Pakistan
6.
Université de Sousse, Institut Supérieur d'Informatique et des Techniques de Communication, H. Sousse 4000, Tunisia
7.
Department of Mathematics and Applied Mathematics, Sefako Makgatho Health Sciences University, Ga-Rankuwa, South Africa

Author Bio: Email: aruljoseph.alex@gmail.com(A. J. Gnanaprakasam); Email: kumarssenthil253@gmail.com(S. K. Prakasam); Email: mathsguna@yahoo.com(G. Mani); Email: khaliljaved15@gmail.com(K. Javed); Email: hassen.aydi@isima.rnu.tn(H. Aydi)
Corresponding author: Email: h.alqawaqneh@zuj.edu.jo(H. Qawaqneh)

Abstract

Abstract

In this paper, we present the concept of an orthogonal double controlled orthogonal $ \mathfrak{m} $-metric space by employing two control maps $ \alpha $ and $ \xi $ on right-hand side of the triangular inequality of $ \mathfrak{m} $-metric space. We also present an example to illustrate our results. Using the resulting conclusions, analytical solutions to integral equations have been discovered. A numerical solution is used to validate the analytical solutions.
- Fixed point /
- orthogonal double controlled orthogonal $\mathfrak{m}$-metric space /
- integral equation
MSC: 54H25, 46H20, 45B05, 45D05

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References

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