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Open Access ·Peer-reviewed·ISSN (Online): 2169-012X·ISSN (Print): 0972-0502

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Open Access Research Article

Fixed point theorem over orthogonal vector metric space and application for solve integral equation

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pp. 1021–1030Vol. 28Issue 3-BApril 2025DOI: 10.47974/JIM-2011XML
Received:
15 Oct 2024
Published Online:
08 May 2025
Article type:
Research Article
Language:
EN
Article no.:
JIM-2011
Pages:
1021–1030

Abstract

This research introduces the concept of an orthogonal set and explores the idea of orthogonality within the setting of a vector metric space. In addition, we provide fixed point theorems for the proposed concept and provide illustrated examples to demonstrate that our conclusions effectively generalize existing findings in the literature. In addition, the primary results are utilized to establish fixed point solutions for orthogonal in vector metric space. In addition, a unique and specific solution was created for the orthogonal shape in the vector space that we mentioned earlier. Finally, a solution to a problem was discovered through practical application.

Keywords

Subject Classifications

31A1033E30

References

[1] C. Cevik, and I. Altun, “Vector metric spaces and some properties”, Topol. Method Nonl. An. (2009).
[2] C. Cevik ,“On the continuity of functions between vector metric space,” Hindawi Pub. Corporation, J. Funct. Space, (2014).
[3] I. Altun, and C. Cevik, “Some common fixed point theorem in vector metric space” Filomat, (2011).
[4] K. Javed, H. Aydi, F. Uddin and M. Arshad, “On orthogonal partial b- metric spaces with an application,” Journal of Mathematics, (2021).   
[5] M. Gordgi, M. Ramezani, M. De La Sen, and Y. Cho, “On orthogonal sets and banach fixed point theorem”. Fixed point theory, (2017).
[6] M. Eshaghi, and H. Habibi, “Fixed point theory in generalized orthogonal metric space,” Journal of Linear and Topological Algebra, (2017).
[7] M. Kamra, S. Karma, and K. Sarita, “Some fixed-point theorems for self-mappings on vector b- metric space,” Global Journal of Pure and Applied Mathematics, (2018).
[8] O.Yamaod and W. Sintunavarat, On new orthogonal contractions in b-metric spaces, International Journal of Pure Mathematics, (2018).
[9] Z. Abood, “Convergence order –unit of vector metric space”, Journal of Karbala un. (2017).
[10] M. Eshaghi Gordji, M. Ramezani, M. De La Sen, and Y. J. Cho, “On orthogonal sets and Banach fixed point theorem,” Fixed Point Theory, vol. 18, no. 2, pp. 401-412 (2017).
[11]  K. Javed, H. Aydi, F. Uddin, and M. Arshad, “On orthogonal partial b-metric spaces with an application,” Journal of Mathematics, vol. 53, no. 2, pp. 1-13 (2021).
[12] O. Yamaod and W. Sintunavarat, “On new orthogonal contractions in b-metric spaces,” International Journal of Pure Mathematics, vol. 120, no. 4, pp. 537-548 (2018).
[13] J. R. Morales and E. M. Rojas, “Fixed point theorems for set-valued contractions in metric spaces,” Fixed Point Theory Appl., vol. 2013, no. 1, pp. 1-12 (2013).
[14] A. Amini-Harandi, “Endpoints of set-valued contractions in metric spaces,” Nonlinear Anal., vol. 72, no. 3-4, pp. 1328-1334 (2010).
[15] S. Czerwik, “Nonlinear set-valued contraction mappings in b-metric spaces,” Atti Sem. Mat. Fis. Univ. Modena, vol. 46, no. 2, pp. 263-276 (1998).
[16] M. Burhanuddin, “Assessing the vulnerability of quantum cryptography systems to emerging cyber threats,” SHIFRA, pp. 26–33 (2023). doi: 10.70470/SHIFRA/2023/004
[17] M. M. Abbood, H. H. Ebrahim, A. Al-Fayadh, and A. J. Obaid, “Measure defined on Γ-algebra and some of their generalizations,” Journal of Interdisciplinary Mathematics, vol. 26, no. 5, pp. 821–827 (2023). doi: 10.47974/JIM-1502
[18] M. H. Alobaidi, I. S. Ahmed, and S. H. Asaad, “Study of the generalized P-contractions on banach spaces and uniqueness for stability fixed points,” Int. J. Nonlinear Anal. Appl., vol. 12, no. 2, pp. 1903–1908 (2021), doi: 10.22075/IJNAA.2021.5324.
[19] A. S. Mohammed, I. S. Ahmed, and S. H. Asaad, “Study of the rings in which each element express as the sum of an idempotent and pure,” Int. J. Nonlinear Anal. Appl., vol. 12, no. 2, pp. 1719–1724 (2021), doi: 10.22075/IJNAA.2021.5311.

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