TARU PUBLICATIONS
Journal of Interdisciplinary Mathematics cover
Open Access ·Peer-reviewed·ISSN (Online): 2169-012X·ISSN (Print): 0972-0502

Monthly Journal: Publishes the methodological and theoretical role of mathematics and mathematical applications underpinning scientific research.

Issues up to 2022 co-published with and available at:Taylor & Francis Online
submissions@tarupublications.com
Open Access Research Article

A new form of hemivariational inequality system and its possible solutions

*

* Corresponding author · click or hover a name for details

pp. 771–779Vol. 28Issue 3-AApril 2025DOI: 10.47974/JIM-1972XML
Received:
08 May 2024
Published Online:
08 May 2025
Article type:
Research Article
Language:
EN
Article no.:
JIM-1972
Pages:
771–779

Abstract

This paper aims to show that there are solutions to a novel class of hemivariational inequalities (H.VI) whose results are described in a set of a reflexive Banach space X_n. The first section, we discuss the link between our inequality issues and equilibrium issues. The second uses some nonlinearity (H.VI) results for their extension.

Keywords

Subject Classifications

35J8839B7258E5070G7574M15

References

[1] G. Stampacchia, “Formes bilineaires coercitives sur les ensembles convexes,” Comptes Rendus Hebdomadaires des Séances de l’Académie des Sciences, vol. 258, no. 18, pp. 4413–4416 (1964).
[2] Z. Naniewicz and P. D. Panagiotopoulos, Mathematical Theory of Hemivariational Inequalities and Applications. New York: Marcel Dekker (1995).
[3] P. D. Panagiotopoulos, Hemivariational Inequalities: Applications to Mechanics and Engineering. Berlin: Springer (1993).
[4] P. D. Panagiotopoulos, “Nonconvex energy functions: Hemivariational inequalities and substationarity principles,” Acta Mechanica, vol. 48, no. 3-4, pp. 111–130 (1983).
[5] Y. Baia, N. Costea, and S. Zeng, “Existence results for variational-quasi-hemivariational inequality systems with nonlinear couplings,” (2023).
[6] I. Andrei and N. Costea, “Nonlinear hemivariational inequalities and applications to nonsmooth mechanics,” Advances in Nonlinear Variational Inequalities, vol. 13, no. 1, pp. 1–17 (2010).
[7] W. S. Abed, A. E. Hashoosh, and D. M. Abbas, “Existence results for some equilibrium problems involving βhβh-monotone trifunction,” in AIP Conference Proceedings, vol. 2414, no. 1, AIP Publishing (2023).
[8] D. M. Abbas, A. E. Hashoosh, and W. S. Abed, “The existence of uniqueness non-standard equilibrium problems,” International Journal of Nonlinear Analysis and Applications, vol. 12, no. 1, pp. 1251–1260 (2021).
[9] A. E. Hashoosh and A. K. Khisbag, “New concepts of vector variational-like inequalities involving ββ-ηη-monotone operator,” Mathematics in Engineering, Science & Aerospace (MESA), vol. 12, no. 1 (2021).
[10] J. P. Aubin and F. H. Clarke, “Shadow prices and duality for a class of optimal control problems,” SIAM Journal on Control and Optimization, vol. 17, no. 5, pp. 567–586 (1979).
[11] S. Migórski, Y. Bai, and S. Zeng, “A class of generalized mixed variational–hemivariational inequalities II: Applications,” Nonlinear Analysis: Real World Applications, vol. 50, pp. 633–650 (2019).
[12] S. Carl and D. Motreanu, “Extremal solutions of quasilinear parabolic inclusions with generalized Clarke’s gradient,” Journal of Differential Equations, vol. 191, no. 1, pp. 206–233 (2003).
[13] S. D. Mohsen, “Some generalizations of fuzzy soft (k–A^)(k–A^)-quasinormal operators in fuzzy soft Hilbert spaces,” Journal of Interdisciplinary Mathematics, vol. 26, no. 6, pp. 1133–1143 (2023).
[14] H. M. B. Alrikabi, A. E. Hashoosh, and A. A. Alkhalidi, “Existence results for nonlocal problems of (p,q)(p,q)-Kirchhoff form,” Journal of Interdisciplinary Mathematics, vol. 24, no. 4, pp. 983–993 (2021).
[15] A. E. Hashoosh, M. Alimohammady, and G. A. Almusawi, “Existence results for nonlinear quasi-hemivariational inequality systems,” University of Thi-Qar Journal, vol. 11, no. 4, pp. 90–109 (2016).
[16] D. Repovš and C. Varga, “A Nash type solution for hemivariational inequality systems,” Nonlinear Analysis: Theory, Methods & Applications, vol. 74, no. 16, pp. 5585–5590 (2011).
[17] T. C. Lin, “Convex sets, fixed points, variational and minimax inequalities,” Bulletin of the Australian Mathematical Society, vol. 34, no. 1, pp. 107–117 (1986).
[18] E. Blum, “From optimization and variational inequalities to equilibrium problems,” Mathematical Student, vol. 63, pp. 123–145 (1994).
[19] F. H. Clarke, Optimization and Nonsmooth Analysis. New York: Wiley (1983).
[20] F. H. Clarke, Optimization and Nonsmooth Analysis. Philadelphia: Society for Industrial and Applied Mathematics (1990).
[21] E. Tarafdar, “A fixed point theorem equivalent to the Fan-Knaster-Kuratowski-Mazurkiewicz theorem,” Journal of Mathematical Analysis and Applications, vol. 128, no. 2, pp. 475–479 (1987).
[22] M. M. Abbood, H. H. Ebrahim, A. Al-Fayadh, and A. J. Obaid, “Measure defined on ΓΓ–algebra and some of their generalizations,” Journal of Interdisciplinary Mathematics, vol. 26, no. 5, pp. 821–827 (2023), DOI: 10.47974/JIM-1502.

Views: 174Downloads: 76Citations: 0