الخوارزميات التكرارية لفئة من المتراجحات شبه التغاير الضمنية
DOI:
https://doi.org/10.54153/sjpas.2026.v8i1.1055الملخص
من المعروف أن إحدى المسائل الأكثر أهمية وتعقيدًا في نظرية متراجحة التغاير (VIT) هي تطوير مخططات تقريبية فعالة وقابلة للتنفيذ لحل فئات متنوعة من متراجحة التغاير. وبالتالي، من خلال هذه الدراسة، نقدم مخططات تكرارية جديدة بها أخطاء لحل متراجحات شبه التغاير الضمنية غير الخطية المعممة بقوة (GSNIQVI) بواسطة نقطة ثابتة معرفة لتطبيق مجموعة القيمة مع قيم محدبة مغلقة في فضاء هلبرت Ξ. تم تصميم هذه المخططات التكرارية لتطبيقات لبشز المستمرة، Γ - الرتيبة بقوة، والتطبيقات ℮-الرتيبة بقوة في ظل بعض الظروف المناسبة. تعمل هذه المخططات التكرارية على حل حالة خاصة من GSNIQVI مع وجود أخطاء وبدون أخطاء. لقد أثبتنا وجود نتائج وحيدة لحل GNIQVIP وتقارب الخوارزميات التكرارية الجديدة مع وجود أخطاء، وبدون أخطاء، لعدة تطبيقات: الأول هو Γ: Ξ⟶ Ξ لتطبيق لبشز المستمر ، والثاني Â, Ĉ, Ê, Û عبارة عن تطبيقات لبشز المستمرة ، والثالث Ň هو تطبيق بحيث يكون رتيب بقوة فيما يتعلق بـ Â في ، Γ- رتيب بقوة فيما يتعلق بـ Ĉ في ، ℮ - رتيب بقوة فيما يتعلق بـ Ê في و مستمر لبشز فيما يتعلق بـ ، ، ، والرابع هو الإسقاط المتري وهو مستمر لبشز. تم إستيحاء نتائجنا وتشجيعها للعديد من الأعمال البحثية في المصادر.
المراجع
1. Y. Cho, J. Kim, N. Huang, and S. Kang, "Ishikawa and Mann iterative processes with errors for generalized strongly nonlinear implicit quasi-variational inequalities," J Publicationes Mathematicae-Debrecen, vol. 58, no. 4, pp. 635-649, 2001. https://publi.math.unideb.hu/loa-d_doc.php?p=704&t=pap
2. Y.-P. Fang, N.-J. Huang, J. I. Kang, and Y. J. Cho, "Generalized nonlinear implicit quasivariational inclusions," Journal of Inequalities Applications vol. 2005, pp. 1-15, 2005. https://doi.or-g/10.1155/JIA.2005.261
3. N.-j. Huang, "On the generalized implicit quasivariational inequalities," Journal of Mathematical Analysis Applications vol. 216, no. 1, pp. 197-210, 1997. https://doi.org/10.1016/S0898-1221(98)00067-4
4. N.-J. Huang, "Mann and Ishikawa type perturbed iterative algorithms for generalized nonlinear implicit quasi-variational inclusions," J Computers Mathematics with Applications, vol. 35, no. 10, pp. 1-7, 1998. https://doi.org/10.1006/jmaa.1997.5671
5. N.-J. Huang, "A new completely general class of variational inclusions with noncompact valued mappings," J Computers Mathematics with Application, vol. 35, no. 10, pp. 9-14, 1998. https://doi.org/10.1016/S0898-1221(98)00066-2
6. M. Ishtyak and R. Ahmad, "An Ishikawa-type Iterative Algorithm for Solving A Generalized Variational Inclusion Problem Involving Difference of Monotone Operators," J Applications Applied Mathematics: An International Journal vol. 13, no. 1, p. 17, 2018. http://pvamu.edu/aam, https://digitalcommons.pvamu.edu/aam
7. M. A. Noor, K. I. Noor, and M. T. Rassias, "A unified approach to extended general quasi variational inclusions," in Exploring Mathematical Analysis, Approximation Theory, and Optimization: 270 Years Since A.-M. Legendre’s Birth: Springer, 2023, pp. 237-257. https://doi.org/10.1007/978-3-031-46487-4_13
8. G. Stampacchia, "Formes bilineaires coercitives sur les ensembles convexes," Comptes Rendus Hebdomadaires Des Seances De L Academie Des Sciences, vol. 258, no. 18, pp. 4413-4416, 1964. https://zbmath.org/?q=an:0124.06401
9. R. Verma, "Generalized pseudocontractions and nonlinear variational inequalities," J Publ. Math. Debrecen, vol. 53, no. 1-2, pp. 23-28, 1998. https://publi.math.unideb.hu/load_doc.ph-p?p=456&t=pap
10. H. Bauschke and P. Combettes, Convex Analysis and Monotone Operator Theory in Hilbert Spaces (CMS books in mathematics). New York: Springer, 2011, pp. 978-1. https://doi.org/10.1007/978-3-319-48311-5
11. E. Zeidler, Applied functional analysis. Applications to Mathematical Physics . Springer. New York 1995, p. 173. https://doi.org/10.1007/978-1-4612-0815-0
12. C. Chidume, Some geometric properties of Banach spaces. Springer, 2009. https://doi.or-g/10.1007/978-1-84882-190-3
13. L.-S. Liu, "Ishikawa and Mann iterative process with errors for nonlinear strongly accretive mappings in Banach spaces," Journal of Mathematical Analysis Applications vol. 194, no. 1, pp. 114-125, 1995. https://doi.org/10.1006/jmaa.1995.1289
14. U. Mosco, "Implicit variational problems and quasi variational inequalities," in Nonlinear Operators and the Calculus of Variations: Summer School Held in Bruxelles 8–19 September 1975: Springer, 1976, pp. 83-156. https://doi.org/10.1007/BFb0079943
15. F. E. Browder and W. V. Petryshyn, "Construction of fixed points of nonlinear mappings in Hilbert space," Journal of Mathematical Analysis Applications, vol. 20, no. 2, pp. 197-228, 1967. https://doi.org/10.1016/0022-247X(67)90085-6
16. S. S. Abed and N. S. Taresh, "On Stability of iterative sequences with error," J Mathematics, vol. 7, no. 8, p. 765, 2019. https://doi.org/10.3390/math7080765
17. L. J. Khaleel and B. A. Ahmed, "Fixed Point Theorem for Set Valued Mapping with Rational Condition," J Iraqi Journal of Science, vol. 61, no. 4, pp. 805-810, 2020. https://doi.org/10.24996/ijs.2020.61.4.12
18. Z. A. M. Monje and B. A. Ahmed, "A study of stability of first-order delay differential equations using fixed point theorem Banach," Iraqi Journal of Science, vol. 60, no. 12, pp. 2719-2724, 2019. https://doi.org/10.24996/ijs.2019.60.12.22
19. R. I. Sabri and B. A. Ahmed, "Fixed Point Results for Almost Contraction Mappings in Fuzzy Metric Space," Baghdad Science Journal, 2024. https://doi.org/10.21123/bsj.2024.9288
20. L. A. Al-Swidi and F. S. J. B. s. j. Awad, "On soft turning points," Baghdad science journal, vol. 15, no. 3, pp. 0352-0352, 2018. https://doi.org/10.21123/bsj.2018.15.3.0352
21. H. A. Satar and R. K. Naji, "Stability and bifurcation in a prey–predator–scavenger system with Michaelis–Menten type of harvesting function," Differential Equations Dynamical Systems, vol. 30, pp. 1-24, 2019. https://doi.org/10.1007/s12591-018-00449-5
22. Sh. Albundi, "Iterated function system in ϑ-metric spaces," Boletim da Sociedade Paranaense de Matemática, vol. 40, no. 2022, pp. 1-10, 2022. https://doi.org/10.5269/bspm.52556
23. N. S. Taresh and S. a. e. a. Albundi, "Convergence of Iterative Algorithms in Cat (0) Spaces," Iraqi Journal of Science, vol. 63, no. 1, pp. 233-240, 2022. https://doi.org/10.24996/ij-s.2022.63.1.24
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