New Classes of Generalized Contraction Multi-Valued Mappings and Various Categories of Fixed Point Theorems with an Application

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DOI: https://doi.org/10.28924/2291-8639-24-2026-190
Published: Jun 22, 2026
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Abduljabar. K. Abbas, Ali. A. Shihab, Alaa. M. F. Al-Jumaili, New Classes of Generalized Contraction Multi-Valued Mappings and Various Categories of Fixed Point Theorems with an Application, Int. J. Anal. Appl., 24 (2026), 190.

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Abduljabar. K. Abbas, Ali. A. Shihab, Alaa. M. F. Al-Jumaili

Abstract

The importance of fixed point theory and it is implementations in various fields of mathematics and other branches of sciences has encouraged many researchers to study various categories of coincidence and common fixed point theorems of extended contraction multi-valued mappings. Therefore, the major objective of present our manuscript is to define and applies new ideas of extended contraction conditions to verify the uniqueness of some new categories of coincidence and common fixed point theorems for multi-valued maps in the context of complete -symmetric spaces. Various practical implementations of the existence fixed point as a solution for certain non-linear integral equations have been elucidated. Additionally, our suggested results are novel and develop various recognized comparable outcomes related to these categories of coincidence and common fixed point theorems for extended classes of contraction multi-valued maps existing in the literature. Furthermore, a appropriate example that supports our major results has been equipped.

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References

  1. J. Dugundji, A. Granas, Weakly Contractive Maps and Elementary Domain Invariance Theorem, Bull. Greek Math. Soc. 19 (1978), 141-151.
  2. B.C. Dhage, Generalized Metric Space and Mapping with Fixed Point, Bull. Calcutta Math. Soc. 84 (1992), 329-336.
  3. B. C. Dhage, Generalized Metric Space and Topological Structure I, An. Științ. Univ. Al. I. Cuza Iași, Mat. (N.S.) 46 (2000), 3-24.
  4. Z. Mustafa, B. Sims, Some Remarks Concerning D-Metric Spaces, in: Proceedings of the International Conference on Fixed Point Theory and Applications, Valencia, Spain, pp. 189-198, (2003).
  5. D. El-Moutawakil, A Fixed Point Theorem for Multivalued Maps in Symmetric Spaces, Appl. Math. E-Notes 4 (2004), 26-32.
  6. S. Sedghi, N. Shobe, H. Zhou, A Common Fixed Point Theorem in D*-Metric Spaces, Fixed Point Theory Appl. 2007 (2007), 027906. https://doi.org/10.1155/2007/27906.
  7. H. Chandra, A. Bhatt, Some Fixed Point Theorems for Set Valued Maps in Symmetric Spaces, Int. J. Math. Anal. 3 (2009), 839-846.
  8. M. Abbas, R. Khan, T. Nazir, Common Fixed Point of Multivalued Mappings in Ordered Generalized Metric Spaces, Filomat 26 (2012), 1045-1053. https://doi.org/10.2298/fil1205045a.
  9. D. Wardowski, Fixed Points of a New Type of Contractive Mappings in Complete Metric Spaces, Fixed Point Theory Appl. 2012 (2012), 94. https://doi.org/10.1186/1687-1812-2012-94.
  10. M. Abbas, B. Ali, S. Romaguera, Fixed and Periodic Points of Generalized Contractions in Metric Spaces, Fixed Point Theory Appl. 2013 (2013), 243. https://doi.org/10.1186/1687-1812-2013-243.
  11. K.S. Eke, J. Olaleru, Common Fixed Point Results for Occasionally Weakly Compatible Maps in G-Symmetric Spaces, Appl. Math. 05 (2014), 744-752. https://doi.org/10.4236/am.2014.54071.
  12. K.S. Eke, J.O. Olaleru, Common Fixed Point Results for Pairs of Hybrid Maps in G-Symmetric Spaces, Int. J. Pure Appl. Math. 101 (2015), 117-132.
  13. Z. Mustafa, M. Arshad, S.U. Khan, J. Ahmad, M.M.M. Jaradat, Common Fixed Points for Multivalued Mappings in G-Metric Spaces with Applications, J. Nonlinear Sci. Appl. 10 (2017), 2550-2564. https://doi.org/10.22436/jnsa.010.05.23.
  14. A.M. Al-Jumaili, M.M. Abed, F.G. Al-sharqi, On Fixed Point Theorems and ∇-Distance in Complete Partially Ordered G-Cone Metric Spaces, J. Anal. Appl. 17 (2019), 1-20.
  15. N.A. Majid, A.A. Jumaili, Z.C. Ng, S.K. Lee, Some Applications of Fixed Point Results for Monotone Multivalued and Integral Type Contractive Mappings, Fixed Point Theory Algorithms Sci. Eng. 2023 (2023), 11. https://doi.org/10.1186/s13663-023-00748-9.
  16. N.A. Majid, A. AL. Jumaili, Z.C.N. Ng, S.K.L. Lee, Enhanced Results in Common and Coincidence Fixed Point Theory with Applications to Simulation Mappings, Eur. J. Pure Appl. Math. 17 (2024), 1877-1893. https://doi.org/10.29020/nybg.ejpam.v17i3.5268.
  17. A.H. Abed, A.M.F. Al-Jumaili, Occasionally Weakly Compatible Maps and Common Fixed Point Theorems in Certain New Generalized Symmetric Space, Iraqi J. Sci. 65 (2024), 4419-4427. https://doi.org/10.24996/ijs.2024.65.8.24.
  18. S.D. Mohsen, Y.H. Thiyab, Some Characteristics of Completeness Property in Fuzzy Soft b-Metric Space, J. Appl. Sci. Eng. 27 (2023), 2227-2232.
  19. S.D. Mohsen, Novel Results of k Quasi (ℷ-M)-Hyponormal Operator, Iraqi J. Sci. 65 (2024), 374-380. https://doi.org/10.24996/ijs.2024.65.1.30.
  20. A.A. Hijab, L.K. Shaakir, New Generalization of Strong-Composed Metric Type Spaces with Special (ψ,φ)-Contraction, Adv. Fixed Point Theory 15 (2025), 5. https://doi.org/10.28919/afpt/9016.
  21. A.A. Hijab, L.K. Shaakir, S. Aljohani, N. Mlaiki, Results on Common Fixed Points in Strong-Composed-Cone Metric Spaces, Int. J. Anal. Appl. 23 (2025), 75. https://doi.org/10.28924/2291-8639-23-2025-75.
  22. W.A. Wilson, On Semi-Metric Spaces, Am. J. Math. 53 (1931), 361-373. https://doi.org/10.2307/2370790.
  23. G. Jungck, B.E. Rhoades, Fixed Point Theorems for Occasionally Weakly Compatible Mappings, Fixed Point Theory 7 (2006), 287-296.
  24. G. Jungck, Common Fixed Points for Non-continuous Non-self Maps on Non-metric Spaces, Far East J. Math. Sci. 4 (1996), 199-215.
  25. M. Abbas, B.E. Rhoades, Common Fixed Point Results for Noncommuting Mappings without Continuity in Generalized Metric Spaces, Appl. Math. Comput. 215 (2009), 262-269. https://doi.org/10.1016/j.amc.2009.04.085.
  26. S.B. Nadler, Multi-Valued Contraction Mappings, Pac. J. Math. 30 (1969), 475-488. https://doi.org/10.2140/pjm.1969.30.475.
  27. A. Kaewcharoen, A. Kaewkhao, Common Fixed Points for Single-Valued and Multi-Valued Mappings in G-Metric Spaces, Int. J. Math. Anal. 5 (2011), 1775-1790.
  28. N. Tahat, H. Aydi, E. Karapinar, W. Shatanawi, Common Fixed Points for Single-Valued and Multi-Valued Maps Satisfying a Generalized Contraction in G-Metric Spaces, Fixed Point Theory Appl. 2012 (2012), 48. https://doi.org/10.1186/1687-1812-2012-48.
  29. M. Javahernia, A. Razani, F. Khojasteh, Common Fixed Point of the Generalized Mizoguchi-Takahashi’s Type Contractions, Fixed Point Theory Appl. 2014 (2014), 195. https://doi.org/10.1186/1687-1812-2014-195.