Nonlinear Functional Analysis and Applications

Kyungnam University, Department of Mathematics Eduaction (경남대학교 수학교육과)
권호 표지
DOI QR코드

DOI QR Code

GENERAL MIXED HARMONIC VARIATIONAL INEQUALITIES

  • Jong Kyu Kim (Department Mathematics Education, Kyungnam University) ;
  • Avinash Lakhnotra (Department of Mathematics, University of Jammu) ;
  • Tirth Ram (Department of Mathematics, University of Jammu)
  • Received : 2023.09.25
  • Accepted : 2024.03.01
  • Published : 2024.06.15
Download PDF
⟨ Previous Next ⟩

Abstract

In this paper, some iterative methods are used to discuss the behavior of general mixed-harmonic variational inequalities. We employ the auxiliary principle technique and g-strongly harmonic monotonicity of the operator to obtain results on the existence of solutions to a generalized class of mixed harmonic variational inequality.

Keywords

References

  1. C. Baiocchi and A. Capelo, Variational and Quasi Variational Inequalities, John Wiley, New York, 1984.
  2. B. Bin-Mohsin, M.A. Noor, K.I. Noor and S. Iftikhar, Relative strongly harmonic convex functions and their characterizations, J. Nonlinear Sci. Appl., 11 (2018), 1070-1076.
  3. M.V. Cortez, M.U. Awan, M.Z. Javed, M.A. Noor and K.I. Noor, A study of uniform harmonic χ-convex functions with respect to Hermite-Hadamard's inequality amd its Caputo-Fabrizio fractional analogue and applications, J. Funct. Spaces, (https://doi.org/10.1155/2021/7819882) (2021).
  4. F. Giannessi and A. Maugeri, Variational Inequalities and Network Equilibrium Problems, Plenum Press, New York, 1995.
  5. R. Glowinski, J.L. Lions and R. Tremolieres, Numerical Analysis of Variational Inequalities, North-Holland, Amsterdam, Holland, 1981.
  6. I. Iscan, Hermite-Hadamard type inequalities for harmonically convex functions, Hacett, J. Math. Stats., 43(2014), 935-942.
  7. J.L. Lions and G. Stampacchia, Variational inequalities, Commu. Pure Appl. Math., 20(1967), 493-519.
  8. S.N. Mishra, P.K. Das and S.K. Mishra, On generalized harmonic vector variational inequalities using HC*-condition, Nonlinear Funct. Anal. Appl., 24(3) (2019), 639-649.
  9. S.N. Mishra, P.K. Das and G.C. Nayak, On generalized Hermite-Hadamard type inequalities for generalized harmonic variational inequalities, Int. J. Pure Appl. Math., 115(4) (2017), 813-820.
  10. G.C. Nayak and P.K. Das, Harmonic invex sets and generalized harmonic variational inequality problems, Nonlinear Funct. Anal. Appl., 23 (1) (2018), 49-61.
  11. M.A. Noor, General variational inequalities, Appl. Math. Lett., 1 (1988), 119-121.
  12. M.A. Noor, Mixed Variational inequalities, Appl. Math. Lett., 3(2) (1990), 73-75.
  13. M.A. Noor, Wiener-Hopf equations and variational inequalities, J. Optim. Theory Appl., 79 (1993), 197-206.
  14. M.A. Noor, Some recent advances in variational inequalities, New Zealand J. Math., 26 (1997), 229-255.
  15. M.A. Noor, A new iterative method for monotone mixed variational inequalities, Mathl. Comput. Model., 26(7) (1997), 29-34.
  16. M.A. Noor, Algorithms for general monotone mixed variational inequalities, J. Math. Anal. Appl., 229 (1999), 330-343.
  17. M.A. Noor, Some algorithms for general monotone mixed variational inequalities, Math. Comput. Model., 29(7) (1999), 1-9.
  18. M.A. Noor, Some iterative techniques for general monotone variational inequalities, Optimization, 46(4) (1999), 391-401.
  19. M.A. Noor, An iterative method for general mixed Variational inequalities, Comput. Math. Appl., 40 (2000), 171-176.
  20. M.A. Noor, A class of new iterative methods for general mixed variational inequalities, Math. Comput. Model., 31(13) (2000), 11-19.
  21. M.A. Noor, New approximation schemes for general variational inequalities, J. Math. Anal. Appl., 251 (2000), 217-229.
  22. M.A. Noor, Some development in general variational inequalities, Appl. Math. Comput., 152 (2004), 199-277.
  23. M.A. Noor, Extended general variational inequalities, Appl. Math. Lett., 22 (2009), 182-186.
  24. M.A. Noor, A.G. Khan, A. Pervez and K.I. Noor, Solutions of harmonic variational inequalities by two-step iterative scheme, Turkish J. Ineq.,1(1) (2017), 46-52.
  25. M.A. Noor and K.I. Noor, Harmonic variational inequalities, Appl. Math. Inf. Sci.,10 (2016), 1811-1814.
  26. M.A. Noor and K.I. Noor, Some implicit methods for solving harmonic variational inequalities, Int. J. Anal. Appl., 12 (2016), 10-14.
  27. M.A. Noor and K.I. Noor, Some new trends in mixed variational inequalities, J. Adv. Math. Stud., 15(2) (2022), 105-140.
  28. M.A. Noor, K.I. Noor and S. Iftikhar, Hermite-Hadamard inequalities for strongly harmonic convex functions, J. Ineq. Spec. Funct., 7 (2016), 99-113.
  29. M.A. Noor, K.I. Noor, S. Iftikhar and M.U. Awan, Strongly generalized harmonic convex functions and integral inequalities, J. Math. Anal., 7 (2016), 66-77.
  30. M.A. Noor, K.I. Noor, S. Iftikar and F. Safdar, Generalized (h,r)-harmonic convex functions and inequalities, Int. J. Anal. Appl., 16 (4) (2018), 542-555.
  31. G. Stampacchia, Formes bilineaires coercivities sur les sensembles convexes, C. R. Acad. Sci. Paris, 258 (1964), 4413-4416.