Mixed harmonic directional variational inequalities

Noor, Muhammad Aslam; Noor, Khalida Inayat; Kankam, Kunrada

doi:10.2478/gm-2024-0005

Abstract

In this paper, we introduce and investigate some new classes of mixed harmonic directional variational inequalities. Several important new problems are obtained as special cases. The auxiliary principle technique is applied to suggest and analyze some hybrid inertial iterative methods for solving the mixed harmonic directional variational inequality. The convergence analysis of these iterative methods is also considered under some mild conditions. Some special cases are also pointed out. Results proved in this paper can be viewed as a significant refinement and improvement of the known results.

References

A. A. Alshejari, M. A. Noor, K. I. Noor, Inertial algorithms for bifunction harmonic variational inequalities, Int. J. Anal. Appl., vol. 22, 2024, ID=46, 1-19, doi.org/10.28924/2291-8639-22-2024-46.
Search in Google Scholar Back to article
A. A. Alshejari, M. A. Noor, K. I. Noor, New auxiliary principle technique for generalharmonic diectional variational inequalities, Int. J. Anal. Appl., vol. 22
Search in Google Scholar Back to article
F. Al-Azemi, O. Calin, Asian options with harmonic average, Appl. Math. Inform. Sci., vol. 9, 2015, 1-9
Search in Google Scholar Back to article
F. Alvarez, Weak convergence of a relaxed and inertial hybrid projection- proximal point algorithm for maximal monotone operators in Hilbert space, SIAM J. Optim., vol. 14, 2003, 773-782
Search in Google Scholar Back to article
G. D. Anderson, M. K. Vamanamurthy, M. Vuorinen, Generalized convexity and inequalities, J. Math. Anal. Appl., vol. 335, 2007, 1294-1308
Search in Google Scholar Back to article
F. H. Clarke, Optimization and Nonsmooth Analysis, John Wiley and Sons, New York, 1983
Search in Google Scholar Back to article
R. W. Cottle, Jong-S. Pang, R. E. Stone, The Linear Complementarity Problem, SIAM Publication, Philadelphia, USA, 1992
Search in Google Scholar Back to article
G. Cristescu, L. Lupsa, Non-Connected Convexities and Applications, Kluwer Academic Publishers, Dordrecht, Holland, 2002
Search in Google Scholar Back to article
F. Giannessi, A. Maugeri, M. S. Pardalos, Equilibrium Problems: Nonsmooth Optimization and va riational Inequality Models, Kluwer Academic, Dordrecht, Holland, 2001
Search in Google Scholar Back to article
R. Glowinski, J-L. Lions, R. Tremolieres, Numerical Analysis of va riational Inequalities, North-Holland, Amsterdam, Holland, 1981
Search in Google Scholar Back to article
J. K. Kim, A. Lakhnotra, T. Ram, General mixed harmonic variational inequalities, Nonlinear Functional Analysis and Applications, vol. 29, no. 2, 2024, 517-526 https://doi.org/10.22771/nfaa.2024.29.02.12
Search in Google Scholar Back to article
J. L. Lions, G. Stampacchia, va riational inequalities, Commun. Pure Appl. Math., vol. 20, 1967, 492-512
Search in Google Scholar Back to article
M. A. Noor, On va riational Inequalities, PhD Thesis, Brunel University, London, UK, 1975
Search in Google Scholar Back to article
M. A. Noor, Fixed point approach for complementaritty problems, J. Math. Anal. Appl., vol. 133, 1988, 437-448
Search in Google Scholar Back to article
M. A. Noor, General algorithm for variational inequalities, J. Optim. Theory Appl., vol. 73, 1992, 409-413
Search in Google Scholar Back to article
M. A. Noor, New approximation schemes for general variational inequalities, J. Math. Anal. Appl., vol. 251, 2000, 217-229
Search in Google Scholar Back to article
M. A. Noor, K. I. Noor, Some novel aspects and applications of Noor iteration and Noor orbits, J. Advanced Math. Studies, vol. 17, no. 3, 2024, 276-284
Search in Google Scholar Back to article
M. A. Noor, Some developments in general variational inequalities, Appl. Math. Comput., vol. 152, 2004, 199-277
Search in Google Scholar Back to article
M. A. Noor, K. I. Noor, Some new trends in mixed variational inequalities, J. Advanc. Math. Studies, vol. 15, no. 2, 2022, 105-140
Search in Google Scholar Back to article
M. A. Noor, K. I. Noor, Harmonic variational inequalities, Appl. Math. Inform. Sci., vol. 10, no. 5, 2016, 1811-1814
Search in Google Scholar Back to article
M. A. Noor, K. I. Noor, Some imlpicit shemses for harmonic variational inequalities, Inter. J. Anal. Appl., vol. 12, no. 1, 2016, 10-14
Search in Google Scholar Back to article
M. A. Noor, K. I. Noor, Some New classes of harmonic hemivariational in-equalities, Earthline J. Math. Sci., vol. 13, no. 2, 2023, 473-495
Search in Google Scholar Back to article
M. A. Noor, K. I. Noor, Auxiliary principle technique for solving trifunction harmonic variational inequalities, RAD HAZU Matemat.Znanost, vol. 28/558, 2024, In Press
Search in Google Scholar Back to article
M. A. Noor, K. I. Noor, S. Iftikhar, Strongly generalized harmonic convex func-tions and integral inequalities, J. Math. Anal., vol. 7, no. 3, 2016, 66-77
Search in Google Scholar Back to article
M. A. Noor, K. I. Noor, M. Th. Rassias, New trends in general variational inequalitiess, Acta Applicand. Math., vol. 170, no. 1, 2020, 981-1046
Search in Google Scholar Back to article
M. A. Noor, K. I. Noor, Th. M. Rassias, Some aspects of variational inequalities, J. Comput. Appl. Math., vol. 47, 1993, 285-312
Search in Google Scholar Back to article
M. A. Noor, K. I. Noor, Th. M. Rassias, Set-valued resolvent equations and mixed variational inequalities, J. Math. Anal. Appl., vol. 220, 1998, 741-759
Search in Google Scholar Back to article
M. A. Noor, W. Oettli, On general nonlinear complementarity problems and quasi equilibria, Le Math.(Catania), vol. 49, 1994, 313-331
Search in Google Scholar Back to article
M. Patriksson, Nonlinear Programming and va riational Inequalities: A Unified Approach, Kluwer Academic Publishers, Dordrecht, Holland, 1999
Search in Google Scholar Back to article
B. T. Polyak, Some methods of speeding up the convergence of iterative methods, USSR Comput. Math. Math. Phys., vol. 4, 1964, 1-17
Search in Google Scholar Back to article
G. Stampacchia, Formes bilineaires coercitives sur les ensembles convexes, Comptes Rendus de l’Academie des Sciences, Paris, vol. 258, 1964, 4413-4416
Search in Google Scholar Back to article

Mixed harmonic directional variational inequalities

Abstract

Paradigm

My account