-
Previous Article
$ \theta $ scheme with two dimensional wavelet-like incremental unknowns for a class of porous medium diffusion-type equations
- NACO Home
- This Issue
-
Next Article
Numerical solutions of Volterra integro-differential equations using General Linear Method
System of generalized mixed nonlinear ordered variational inclusions
Department of Mathematics, Jazan University, Jazan, 45142, KSA |
In this paper, we consider a system of generalized mixed nonlinear ordered variational inclusions in partially ordered Banach spaces and suggest an algorithm for a solution of the considered system. We prove an existence and convergence result for the solution of the system of generalized mixed nonlinear ordered variational inclusions.
References:
[1] |
R. Ahmad, M. F. Khan and Sa lahuddin,
Mann and Ishikawa type perturbed iterative algorithm for generalized nonlinear variational inclusions, Math. Comput. Appl., 6 (2001), 47-52.
doi: 10.3390/mca6010047. |
[2] |
M. K. Ahmad and Sa lahuddin,
Resolvent equation technique for generalized nonlinear variational inclusions, Adv. Nonlinear Var. Inequal., 5 (2002), 91-98.
|
[3] |
M. K. Ahmad and Salahuddin, Perturbed three step approximation process with errors for a general implicit nonlinear variational inequalities, Int. J. Math. Math. Sci., Article ID 43818, (2006), 1–14.
doi: 10.1155/IJMMS/2006/43818. |
[4] |
M. K. Ahmad and Salahuddin, Generalized strongly nonlinear implicit quasi-variational inequalities, J. Inequal. Appl., 2009 (2009), Article ID 124953, 1–16.
doi: 10.1155/2009/124953. |
[5] |
H. Amann,
On the number of solutions of nonlinear equations in ordered Banach spaces, J. Funct. Anal., 11 (1972), 346-384.
doi: 10.1016/0022-1236(72)90074-2. |
[6] |
X. P. Ding and H. R. Feng,
Algorithm for solving a new class of generalized nonlinear implicit quasi variational inclusions in Banach spaces, Appl. Math. Comput., 208 (2009), 547-555.
doi: 10.1016/j.amc.2008.12.028. |
[7] |
X. P. Ding and Sa lahuddin,
On a system of general nonlinear variational inclusions in Banach spaces, Appl. Math. Mech., 36 (2015), 1663-1672.
doi: 10.1007/s10483-015-2001-6. |
[8] |
Y. P. Du,
Fixed points of increasing operators in ordered Banach spaces and applications, Anal., 38 (1990), 1-20.
doi: 10.1080/00036819008839957. |
[9] |
Y. P. Fang, N. J. Huang and H. B. Thompson,
A new system of variational inclusions with $(H, \eta)$-monotone operators in Hilbert spaces, Comput. Math. Appl., 49 (2005), 365-374.
doi: 10.1016/j.camwa.2004.04.037. |
[10] |
X. F. He, J. L. Lou and Z. He,
Iterative methods for solving variational inclusions in Banach spaces, J. Comput. Appl. Math., 203 (2007), 80-86.
doi: 10.1016/j.cam.2006.03.011. |
[11] |
N. J. Huang and Y. P. Fang,
Generalized $m$-accretive mappings in Banach spaces, J. Sichuan Univ., 38 (2001), 591-592.
|
[12] |
S. Hussain, M. F. Khan and Sa lahuddin,
Mann and Ishikawa type perturbed iterative algorithms for completely generalized nonlinear variational inclusions, Int. J. Math. Anal., 3 (2006), 51-62.
|
[13] |
P. Junlouchai, S. Plubtieng and Sa lahuddin,
On a new system of nonlinear regularized nonconvex variational inequalities in Hilbert spaces, J. Nonlinear Anal. Optim., 7 (2016), 103-115.
|
[14] |
M. F. Khan and Sa lahuddin,
Mixed multivalued variational inclusions involving H-accretive operators, Adv. Nonlinear Var. Inequal., 9 (2006), 29-47.
|
[15] |
M. F. Khan and Salahuddin, Generalized co-complementarity problems in p-uniformly smooth Banach spaces, JIPAM, J. Inequal. Pure Appl. Math., 7 (2006), 1–11, Article ID 66. |
[16] |
M. F. Khan and Sa lahuddin,
Generalized multivalued nonlinear co-variational inequalities in Banach spaces, Funct. Diff. Equat., 14 (2007), 299-313.
|
[17] |
B. S. Lee and Sa lahuddin,
Fuzzy general nonlinear ordered random variational inequalities in ordered Banach spaces, East Asian Math. J., 32 (2016), 685-700.
|
[18] |
B. S. Lee, M. F. Khan and Sa lahuddin,
Generalized nonlinear quasi-variational inclusions in Banach spaces, Comput. Math. Appl., 56 (2008), 1414-1422.
doi: 10.1016/j.camwa.2007.11.053. |
[19] |
B. S. Lee, M. F. Khan and Sa lahuddin,
Hybrid-type set-valued variational-like inequalities in Reflexive Banach spaces, J. Appl. Math. Inform., 27 (2009), 1371-1379.
|
[20] |
H. G. Li, L. P. Li, J. M. Zheng and M. M. Jin, Sensitivity analysis for generalized set-valued parametric ordered variational inclusion with $(\alpha, \lambda)$-nodsm mappings in ordered Banach spaces, Fixed Point Theory Appl., 2014 (2014), 122.
doi: 10.1186/1687-1812-2014-122. |
[21] |
H. G. Li, D. Qui and Y. Zou, Characterization of weak-anodd set-valued mappings with applications to approximate solution of gnmoqv inclusions involving $\oplus$ operator in ordered Banach spaces, Fixed Point Theory Appl., 2013 (2013), 241.
doi: 10.1186/1687-1812-2013-241. |
[22] |
H. G. Li, L. P. Li and M. M. Jin, A class of nonlinear mixed ordered inclusion problems for oredered $(\alpha_a, \lambda)$-ANODM set-valued mappings with strong comparison mapping, Fixed Point Theory Appl., 2014 (2014), 79.
doi: 10.1186/1687-1812-2014-79. |
[23] |
H. G. Li,
A nonlinear inclusion problem involving $(\alpha, \lambda)$-NODM set-valued mappings in ordered Hilbert space, Appl. Math. Lett., 25 (2012), 1384-1388.
doi: 10.1016/j.aml.2011.12.007. |
[24] |
H. G. Li,
Approximation solution for general nonlinear ordered variational inequalities and ordered equations in ordered Banach space, Nonlinear Anal. Forum, 13 (2008), 205-214.
|
[25] |
H. G. Li, D. Qiu and M. M. Jin, GNM ordered variational inequality system with ordered Lipschitz continuous mappings in an ordered Banach space, J. Inequal. Appl., 2013 (2013), 514.
doi: 10.1186/1029-242X-2013-514. |
[26] |
H. G. Li, X. B. Pan, Z. Y. Deng and C. Y. Wang, Solving GNOVI frameworks involving $(\gamma_g, \lambda)$-weak-GRD set-valued mappings in positive Hilbert spaces, Fixed Point Theory Appl., 2014 (2014), 146.
doi: 10.1186/1687-1812-2014-146. |
[27] |
H. H. Schaefer, Banach Lattices and Positive Operators, Springer, Berlin, 1994. |
[28] |
Sa lahuddin,
Regularized equilibrium problems in Banach spaces, Korean J. Math., 24 (2016), 51-63.
doi: 10.11568/kjm.2016.24.1.51. |
[29] |
Sa lahuddin,
Solvability for a system of generalized nonlinear ordered variational inclusions in ordered Banach spaces, Korean J. Math., 25 (2017), 359-377.
|
[30] |
Sa lahuddin and S. S. Irfan,
Proximal methods for quasi-variational inequalities, Math. Computat. Appl., 9 (2004), 165-172.
doi: 10.3390/mca9020165. |
[31] |
A. H. Siddiqi, M. K. Ahmad and Sa lahuddin,
Existence results for generalized nonlinear variational inclusions, Appl. Math. Lett., 18 (2005), 859-864.
doi: 10.1016/j.aml.2004.08.015. |
[32] |
Y. K. Tang, S. S. Chang and Salahuddin, A system of nonlinear set valued variational inclusions, SpringerPlus, 3 (2014), 318. |
[33] |
R. U. Verma,
Projection methods, algorithms and a new system of nonlinear variational inequalities, Comput. Math. Appl., 41 (2001), 1025-1031.
doi: 10.1016/S0898-1221(00)00336-9. |
[34] |
R. U. Verma, M. F. Khan and Sa lahuddin,
Fuzzy generalized complementarity problems in Banach spaces, PanAmer. Math. J., 17 (2007), 71-80.
|
[35] |
R. U. Verma and Sa lahuddin,
Extended systems of nonlinear vector quasi variational inclusions and extended systems of nonlinear vector quasi optimization problems in locally FC-spaces, Commun. Appl. Nonlinear Anal., 23 (2016), 71-88.
|
show all references
References:
[1] |
R. Ahmad, M. F. Khan and Sa lahuddin,
Mann and Ishikawa type perturbed iterative algorithm for generalized nonlinear variational inclusions, Math. Comput. Appl., 6 (2001), 47-52.
doi: 10.3390/mca6010047. |
[2] |
M. K. Ahmad and Sa lahuddin,
Resolvent equation technique for generalized nonlinear variational inclusions, Adv. Nonlinear Var. Inequal., 5 (2002), 91-98.
|
[3] |
M. K. Ahmad and Salahuddin, Perturbed three step approximation process with errors for a general implicit nonlinear variational inequalities, Int. J. Math. Math. Sci., Article ID 43818, (2006), 1–14.
doi: 10.1155/IJMMS/2006/43818. |
[4] |
M. K. Ahmad and Salahuddin, Generalized strongly nonlinear implicit quasi-variational inequalities, J. Inequal. Appl., 2009 (2009), Article ID 124953, 1–16.
doi: 10.1155/2009/124953. |
[5] |
H. Amann,
On the number of solutions of nonlinear equations in ordered Banach spaces, J. Funct. Anal., 11 (1972), 346-384.
doi: 10.1016/0022-1236(72)90074-2. |
[6] |
X. P. Ding and H. R. Feng,
Algorithm for solving a new class of generalized nonlinear implicit quasi variational inclusions in Banach spaces, Appl. Math. Comput., 208 (2009), 547-555.
doi: 10.1016/j.amc.2008.12.028. |
[7] |
X. P. Ding and Sa lahuddin,
On a system of general nonlinear variational inclusions in Banach spaces, Appl. Math. Mech., 36 (2015), 1663-1672.
doi: 10.1007/s10483-015-2001-6. |
[8] |
Y. P. Du,
Fixed points of increasing operators in ordered Banach spaces and applications, Anal., 38 (1990), 1-20.
doi: 10.1080/00036819008839957. |
[9] |
Y. P. Fang, N. J. Huang and H. B. Thompson,
A new system of variational inclusions with $(H, \eta)$-monotone operators in Hilbert spaces, Comput. Math. Appl., 49 (2005), 365-374.
doi: 10.1016/j.camwa.2004.04.037. |
[10] |
X. F. He, J. L. Lou and Z. He,
Iterative methods for solving variational inclusions in Banach spaces, J. Comput. Appl. Math., 203 (2007), 80-86.
doi: 10.1016/j.cam.2006.03.011. |
[11] |
N. J. Huang and Y. P. Fang,
Generalized $m$-accretive mappings in Banach spaces, J. Sichuan Univ., 38 (2001), 591-592.
|
[12] |
S. Hussain, M. F. Khan and Sa lahuddin,
Mann and Ishikawa type perturbed iterative algorithms for completely generalized nonlinear variational inclusions, Int. J. Math. Anal., 3 (2006), 51-62.
|
[13] |
P. Junlouchai, S. Plubtieng and Sa lahuddin,
On a new system of nonlinear regularized nonconvex variational inequalities in Hilbert spaces, J. Nonlinear Anal. Optim., 7 (2016), 103-115.
|
[14] |
M. F. Khan and Sa lahuddin,
Mixed multivalued variational inclusions involving H-accretive operators, Adv. Nonlinear Var. Inequal., 9 (2006), 29-47.
|
[15] |
M. F. Khan and Salahuddin, Generalized co-complementarity problems in p-uniformly smooth Banach spaces, JIPAM, J. Inequal. Pure Appl. Math., 7 (2006), 1–11, Article ID 66. |
[16] |
M. F. Khan and Sa lahuddin,
Generalized multivalued nonlinear co-variational inequalities in Banach spaces, Funct. Diff. Equat., 14 (2007), 299-313.
|
[17] |
B. S. Lee and Sa lahuddin,
Fuzzy general nonlinear ordered random variational inequalities in ordered Banach spaces, East Asian Math. J., 32 (2016), 685-700.
|
[18] |
B. S. Lee, M. F. Khan and Sa lahuddin,
Generalized nonlinear quasi-variational inclusions in Banach spaces, Comput. Math. Appl., 56 (2008), 1414-1422.
doi: 10.1016/j.camwa.2007.11.053. |
[19] |
B. S. Lee, M. F. Khan and Sa lahuddin,
Hybrid-type set-valued variational-like inequalities in Reflexive Banach spaces, J. Appl. Math. Inform., 27 (2009), 1371-1379.
|
[20] |
H. G. Li, L. P. Li, J. M. Zheng and M. M. Jin, Sensitivity analysis for generalized set-valued parametric ordered variational inclusion with $(\alpha, \lambda)$-nodsm mappings in ordered Banach spaces, Fixed Point Theory Appl., 2014 (2014), 122.
doi: 10.1186/1687-1812-2014-122. |
[21] |
H. G. Li, D. Qui and Y. Zou, Characterization of weak-anodd set-valued mappings with applications to approximate solution of gnmoqv inclusions involving $\oplus$ operator in ordered Banach spaces, Fixed Point Theory Appl., 2013 (2013), 241.
doi: 10.1186/1687-1812-2013-241. |
[22] |
H. G. Li, L. P. Li and M. M. Jin, A class of nonlinear mixed ordered inclusion problems for oredered $(\alpha_a, \lambda)$-ANODM set-valued mappings with strong comparison mapping, Fixed Point Theory Appl., 2014 (2014), 79.
doi: 10.1186/1687-1812-2014-79. |
[23] |
H. G. Li,
A nonlinear inclusion problem involving $(\alpha, \lambda)$-NODM set-valued mappings in ordered Hilbert space, Appl. Math. Lett., 25 (2012), 1384-1388.
doi: 10.1016/j.aml.2011.12.007. |
[24] |
H. G. Li,
Approximation solution for general nonlinear ordered variational inequalities and ordered equations in ordered Banach space, Nonlinear Anal. Forum, 13 (2008), 205-214.
|
[25] |
H. G. Li, D. Qiu and M. M. Jin, GNM ordered variational inequality system with ordered Lipschitz continuous mappings in an ordered Banach space, J. Inequal. Appl., 2013 (2013), 514.
doi: 10.1186/1029-242X-2013-514. |
[26] |
H. G. Li, X. B. Pan, Z. Y. Deng and C. Y. Wang, Solving GNOVI frameworks involving $(\gamma_g, \lambda)$-weak-GRD set-valued mappings in positive Hilbert spaces, Fixed Point Theory Appl., 2014 (2014), 146.
doi: 10.1186/1687-1812-2014-146. |
[27] |
H. H. Schaefer, Banach Lattices and Positive Operators, Springer, Berlin, 1994. |
[28] |
Sa lahuddin,
Regularized equilibrium problems in Banach spaces, Korean J. Math., 24 (2016), 51-63.
doi: 10.11568/kjm.2016.24.1.51. |
[29] |
Sa lahuddin,
Solvability for a system of generalized nonlinear ordered variational inclusions in ordered Banach spaces, Korean J. Math., 25 (2017), 359-377.
|
[30] |
Sa lahuddin and S. S. Irfan,
Proximal methods for quasi-variational inequalities, Math. Computat. Appl., 9 (2004), 165-172.
doi: 10.3390/mca9020165. |
[31] |
A. H. Siddiqi, M. K. Ahmad and Sa lahuddin,
Existence results for generalized nonlinear variational inclusions, Appl. Math. Lett., 18 (2005), 859-864.
doi: 10.1016/j.aml.2004.08.015. |
[32] |
Y. K. Tang, S. S. Chang and Salahuddin, A system of nonlinear set valued variational inclusions, SpringerPlus, 3 (2014), 318. |
[33] |
R. U. Verma,
Projection methods, algorithms and a new system of nonlinear variational inequalities, Comput. Math. Appl., 41 (2001), 1025-1031.
doi: 10.1016/S0898-1221(00)00336-9. |
[34] |
R. U. Verma, M. F. Khan and Sa lahuddin,
Fuzzy generalized complementarity problems in Banach spaces, PanAmer. Math. J., 17 (2007), 71-80.
|
[35] |
R. U. Verma and Sa lahuddin,
Extended systems of nonlinear vector quasi variational inclusions and extended systems of nonlinear vector quasi optimization problems in locally FC-spaces, Commun. Appl. Nonlinear Anal., 23 (2016), 71-88.
|
[1] |
Horst R. Thieme. Remarks on resolvent positive operators and their perturbation. Discrete and Continuous Dynamical Systems, 1998, 4 (1) : 73-90. doi: 10.3934/dcds.1998.4.73 |
[2] |
Sumit Arora, Manil T. Mohan, Jaydev Dabas. Approximate controllability of a Sobolev type impulsive functional evolution system in Banach spaces. Mathematical Control and Related Fields, 2021, 11 (4) : 857-883. doi: 10.3934/mcrf.2020049 |
[3] |
Mohammad Nasiruzzaman. Convergence on sequences of Szász-Jakimovski-Leviatan type operators and related results. Mathematical Foundations of Computing, 2022 doi: 10.3934/mfc.2022019 |
[4] |
B. S. Lee, Arif Rafiq. Strong convergence of an implicit iteration process for a finite family of Lipschitz $\phi -$uniformly pseudocontractive mappings in Banach spaces. Numerical Algebra, Control and Optimization, 2014, 4 (4) : 287-293. doi: 10.3934/naco.2014.4.287 |
[5] |
Felipe Alvarez, Juan Peypouquet. Asymptotic equivalence and Kobayashi-type estimates for nonautonomous monotone operators in Banach spaces. Discrete and Continuous Dynamical Systems, 2009, 25 (4) : 1109-1128. doi: 10.3934/dcds.2009.25.1109 |
[6] |
Sonja Cox, Arnulf Jentzen, Ryan Kurniawan, Primož Pušnik. On the mild Itô formula in Banach spaces. Discrete and Continuous Dynamical Systems - B, 2018, 23 (6) : 2217-2243. doi: 10.3934/dcdsb.2018232 |
[7] |
Michela Eleuteri, Pavel Krejčí. An asymptotic convergence result for a system of partial differential equations with hysteresis. Communications on Pure and Applied Analysis, 2007, 6 (4) : 1131-1143. doi: 10.3934/cpaa.2007.6.1131 |
[8] |
Daliang Zhao, Yansheng Liu, Xiaodi Li. Controllability for a class of semilinear fractional evolution systems via resolvent operators. Communications on Pure and Applied Analysis, 2019, 18 (1) : 455-478. doi: 10.3934/cpaa.2019023 |
[9] |
Yuri Latushkin, Valerian Yurov. Stability estimates for semigroups on Banach spaces. Discrete and Continuous Dynamical Systems, 2013, 33 (11&12) : 5203-5216. doi: 10.3934/dcds.2013.33.5203 |
[10] |
Goro Akagi, Mitsuharu Ôtani. Evolution equations and subdifferentials in Banach spaces. Conference Publications, 2003, 2003 (Special) : 11-20. doi: 10.3934/proc.2003.2003.11 |
[11] |
Fatihcan M. Atay, Lavinia Roncoroni. Lumpability of linear evolution Equations in Banach spaces. Evolution Equations and Control Theory, 2017, 6 (1) : 15-34. doi: 10.3934/eect.2017002 |
[12] |
Arnulf Jentzen, Felix Lindner, Primož Pušnik. On the Alekseev-Gröbner formula in Banach spaces. Discrete and Continuous Dynamical Systems - B, 2019, 24 (8) : 4475-4511. doi: 10.3934/dcdsb.2019128 |
[13] |
Viviane Baladi, Sébastien Gouëzel. Banach spaces for piecewise cone-hyperbolic maps. Journal of Modern Dynamics, 2010, 4 (1) : 91-137. doi: 10.3934/jmd.2010.4.91 |
[14] |
Cecilia González-Tokman, Anthony Quas. A concise proof of the multiplicative ergodic theorem on Banach spaces. Journal of Modern Dynamics, 2015, 9: 237-255. doi: 10.3934/jmd.2015.9.237 |
[15] |
Filippo Gazzola, Mirko Sardella. Attractors for families of processes in weak topologies of Banach spaces. Discrete and Continuous Dynamical Systems, 1998, 4 (3) : 455-466. doi: 10.3934/dcds.1998.4.455 |
[16] |
Ji Gao. On the generalized pythagorean parameters and the applications in Banach spaces. Discrete and Continuous Dynamical Systems - B, 2007, 8 (3) : 557-567. doi: 10.3934/dcdsb.2007.8.557 |
[17] |
Dalila Azzam-Laouir, Fatiha Selamnia. On state-dependent sweeping process in Banach spaces. Evolution Equations and Control Theory, 2018, 7 (2) : 183-196. doi: 10.3934/eect.2018009 |
[18] |
Sergiu Aizicovici, Yimin Ding, N. S. Papageorgiou. Time dependent Volterra integral inclusions in Banach spaces. Discrete and Continuous Dynamical Systems, 1996, 2 (1) : 53-63. doi: 10.3934/dcds.1996.2.53 |
[19] |
Vincenzo Recupero. Hysteresis operators in metric spaces. Discrete and Continuous Dynamical Systems - S, 2015, 8 (4) : 773-792. doi: 10.3934/dcdss.2015.8.773 |
[20] |
Marcin Studniarski. Finding all minimal elements of a finite partially ordered set by genetic algorithm with a prescribed probability. Numerical Algebra, Control and Optimization, 2011, 1 (3) : 389-398. doi: 10.3934/naco.2011.1.389 |
Impact Factor:
Tools
Metrics
Other articles
by authors
[Back to Top]