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ALGORITHM OF SOLUTIONS FOR MIXEDNONLINEAR VARIATIONAL-LIKE INEQUALITIES IN REFLEXIVE BANACH SPACE
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作者 丁协平 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 1998年第6期521-529,共9页
In this paper, the author studies a class of mixed nonlinear variational-like inequalities in reflexive Banach space. By applying a minimax inequality obtained by the author, some existence uniqueness theorems of solu... In this paper, the author studies a class of mixed nonlinear variational-like inequalities in reflexive Banach space. By applying a minimax inequality obtained by the author, some existence uniqueness theorems of solutions for the mixed nonlinear variational-like inequalities are proved. Next, by applying the auxiliary problem technique, rite author suggests an innovative iterative algorithm to compute the approximate solutions of the mixed nonlinear variational-like inequalities. Finally, the convergence criteria is also discussed. 展开更多
关键词 mixed nonlinear variational-like inequality minimax inequality auxiliary variational inequality general algorithm reflexive banach space
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Bilevel generalized mixed equilibrium problems involving generalized mixed variational-like inequality problems in reflexive Banach spaces
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作者 丁协平 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2011年第11期1457-1474,共18页
A new bilevel generalized mixed equilibrium problem (BGMEP) involving generalized mixed variational-like inequality problems (GMVLIPs) is introduced and studied in the reflexive Banach spaces. First, an auxiliary ... A new bilevel generalized mixed equilibrium problem (BGMEP) involving generalized mixed variational-like inequality problems (GMVLIPs) is introduced and studied in the reflexive Banach spaces. First, an auxiliary generalized mixed equilibrium problem (AGMEP) is introduced to compute the approximate solutions of the BGMEP involving the GMVLIPs. By using a minimax inequality, the existence and the unique- ness of solutions of the AGMEP are proved under mild conditions without any coercive assumptions. By using an auxiliary principle technique, the new iterative algorithms are proposed and analyzed, with which the approximate solutions of the BGMEP are computed. The strong convergence of the iterative sequence generated by the algorithms is shown under mild conditions without any coercive assumptions. These new results can generalize some recent results in this field. 展开更多
关键词 bilevel generalized mixed equilibrium problem (BGMEP) generalizedmixed variational-like inequality problem (GMVLIP) auxiliary principle iterative algo-rithm reflexive banach space
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Auxiliary principle and approximation solvability for system of new generalized mixed equilibrium problems in reflexive Banach spaces
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作者 丁协平 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2011年第2期231-240,共10页
A new system of generalized mixed equilibrium problems (SGMEPs) involving generalized mixed variational-like inequality problems is introduced and studied in reflexive Banach spaces. A system of auxiliary generalize... A new system of generalized mixed equilibrium problems (SGMEPs) involving generalized mixed variational-like inequality problems is introduced and studied in reflexive Banach spaces. A system of auxiliary generalized mixed equilibrium problems (SAGMEPs) for solving the SGMEPs is first introduced. Existence and uniqueness of the solutions to the SAGMEPs is proved under quite mild assumptions without any coercive conditions in reflexive Banach spaces. Using the auxiliary principle technique, a new iterative algorithm for solving the SGMEPs is proposed and analyzed. Strong convergence of the iterative sequences generated by the algorithm is also proved under quite mild assumptions without any coercive conditions. These results improve, unify, and generalize some recent results in this field. 展开更多
关键词 system of generalized mixed equilibrium problem auxiliary principle iterative algorithm reflexive banach space
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Feedback Systems on a Reflexive Banach Space—Linearization
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作者 Messaoudi Khelifa 《International Journal of Modern Nonlinear Theory and Application》 2020年第2期34-50,共17页
The aim of our work is to formulate and demonstrate the results of the normality, the Lipschitz continuity, of a nonlinear feedback system described by the monotone maximal operators and hemicontinuous, defined on rea... The aim of our work is to formulate and demonstrate the results of the normality, the Lipschitz continuity, of a nonlinear feedback system described by the monotone maximal operators and hemicontinuous, defined on real reflexive Banach spaces, as well as the approximation in a neighborhood of zero, of solutions of a feedback system [A,B] assumed to be non-linear, by solutions of another linear, This approximation allows us to obtain appropriate estimates of the solutions. These estimates have a significant effect on the study of the robust stability and sensitivity of such a system see <a href="#ref1">[1]</a> <a href="#ref2">[2]</a> <a href="#ref3">[3]</a>. We then consider a linear FS <img src="Edit_4629d4d0-bbb2-478d-adde-391efde3d1e0.bmp" alt="" />, and prove that, if <img src="Edit_435aae08-e821-4b4d-99d2-e2a2b47609c1.bmp" alt="" />;<img src="Edit_4fa030bc-1f97-4726-8257-ca8d00657aac.bmp" alt="" /> , with <img src="Edit_63ab4faa-ba40-45fe-8b8a-7a6caef91794.bmp" alt="" />the respective solutions of FS’s [A,B] and <img src="Edit_e78e2e6d-8934-4011-93eb-8b7eb52fa856.bmp" alt="" /> corresponding to the given (u,v) in <img src="Edit_0e18433c-8c7a-454f-8eec-6eb9fb69469a.bmp" alt="" /> . There exists,<img src="Edit_3dcd8afc-8cea-4c06-a920-e4148a5f793e.bmp" alt="" />, positive real constants such that, <img src="Edit_edb88446-3e39-4fe0-865a-114de701e78e.bmp" alt="" />. These results are the subject of theorems 3.1, <span style="font-size:10.0pt;font-family:;" "="">... </span>, 3.3. The proofs of these theorems are based on our lemmas 3.2, <span style="font-size:10.0pt;font-family:;" "="">... </span>, 3.5, devoted according to the hypotheses on A and B, to the existence of the inverse of the operator <em>I+BA</em> and <img src="Edit_2db1326b-cb5b-44cf-8d1f-df22bd6da45f.bmp" alt="" />. The results obtained and demonstrated along this document, present an extension in general Banach space of those in <a href="#ref4">[4]</a> on a Hilbert space <em>H</em> and those in <a href="#ref5">[5]</a> on a extended Hilbert space <img src="Edit_b70ce337-1812-4d4b-ae7d-a24da7e5b3cf.bmp" alt="" />. 展开更多
关键词 Nonlinear Feedback System LINEARIZATION reflexive banach space NORMALITY Lipschitz Continuity
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APPROXIMATION OF FIXED POINTS AND VARIATIONAL SOLUTIONS FOR PSEUDO-CONTRACTIVE MAPPINGS IN BANACH SPACES 被引量:2
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作者 Yekini SHEHU 《Acta Mathematica Scientia》 SCIE CSCD 2014年第2期409-423,共15页
Let K be a nonempty, closed and convex subset of a real reflexive Banach space E which has a uniformly Gateaux differentiable norm. Assume that every nonempty closed con- vex and bounded subset of K has the fixed poin... Let K be a nonempty, closed and convex subset of a real reflexive Banach space E which has a uniformly Gateaux differentiable norm. Assume that every nonempty closed con- vex and bounded subset of K has the fixed point property for nonexpansive mappings. Strong convergence theorems for approximation of a fixed point of Lipschitz pseudo-contractive map- pings which is also a unique solution to variational inequality problem involving φ-strongly pseudo-contractive mappings are proved. The results presented in this article can be applied to the study of fixed points of nonexpansive mappings, variational inequality problems, con- vex optimization problems, and split feasibility problems. Our result extends many recent important results. 展开更多
关键词 Pseudo-contractive mappings reflexive banach spaces uniformly Gateaux differentiable norm variational inequality
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STRONG CONVERGENCE THEOREMS FOR EQUILIBRIUM PROBLEM AND BREGMAN TOTALLY QUASI-ASYMPTOTICALLY NONEXPANSIVE MAPPING IN BANACH SPACES
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作者 朱胜 黄建华 《Acta Mathematica Scientia》 SCIE CSCD 2016年第5期1433-1444,共12页
In this paper, we propose a new hybrid iterative scheme for finding a common solution of an equilibrium problem and fixed point of Bregman totally quasi-asymptotically nonexpansive mapping in reflexive Banach spaces. ... In this paper, we propose a new hybrid iterative scheme for finding a common solution of an equilibrium problem and fixed point of Bregman totally quasi-asymptotically nonexpansive mapping in reflexive Banach spaces. Moreover, we prove some strong convergence theorems under suitable control conditions. Finally, the application to zero point problem of maximal monotone operators is given by the result. 展开更多
关键词 equilibrium problem Bregman totally quasi-asymptotically nonexpansive mapping Bregman distance reflexive banach space
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Perturbation of the Moore–Penrose Metric Generalized Inverse in Reflexive Strictly Convex Banach Spaces 被引量:1
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作者 Jian Bing CAO Wan Qin ZHANG 《Acta Mathematica Sinica,English Series》 SCIE CSCD 2016年第6期725-735,共11页
Let X, Y be reflexive strictly convex Banach spaces, let T, δT : X → Y be bounded linear operators with closed range R(T). Put T= T + δT. In this paper, by using the concept of quasiadditivity and the so called... Let X, Y be reflexive strictly convex Banach spaces, let T, δT : X → Y be bounded linear operators with closed range R(T). Put T= T + δT. In this paper, by using the concept of quasiadditivity and the so called generalized Neumman lemma, we will give some error estimates of the bounds of ||T^M||. By using a relation between the concepts of the reduced minimum module and the gap of two subspaces, some new existence characterization of the Moore-Penrose metric generalized inverse T^M of the perturbed operator T will be also given. 展开更多
关键词 Metric generalized inverse PERTURBATION reflexive strictly convex banach space
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Modified Mann Iterations for Nonexpansive Semigroups in Banach Space
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作者 Ru Dong CHEN Hui Min HE Muhammad Aslam NOOR 《Acta Mathematica Sinica,English Series》 SCIE CSCD 2010年第1期193-202,共10页
Let E be a real reflexive Banach space which admits a weakly sequentially continuous duality mapping from E to E^*, and C be a nonempty closed convex subset of E. Let {T(t) : t ≥ 0} be a nonexpansive semigroup on... Let E be a real reflexive Banach space which admits a weakly sequentially continuous duality mapping from E to E^*, and C be a nonempty closed convex subset of E. Let {T(t) : t ≥ 0} be a nonexpansive semigroup on C such that F :=∩t≥0 Fix(T(t)) ≠ 0, and f : C → C be a fixed contractive mapping. If {αn}, {βn}, {an}, {bn}, {tn} satisfy certain appropriate conditions, then we suggest and analyze the two modified iterative processes as:{yn=αnxn+(1-αn)T(tn)xn,xn=βnf(xn)+(1-βn)yn{u0∈C,vn=anun+(1-an)T(tn)un,un+1=bnf(un)+(1-bn)vnWe prove that the approximate solutions obtained from these methods converge strongly to q ∈∩t≥0 Fix(T(t)), which is a unique solution in F to the following variational inequality:〈(I-f)q,j(q-u)〉≤0 u∈F Our results extend and improve the corresponding ones of Suzuki [Proc. Amer. Math. Soc., 131, 2133-2136 (2002)], and Kim and XU [Nonlear Analysis, 61, 51-60 (2005)] and Chen and He [Appl. Math. Lett., 20, 751-757 (2007)]. 展开更多
关键词 fixed point nonexpansive semigroups strong convergence reflexive banach space
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Iterative algorithm for solutions to new system of generalized mixed implicit equilibrium
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作者 丁协平 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2013年第1期113-126,共14页
A new system of generalized mixed implicit equilibrium problems (SGMIEP) involving nonmonotone set-valued mappings is introduced and studied in real reflexive Banach spaces. First, an auxiliary mixed equilibrium pro... A new system of generalized mixed implicit equilibrium problems (SGMIEP) involving nonmonotone set-valued mappings is introduced and studied in real reflexive Banach spaces. First, an auxiliary mixed equilibrium problem (AMEP) is introduced. The existence and the uniqueness of the solutions to the AMEP are proved under quite mild assumptions without any coercive conditions. Next, by using the solution mapping of the AMEP, a system of generalized equation problems (SGEP) is considered, and its equivalence with the SGMIEP is shown. By using the SGEP, a new iterative algorithm for solving the SGMIEP is proposed and analyzed. The strong convergence of the iterative sequences generated by the algorithm is proved under suitable conditions. These results are new, which unify and generalize some recent results in this field. 展开更多
关键词 system of generalized mixed implicit equilibrium problems (SGMIEP) auxiliary mixed equilibrium problem (AMEP) system of generalized equation problems(SGEP) iterative algorithm reflexive banach space
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STRONG CONVERGENCE THEOREMS FOR FINITE EQUILIBRIUM PROBLEMS AND BREGMAN TOTALLY QUASI-ASYMPTOTICALLY NONEXPANSIVE MAPPING IN BANACH SPACES
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作者 Haipeng He Jianhua Huang Sheng Zhu 《Annals of Applied Mathematics》 2015年第4期372-382,共11页
In this paper, we propose a new hybrid iterative scheme for finding a common solution to a finite of equilibrium problems and fixed point of Bregman totally quasi- asymptotically nonexpansive mapping in reflexive Bana... In this paper, we propose a new hybrid iterative scheme for finding a common solution to a finite of equilibrium problems and fixed point of Bregman totally quasi- asymptotically nonexpansive mapping in reflexive Banach spaces. Moreover, we prove some strong convergence theorems under suitable control conditions. 展开更多
关键词 equilibrium problem Bregman totally quasi-asymptotically nonex-pansive mapping Bregman distance reflexive banach space
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APPROXIMATION OF COMMON FIXED POINT OF FAMILIES OF NONLINEAR MAPPINGS WITH APPLICATIONS
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作者 Eric U.OFOEDU Charles E.ONYI 《Acta Mathematica Scientia》 SCIE CSCD 2015年第5期1225-1240,共16页
It is our purpose in this paper to show that some results obtained in uniformly convex real Banach space with uniformly Gateaux differentiable norm are extendable to more general reflexive and strictly convex real Ban... It is our purpose in this paper to show that some results obtained in uniformly convex real Banach space with uniformly Gateaux differentiable norm are extendable to more general reflexive and strictly convex real Banach space with uniformly G&teaux differentiable norm. Demicompactness condition imposed in such results is dispensed with. Furthermore, Applications of our theorems to approximation of common fixed point of countable infinite family of continuous pseudocontractive mappings and approximation of common solution of countable infinite family of generalized mixed equilibrium problems are also discussed. Our theorems improve, generalize, unify and extend several recently announced results. 展开更多
关键词 nonexpansive mappings reflexive real banach spaces fixed point uniformly Aateaux differentiable norm
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