In this paper, we introduce the concept of generalized g-quasi-contractions in the setting of cone b-metric spaces over Banach algebras. By omitting the assump- tion of normality we establish common fixed point theore...In this paper, we introduce the concept of generalized g-quasi-contractions in the setting of cone b-metric spaces over Banach algebras. By omitting the assump- tion of normality we establish common fixed point theorems for the generalized g- quasi-contractions with the spectral radius r（λ） of the g-quasi-contractive constant vector λ satisfying r（λ） ∈[0,1） in the setting of cone b-metric spaces over Banach al- gebras, where the coefficient s satisfies s ≥ 1. The main results generalize, extend and unify several well-known comparable results in the literature.展开更多
In the present paper, we shall give an extension of the well known Pecaric-Rajic inequality in a quasi-Banach space, we establish the generalized inequality for an arbitrary number of finitely many nonzero elements of...In the present paper, we shall give an extension of the well known Pecaric-Rajic inequality in a quasi-Banach space, we establish the generalized inequality for an arbitrary number of finitely many nonzero elements of a quasi-Banach space, and obtain the corresponding upper and lower bounds. As a result, we get some more general inequalities.展开更多
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
A new system of the set-valued mixed quasi-variational-like inclusions （SSMQVLI） involving H-η-monotone operators is studied in general Banach spaces without uniform smoothness. By using the resolvent operator tech...A new system of the set-valued mixed quasi-variational-like inclusions （SSMQVLI） involving H-η-monotone operators is studied in general Banach spaces without uniform smoothness. By using the resolvent operator technique of H-η-monotone operators, a new iterative algorithm for finding approximate solutions to SSMQVLI is proposed. It is shown that the iterative sequences generated by the algorithm converge strongly to the exact solution of SSMQVLI under appropriate assumptions. These obtained new results have extended and improved previous results.展开更多
The sensitivity analysis for a class of generalized set-valued quasi-variational inclusion problems is investigated in the setting of Banach spaces. By using the resolvent operator technique, without assuming the diff...The sensitivity analysis for a class of generalized set-valued quasi-variational inclusion problems is investigated in the setting of Banach spaces. By using the resolvent operator technique, without assuming the differentiability and monotonicity of the given data, equivalence of these problems to the class of generalized resolvent equations is established.展开更多
By means of the method of coupled lower and upper quasisolutio ns, the paper applies, instead of establishing the comparison theorem, a new ite rative technique to nonlinear impulsive Fredholm integral equations in ...By means of the method of coupled lower and upper quasisolutio ns, the paper applies, instead of establishing the comparison theorem, a new ite rative technique to nonlinear impulsive Fredholm integral equations in Banach sp aces and proves the existence theorem on their coupled extremal quasisolutions . Finally, an infinite system of nonlinear impulsive integral equations is provi ded to demonstrate the obtained results.展开更多
In this paper, we investigate a new perturbation theorem for the Moore-Penrose metric generalized inverses of a bounded linear operator in Banach space. The main tool in this paper is ＂the generalized Neumann lemma＂...In this paper, we investigate a new perturbation theorem for the Moore-Penrose metric generalized inverses of a bounded linear operator in Banach space. The main tool in this paper is ＂the generalized Neumann lemma＂ which is quite different from the method in [12] where ＂the generalized Banach lemma＂ was used. By the method of the perturba- tion analysis of bounded linear operators, we obtain an explicit perturbation theorem and three inequalities about error estimates for the Moore-Penrose metric generalized inverse of bounded linear operator under the generalized Neumann lemma and the concept of stable perturbations in Banach spaces.展开更多
Let X be a complex quasi Banach space and Φ:[0,∞)→[0,∞) an increasing convex function with Φ(0)=0 , lim t→∞Φ(t)=∞ and Φ∈Δ 2 . Then L * Φ(X) is a quasi Banach space with contin...Let X be a complex quasi Banach space and Φ:[0,∞)→[0,∞) an increasing convex function with Φ(0)=0 , lim t→∞Φ(t)=∞ and Φ∈Δ 2 . Then L * Φ(X) is a quasi Banach space with continuous quasi norm and L * Φ(X) has the ARNP if and only if X does.展开更多
基金supported by the National Natural Science Foundation of China(No.11361064)the project No.174024 of the Ministry of Education,Science and Technological Department of the Republic of Serbia
文摘In this paper, we introduce the concept of generalized g-quasi-contractions in the setting of cone b-metric spaces over Banach algebras. By omitting the assump- tion of normality we establish common fixed point theorems for the generalized g- quasi-contractions with the spectral radius r（λ） of the g-quasi-contractive constant vector λ satisfying r（λ） ∈[0,1） in the setting of cone b-metric spaces over Banach al- gebras, where the coefficient s satisfies s ≥ 1. The main results generalize, extend and unify several well-known comparable results in the literature.
文摘In the present paper, we shall give an extension of the well known Pecaric-Rajic inequality in a quasi-Banach space, we establish the generalized inequality for an arbitrary number of finitely many nonzero elements of a quasi-Banach space, and obtain the corresponding upper and lower bounds. As a result, we get some more general inequalities.
基金supported by the Province Natural Science Foundation of China(2014J01008)
文摘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.
基金Project supported by the Natural Science Foundation of Education Department of Sichuan Province ofChina (No. 07ZA092)the Sichuan Province Leading Academic Discipline Project (No. SZD0406)
文摘A new system of the set-valued mixed quasi-variational-like inclusions （SSMQVLI） involving H-η-monotone operators is studied in general Banach spaces without uniform smoothness. By using the resolvent operator technique of H-η-monotone operators, a new iterative algorithm for finding approximate solutions to SSMQVLI is proposed. It is shown that the iterative sequences generated by the algorithm converge strongly to the exact solution of SSMQVLI under appropriate assumptions. These obtained new results have extended and improved previous results.
基金Project supported by the Teaching and Research Award Fund for Outstanding Young Teachers in Higher Education Institutions of Ministry of Education, China (No.0705)the Dawn Program Fund of Shanghai of China (No.BL200404)Shanghai Leading Academic Discipline Project (No.T0401)
文摘The sensitivity analysis for a class of generalized set-valued quasi-variational inclusion problems is investigated in the setting of Banach spaces. By using the resolvent operator technique, without assuming the differentiability and monotonicity of the given data, equivalence of these problems to the class of generalized resolvent equations is established.
文摘By means of the method of coupled lower and upper quasisolutio ns, the paper applies, instead of establishing the comparison theorem, a new ite rative technique to nonlinear impulsive Fredholm integral equations in Banach sp aces and proves the existence theorem on their coupled extremal quasisolutions . Finally, an infinite system of nonlinear impulsive integral equations is provi ded to demonstrate the obtained results.
基金Supported by the Nature Science Foundation of China(11471091 and 11401143)
文摘In this paper, we investigate a new perturbation theorem for the Moore-Penrose metric generalized inverses of a bounded linear operator in Banach space. The main tool in this paper is ＂the generalized Neumann lemma＂ which is quite different from the method in [12] where ＂the generalized Banach lemma＂ was used. By the method of the perturba- tion analysis of bounded linear operators, we obtain an explicit perturbation theorem and three inequalities about error estimates for the Moore-Penrose metric generalized inverse of bounded linear operator under the generalized Neumann lemma and the concept of stable perturbations in Banach spaces.
文摘Let X be a complex quasi Banach space and Φ:[0,∞)→[0,∞) an increasing convex function with Φ(0)=0 , lim t→∞Φ(t)=∞ and Φ∈Δ 2 . Then L * Φ(X) is a quasi Banach space with continuous quasi norm and L * Φ(X) has the ARNP if and only if X does.
