Variational-Like Inequalities with Generalized Monotone Mappings in Banach Spaces

Fang, Ya-Ping; Huang, Nan-jing

doi:10.1023/a:1025499305742

Cited by 103 publications

(75 citation statements)

References 14 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In addition, we provide sufficient conditions for existence solution for the case of unbounded sets. The results of this paper can be viewed as generalization of many known results (see [15,18,19]). Moreover, we recall an application of existence result for a differential inclusion.…”

Section: Definitionsupporting

confidence: 57%

Existence Results for Some Equilibrium Problems Involvingα-Monotone Bifunction

Hashoosh

Alimohammady

Kalleji

2016

International Journal of Mathematics and Mathematical Sciences

View full text Add to dashboard Cite

show abstract

Section: Definitionsupporting

confidence: 57%

Existence Results for Some Equilibrium Problems Involvingα-Monotone Bifunction

Hashoosh

Alimohammady

Kalleji

2016

International Journal of Mathematics and Mathematical Sciences

View full text Add to dashboard Cite

show abstract

“…The concept of well-posedness is motivated by the numerical methods producing approximating sequences. So, many authors were devoted to generalizing the concept of wellposedness of optimization problems (see [1,3]), variational inequalities (see [4][5][6]19]), fixed point problems (see [17]), equilibrium problems (see [14,15,[20][21][22]) and inclusion problems (see [2]) etc.…”

Section: Introductionmentioning

confidence: 99%

On the well-posedness of the generalized split quasi-inverse variational inequalities

Cao¹,

Kong²,

Zeng³

2016

J. Nonlinear Sci. Appl.

View full text Add to dashboard Cite

In this paper, a generalized split quasi-inverse variational inequality ((GSQIVI), for short) is considered and investigated in Hilbert spaces. Since the well-posedness results, not only show us the qualitative properties of problem (GSQIVI), but also it gives us an outlook to the convergence analysis of the solutions for (GSQIVI). Therefore, we first introduce the concepts concerning with the approximating sequences, well-posedness and well-posedness in the generalized sense of (GSQIVI). Then, under those definitions, we establish several metric characterizations and equivalent conditions of well-posedness for the (GSQIVI) by using the measure of noncompactness theory and the generalized Cantor theorem. c 2016 All rights reserved.Keywords: Generalized split quasi-inverse variational inequality, measure of noncompactness, well-posedness, Painlevé-Kuratowski limits. 2010 MSC: 49J53, 49K40, 90C33, 90C46.

show abstract

“…In recent decades, many results concerned the existence of solutions for equilibrium problems and vector equilibrium problems has been established; please see, Ansari and Yao [1]; Bianchi and Schaible [4]; Blum and Oettli [5]; Fang and Huang [10]; Farajzadeh et al [11,12] and the references therein.…”

Section: Introductionmentioning

confidence: 99%