Generalized set-valued variational-like inclusions involving
-η-cocoercive operator in Banach spaces
1 Department of Mathematics, Aligarh Muslim University, Aligarh, 202002, India
2 Department of Applied Mathematics, Chung Yuan Christain University, Chung Li, 32023, Taiwan
3 Center for General Education, Kaohsiung Medical University, Kaohsiung, 807, Taiwan
4 Department of Applied Mathematics, National Sun-Yat Sen University, Kaohsiung, 804, Taiwan
Journal of Inequalities and Applications 2012, 2012:149 doi:10.1186/1029-242X-2012-149Published: 28 June 2012
The aim of this paper is to introduce a new -η-cocoercive operator and its resolvent operator. We study some of the properties of -η-cocoercive operator and prove the Lipschitz continuity of resolvent operator associated with -η-cocoercive operator. Finally, we apply the techniques of resolvent operator to solve a generalized set-valued variational-like inclusion problem in Banach spaces. Our results are new and generalize many known results existing in the literature. Some examples are given in support of definition of -η-cocoercive operator.
MSC: 47H19, 49J40.