caa a22 4500 463169212 CHVBK 20180406164808.0 cr unu---uuuuu 170326e20070901xx s 000 0 eng 10.1007/s10957-007-9236-7 doi (NATIONALLICENCE)springer-10.1007/s10957-007-9236-7 Existence of Solutions of Systems of Generalized Implicit Vector Variational Inequalities [Elektronische Daten] [S. Al-Homidan, Q. Ansari, S. Schaible] We consider five different types of systems of generalized vector variational inequalities and derive relationships among them. We introduce the concept of pseudomonotonicity for afamily of multivalued maps and prove the existence of weak solutions of these problems under these pseudomonotonicity assumptions in the setting of Hausdorff topological vector spaces as well as real Banach spaces. We also establish the existence of astrong solution of our problems under lower semicontinuity for afamily of multivalued maps involved in the formulation of the problems. By using anonlinear scalar function, we introduce gap functions for our problems by which we can solve systems of generalized vector variational inequalities using optimization techniques. Springer Science+Business Media, LLC, 2007 Systems of generalized implicit vector variational inequalities nationallicence Pseudomonotonicity nationallicence Existence results for asolution nationallicence Gap functions nationallicence Lower semicontinuity nationallicence Upper hemicontinuity nationallicence ℋ-Hemicontinuity nationallicence Al-Homidan S. Department of Mathematical Sciences, King Fahd University of Petroleum and Minerals, Dhahran, Saudi Arabia aut Ansari Q. Department of Mathematical Sciences, King Fahd University of Petroleum and Minerals, Dhahran, Saudi Arabia aut Schaible S. A.G. Anderson Graduate School of Management, University of California, Riverside, CA, USA aut Journal of Optimization Theory and Applications Springer US; http://www.springer-ny.com 134/3(2007-09-01), 515-531 0022-3239 134:3<515 2007 134 10957 https://doi.org/10.1007/s10957-007-9236-7 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s10957-007-9236-7 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Al-Homidan S. Department of Mathematical Sciences, King Fahd University of Petroleum and Minerals, Dhahran, Saudi Arabia aut NATIONALLICENCE 700 1- Ansari Q. Department of Mathematical Sciences, King Fahd University of Petroleum and Minerals, Dhahran, Saudi Arabia aut NATIONALLICENCE 700 1- Schaible S. A.G. Anderson Graduate School of Management, University of California, Riverside, CA, USA aut NATIONALLICENCE 773 0- Journal of Optimization Theory and Applications Springer US; http://www.springer-ny.com 134/3(2007-09-01), 515-531 0022-3239 134:3<515 2007 134 10957 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer