Variational problems and its duality in banach spaces

Abstract

The concept of duality for the variational problems is introduced in general Banach spaces. Different forms of duality such as Mangasarian and Mond-Weir type are studied. Mond-Weir type duality is considered to weaken the convexity requirements. Many duality (weak, strong and converse) results are established under generalized convexity assumptions. Again, examples and counterexamples are discussed in support of the investigation.

Keywords:

• Duality of the variational problems
• Convexity
• Mangasarian and Mond-Weir type duality
• Duality results

2010 Mathematics Subject Classifications:

• 65K05
• 65K10
• 65K99
• 32A70