General auxiliary problem and algorithm for a generalized multi-valued variational-like inequality problem in reflexive Banach spaces

Abstract

In this article, some generalized multi-valued variational-like inequality problems and their related general auxiliary problems in real reflexive Banach spaces are introduced. An existence theorem for one of the general auxiliary problems is proved. Furthermore, by exploiting this theorem, an algorithm for the corresponding generalized multi-valued variational-like inequality problem is constructed. The theorems of this article generalize, improve and unify many known corresponding results.

Keywords:

• Generalized multi-valued varitional-like inequality
• General auxiliary problem
• Algorithm
• ε-Monotone mappings
• Hemicontinuous and Lipschitz continuous mappings
• 1991 Mathematics Subject Classifications: 49J20
• 47J25
• 47J30
• 49J40
• 49J53

Notes

^†E-mail: [email protected]

^‡E-mail: [email protected]

Additional information

Notes on contributors

K. R. Kazmi†

†E-mail: [email protected]

H. Zegeye‡

‡E-mail: [email protected]