B α,β-Operator and Fitzpatrick Functions

Abstract

In this paper, we introduce B_α,β-operator as a new techniqne to generalize Fitzpatrick functions. We study the properties of this new operator, such as convexity, weak *-closedness, locally boundedness and Fenchel duality. Further-more, we present new concept that is C^α_n-monotone bifunction. By the application of the new operator, we prove that (equation) for each n ≥ 2. This equation is a generalization for a known result which is studied by many researchers.

Key words and phrases. Monotone bifunction; equilibrium problem; Fitzpatrick function; cyclically monotone.

2000 Mathematics Subject Classification. 90C30, 49J52