In order to study some geometric properties in Banach space
a new geometric property kUKK is given. The definition of kUKK operator and kNUC operator is givenaccording to its definition.The relation between kUKK operator and kNUC operator is proved. Thesufficient and necessary conditions for the operator in Banach space to be kNUCare reflexive and kUKK; The properties of kUKK operators are discussed. Finally
the relationship between kUKK operators and kUKK properties is studied.