Abstract: Fixed point theorems of Altmantype were studied. The existence of the fixed point of completely continuous operator was discussed under the norm inequality conditions that the first exponent parameter was respectively greater than 1 and between 0 and 1， at the same time， the second one was not less than 0. Some new fixed point theorems were proved. These inequality conditions were different from those as shown in earlier works in which the results were extended and supplemented. The conclusions were valid for more general operators such as semiclosed 1setcontraction， convexpower condensing operator and semiclosed convexpower 1setcontraction in references.

Key words: fixed point, completely continuous operator, 1setcontraction, convexpower condensing, convexpower 1setcontraction