### FIXED POINT FOR EXPANSION MAPPINGS IN CONE b-METRIC SPACE

#### Abstract

**Abstract****. **In this paper, we first prove a common fixed point theorem in cone b-metric space of a pair of weakly compatible mappings satisfying an extension mapping. Then we introduce T-extension condition in cone b- metric space. There are some mappings, say S:X→X, which have a fixed point but which can’t be obtained by an extension condition, *i.e., *which do not satisfy an extension condition. If another mapping T: X→X is introduced, then extension condition holds. In this case S is said to satisfy **T-extension condition**. We prove our second fixed point theorem using T-extension condition in cone b-metric space.

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