By using R-weak commutativity of type (Ag) and non-compatible conditions of self-mapping pairs in b-metric space, without the conditions for the completeness of space and the continuity of mappings, we establish some new common fixed point theorems for two self-mappings. Our results differ from other already known results. An example is provided to support our new result. c 2015 All rights reserved.Keywords: b-metric space, common fixed point theorem, R-weakly commuting mappings of type (Ag), non-compatible mapping pairs. 2010 MSC: 47H10, 54H25.
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