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In this article, two new fixed point results in the framework of complex-valued rectangular extended b-metric space are established. Our results include as special cases, some well-known results in the corresponding literature. We provide nontrivial examples and an existence theorem of a Fredholm type integral equation to support our assertions and to indicate a usability of the results presented herein. MSC(2010): 46S40, 47H10, 54H25.doi:10.29252/maco.1.2.11 fatcat:aq5cmonmsfc5nf5bodigfnzv6i