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 comparable 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.

Keywords: Complex valued metric space, Complex Valued Rectangular Extended $b$-metric space, Fixed point, Integral equation.

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