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We introduce the notion of theC    ⁎-algebra-valued    G   -metric space. The existence and uniqueness of some fixed-point theorems for self-mappings with contractive or expansive conditions on completeC    ⁎-algebra-valued    G   -metric spaces are proved. As an application, we prove the existence and uniqueness of the solution of a type of differential equations.

journal of function spaces

<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M1"><mml:mrow><mml:msup><mml:mrow><mml:mi>C</mml:mi></mml:mrow><mml:mrow><mml:mo>⁎</mml:mo></mml:mrow></mml:msup></mml:mrow></mml:math>-Algebra-Valued <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M2"><mml:mrow><mml:mi>G</mml:mi></mml:mrow></mml:math>-Metric Spaces and Related Fixed-Point Theorems

C⁎-Algebra-Valued G-Metric Spaces and Related Fixed-Point Theorems