Summary: | In this paper, we introduce the concept of <inline-formula><math display="inline"><semantics><msup><mi>d</mi><mo>*</mo></msup></semantics></math></inline-formula>-complete topological spaces, which include earlier defined classes of complete metric spaces and quasi <i>b</i>-metric spaces. Further, we prove some fixed point results for mappings defined on <inline-formula><math display="inline"><semantics><msup><mi>d</mi><mo>*</mo></msup></semantics></math></inline-formula>-complete topological spaces, generalizing earlier results of Tasković, Ćirić and Prešić, Prešić, Bryant, Marjanović, Yen, Caccioppoli, Reich and Bianchini.
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