Fixed point results via a Hausdorff controlled type metric
Nayab Alamgir, Quanita Kiran, Hüseyin Işık, Hassen Aydi
Abstract
Abstract In this paper, we establish that every controlled metric space $(X, d_{\alpha })$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mo>(</mml:mo><mml:mi>X</mml:mi><mml:mo>,</mml:mo><mml:msub><mml:mi>d</mml:mi><mml:mi>α</mml:mi></mml:msub><mml:mo>)</mml:mo></mml:math> induces a Hausdorff controlled metric $(\textit{H}_{\alpha }, \textit{CLD}(X))$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mo>(</mml:mo><mml:msub><mml:mtext>H</mml:mtext><mml:mi>α</mml:mi></mml:msub><mml:mo>,</mml:mo><mml:mtext>CLD</mml:mtext><mml:mo>(</mml:mo><mml:mi>X</mml:mi><mml:mo>)</mml:mo><mml:mo>)</mml:mo></mml:math> on the class of closed subsets of X which is also complete if $(X, d_{\alpha })$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mo>(</mml:mo><mml:mi>X</mml:mi><mml:mo>,</mml:mo><mml:msub><mml:mi>d</mml:mi><mml:mi>α</mml:mi></mml:msub><mml:mo>)</mml:mo></mml:math> is complete. Furthermore, we define multivalued almost F -contractions on Hausdorff controlled metric spaces and prove some fixed point results.