| Summary: | Here, we shall introduce the new notion of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mi>C</mi><mo>*</mo></msup></semantics></math></inline-formula>-algebra valued bipolar <i>b</i>-metric spaces as a generalization of usual metric spaces, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mi>C</mi><mo>*</mo></msup></semantics></math></inline-formula>-algebra valued metric space, <i>b</i>-metric spaces. In the above-mentioned spaces, we shall define <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>(</mo><msub><mi>α</mi><mi mathvariant="fraktur">A</mi></msub><mo>−</mo><msub><mi>ψ</mi><mi mathvariant="fraktur">A</mi></msub><mo>)</mo></mrow></semantics></math></inline-formula> contractions and prove some fixed point theorems for these contractions. Some existing results from the literature are also proved by using our main results. As an application Ulam–Hyers stability and well-posedness of fixed point problems are also discussed. Some examples are also given to illustrate our results.
|
|---|