| Summary: | The aim of the present research article is to investigate the existence and uniqueness of a solution to the integral equation and homotopy result. To achieve our objective, we introduce the notion of (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>α</mi><mo>,</mo><mi>η</mi><mo>,</mo><mi>ψ</mi></mrow></semantics></math></inline-formula>)-contraction in the framework of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="fraktur">F</mi></semantics></math></inline-formula>-bipolar metric space and prove some fixed point results for covariant and contravariant mappings. Some coupled fixed point results in <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="fraktur">F</mi></semantics></math></inline-formula>-bipolar metric space are derived as outcomes of our principal theorems. A non-trivial example is also provided to validate the authenticity of the established results.
|
|---|