General New Results on <inline-formula><math display="inline"><semantics><mrow><mrow><mo>(</mo><mrow><mi>ϕ</mi><mo>,</mo><mi mathvariant="script">F</mi></mrow><mo>)</mo></mrow><mo>−</mo></mrow></semantics></math></inline-formula>Contractions in <inline-formula><math display="inline"><semantics><mrow><mi>b</mi><mo>−</mo></mrow></semantics></math></inline-formula>Metric-like-Spaces

Abstract

Thispaper recognizes a general approach related to recent fixed point results about the classes of interpolative and hybrid contractions in metric space and general metric spaces. Considering auxiliary functions, so called Wardowski functions, and a rich set of implicit relations, we introduce types of (αvq,ϕ,F)−contractions and r−order hybrid (αvq,ϕ,F)−contractions in the setting of b−metric-like spaces. They generate and simplify many forms of contractions widely used in the literature. The resulting theorems significantly extend, generalize, and unify an excellent work on fixed point theory.

Keywords

• (<i>α</i><i>_v^q</i>, <i>ϕ</i>, <i>ℱ</i>)−contraction
• <i>r</i>−order hybrid (<i>α_v^q</i>, <i>ϕ</i>, <i>ℱ</i>)−contraction
• <i>b</i>−metric-like space
• fixed point