Almost weakly picard operators

Abstract In the present paper, we will introduce and exemplify the class of almost weakly Picard operator, taking into account some weak forms of the Picard operators, which is one of the most important concepts of metric fixed point theory, available in the literature. Then, we will present a fixed point theorem that shows that this new class is not meaningless by developing the concept of “mapping contracting perimeters of triangles” recently defined by Petrov. Finally, we will define the concept of $$(\phi ,L)$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mo>(</mml:mo> <mml:mi>ϕ</mml:mi> <mml:mo>,</mml:mo> <mml:mi>L</mml:mi> <mml:mo>)</mml:mo> </mml:mrow> </mml:math> -contractive perimeters of triangles using comparison functions and show that such mappings are weakly Picard operators in the complete metric space.