Approximation of fixed point of multivalued ρ-quasi-contractive mappings in modular function spaces

The purpose of this paper is to extend the recent results of Okeke et al. (2018) to the class of multivalued <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"><m:mi>ρ</m:mi></m:math> -quasi-contractive mappings in modular function spaces. We approximate fixed points of this class of nonlinear multivalued mappings in modular function spaces. Moreover, we extend the concepts of <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"><m:mi>T</m:mi></m:math> -stability, almost <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"><m:mi>T</m:mi></m:math> -stability and summably almost <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"><m:mi>T</m:mi></m:math> -stability to modular function spaces and give some results.