Quasi-contractivity, stability and convergence of WCT operators

Abstract In this paper, we characterize quasi-contractive, stable and convergent weighted conditional-type (WCT) operators on <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mrow> <m:msup> <m:mi>L</m:mi> <m:mi>p</m:mi> </m:msup> <m:mo>⁢</m:mo> <m:mrow> <m:mo stretchy="false">(</m:mo> <m:mi>μ</m:mi> <m:mo stretchy="false">)</m:mo> </m:mrow> </m:mrow> </m:math> {L^{p}(\mu)} . Indeed we provide equivalent conditions for quasi-contraction WCT operators. Also, we prove that convergence, uniform stability, strong stability and weak stability of WCT operators are equivalent. Finally, we provide some concrete examples to illustrate our main results.