Abstract
AbstractIn this chapter among other topics, we further study global smoothness over R. A very general positive linear integral type operator is given through a convolution-like iteration of another general positive linear operator with a scaling type function. For it sufficient conditions are given for shift invariance, preservation of global smoothness, convergence to the unit with rates, shape preserving and preservation of continuous probabilistic distribution functions. Furthermore, examples of very general specialized operators are presented fulfilling all the above properties; especially, the inequalities for global smoothness preservation are proven to be sharp. Here we follow the basic study done by the first author and Gonska [30].KeywordsDistribution FunctionUnit OperatorProbabilistic Distribution FunctionPositive Linear OperatorContinuous Distribution FunctionThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
