Absolutely Fuzzy Lipschitz p-summing Maps between Fuzzy Pointed Metric Spaces


  • Manaf Adnan Saleh Saleh Department of Mathematics and Computer Applications, College of Sciences, Al-Nahrain University, Jadriya, Baghdad, Iraq
  • Laith K. Shaakir Department of Mathematics, College of Computer Sciences and Mathematics, Tikrit University, Tikrit, Iraq




Lipschitz ideals, Fuzzy functional analysis, Fuzzy real analysis


Motivated by Lipschitz ideals in the conventional (crisp) theory, we are constructing a new Lipschitz ideal in fuzzy theory. We introduce the notion of fuzzy Lipschitz ideals and give some elementary illustrations. The class of absolutely fuzzy Lipschitz -summing maps  between arbitrary fuzzy pointed metric spaces is a significant category of fuzzy Lipschitz ideals. It is a logical extension of the concept of absolutely (crisp) Lipschitz p-summing maps between arbitrary pointed metric spaces, as established by Farmer Jeffrey and William Johnson. We establish that the fuzzy Lipschitz norm of the previously specified concept is a fuzzy real number. We demonstrate that a complete fuzzy normed fuzzy operator ideal is the resulting class of fuzzy Lipschitz operators between arbitrary fuzzy pointed metric spaces and complete fuzzy normed spaces. Next, we define a basic characterisation of a Lipschitz p-summing map that is completely fuzzy. By demonstrating a fuzzy variant of the nonlinear Pietsch Domination Theorem, this is accomplished. Lastly, we bring forth a few unsolved problems that we find intriguing.


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