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

Abstract

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.