Introducing the Third-Order Fuzzy Superordination Concept and Related Results

Abstract

Third-order fuzzy differential subordination studies were recently initiated by developing the main concepts necessary for obtaining new results on this topic. The present paper introduces the dual concept of third-order fuzzy differential superordination by building on the known results that are valid for second-order fuzzy differential superordination. The outcome of this study offers necessary and sufficient conditions for determining subordinants of a third-order fuzzy differential superordination and, furthermore, for finding the best subordinant for such fuzzy differential superordiantion, when it can be obtained. An example to suggest further uses of the new outcome reported in this work is enclosed to conclude this study.

Keywords

• fuzzy set
• third-order fuzzy differential subordination
• third-order fuzzy differential superordination
• fuzzy subordinant
• best fuzzy subordinant