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Th goal of the pr s nt p p r is to obt in some differ tial sub rdin tion an sup r dination the rems for univalent functions related b differential operator Also, we discussed some sandwich-type results.

We present several new results for higher-order (fourth-order) differential subordination and superordination in this paper by using the new operator Hα,β,δ,ξ,γ,nf(v) and offer numerous new findings for fourth-order differential subordination and superordination. The innovative discoveries presented here are connected to those mentioned in previous articles. The differential subordination theory’s characteristics and outcomes are symmetric to the properties gained. Sandwich-type theorems are created by merging differential superordination theory with sandwich-type theorems.

This paper studies the functions of copula on BL-algebra on n-dimension. Our main idea for this study focuses on linking some statistical concepts with BL-algebra. We have proposed several concepts such as some definitions, theories, characteristics of these functions and test their terms with respect to algebra. In fact, our work focuses on determining the type of generalization of each classical copula type in such a forced system. The conditions of copula, co-copula and its related properties have been demonstrated. In the end, there are many different examples that have been shown on the definitions of each type of copula we have built on BL-algebra.

This work is concerned with the study of copula functions on BL-algebra(Basic logic - algebra). Our main idea of this study focuses on connecting some statistical concepts to some types of algebras. It has been proposed several concepts like some definitions, theorems, and properties of s-function j-function,d-functions and copulas functions and testing their conditions with respect to BL-algebra. Indeed, this work focuses on setting a type of generalization of each classical type of copula on such algebraic system. It has been demonstrating the constructions of copula, and co-copula functions and their relevant properties. Eventually, there are several different examples that have been demonstrated upon the definitions of each type of copula that we have built on BL-algebra.