The purpose of the present paper is to introduce a class $\boldsymbol{D}% _{\lambda, \delta }^{k, \alpha }C_{0}(\beta )$ of bi-concave functions defined by a differential operator. We find estimates on the Taylor-Maclaurin coefficients $\left\vert a_{2}\right\vert $ and $\left\vert a_{3}\right\vert $ for functions in this class. Several consequences of these results are also pointed out in the form of corollaries.

The purpose of the present paper is to introduce a class Dn  ;  C0( ) of bi-concave functions de ned by Al-Oboudi di erential operator. We  nd estimates on the Taylor-Maclaurin coe cients ja2j and ja3j for functions in this class. Several consequences of these results are also pointed out in the form of corollaries.

In this paper, we first study the non-positive decreasing and inverse co-radiant functions defined on a real locally convex topological vector space X. Next, we characterize non-positive increasing, co-radiant and quasi-concave functions over X. In fact, we examine abstract concavity, upper support set and superdifferential of this class of functions by applying a type of duality. Finally, we present abstract concavity of extended real valued increasing, co-radiant and quasi-concave functions.

The fuzzy integrals are a kind of fuzzy measures acting on fuzzy sets. They can be viewed as an average membership value of fuzzy sets. The value of the fuzzy integral in a decision making environment where uncertainty is present has been well established. Most of the integral inequalities studied in the fuzzy integration context normally consider conditions such as monotonicity or comonotonicity. In this paper, we are trying to extend the fuzzy integrals to the concept of concavity. It is shown that the Hermite-Hadamard integral inequality for concave functions is not satisfied in the case of fuzzy integrals. We propose upper and lower bounds on the fuzzy integral of concave functions. We present a geometric interpretation and some examples in the framework of the Lebesgue measure to illustrate the results.

In the current article, we introduce and investigate two new families of strongly Ozaki ,-pseudo bi-close-to-convex functions in the open unit disk. We determine upper bounds for the second and third coe, cients of functions belonging to these new subclasses. Also, we point out several certain special cases for our results.

In the present investigation, we use the Horadam Polynomials to establish upper bounds for the second and third coe, cients of functions belongs to a new subclass of analytic and ,-pseudo-starlike bi-univalent functions de, ned in the open unit disk U. Also, we discuss Fekete-Szeg, o problem for functions belongs to this subclass.

Let 𝝨 be the class of meromorphic bi-univalent functions f of the formf(z)=z+b_0+∑ _(n=1)^∞ ▒ b_n/z^n, which are univalent (analytic and one to one) on the domain Δ ={z∈ C∶ 1.

In this paper, we introduce and investigate a subclass Hh, pS(b) of analytic and bi-univalent functions in the open unit disk U. Upper bounds for the second and third coefficients of functions in this subclass are founded. Our results generalize and improve over the existing results in the literature.

The purpose of the present paper is to introduce and investigate two new subclasses KΣ m(λ , γ ; α ) and K∗ Σ m (λ , γ ; β ) of Σ m consisting of analytic and m-fold symmetric bi-univalent functions defined in the open unit disk U. We obtain upper bounds for the coefficients |am+1| and |a2m+1| for functions belonging to these subclasses. Many of the well-known and new results are shown to follow as special cases of our results.

In this paper, we introduce the notion of hyper BI-algebra and investigate some properties of it. Also, we state and prove some theorems which determine the rela-tionship among R=C=D=T and V-hyper BI-algebras un-der some conditions. Then we study the relation among hyper BI-algebra with some of other hyper logical alge-bras such as hyper BCI/BCK/K/B/BCC-algebras and show that under which condition these hyper structures coincide. In addition, we de ne hyper subalgebra and (weak) ideal of a hyper BI-algebra and obtain some re-sults and the relation between them. Finally, we con-struct the quotient structure of hyper BI-algebra and ex-amine the isomorphism theorems.