Tom 28 (2020): Zeszyt 2 (December 2020)

In this study, the author has established a new lemma and Bullen-type inequalities for conformable fractional integrals. Also, it is given some applications involving Bullen type integral inequalities for differentiable functions to show the results.

The main first goal of this work is to introduce an Urysohn type Chlodovsky operators defined on positive real axis by using the Urysohn type interpolation of the given function f and bounded on every finite subinterval. The basis used in this construction are the Fréchet and Prenter Density Theorems together with Urysohn type operator values instead of the rational sampling values of the function. Afterwards, we will state some convergence results, which are generalization and extension of the theory of classical interpolation of functions to operators.

For some classes of analytic functions f, g, h and k in the open unit disk 𝕌, we consider the general integral operator 𝒢_n, that was introduced in a recent work [1] and we obtain new conditions of univalence for this integral operator. The key tools in the proofs of our results are the Pascu’s and the Pescar’s univalence criteria, as well as the Mocanu’s and Şerb’s Lemma. Some corollaries of the main results are also considered. Relevant connections of the results presented here with various other known results are briefly indicated.

In the current paper, we introduce a new family for holomorphic functions defined by Wanas operator associated with Poisson distribution series. Also we derive some interesting geometric properties for functions belongs to this family.

We consider the equality case in Thunsdorff inequality and Cauchy-Schwarz inequality. For these two equations we prove Ulam stability.

In this article, our aim is to estimate an upper bounds for the second Hankel determinant H₂(2) of a certain class of analytic and bi-univalent functions with respect to symmetric conjugate defined in the open unit disk U.

We consider the classical Szász-Mirakyan and Szász-Mirakyan-Durrmeyer operators, as well as a Kantorovich modification and a discrete version of it. The images of exponential functions under these operators are determined. We establish estimates involving differences and quotients of these images.

By this research notes, the well-known Tremblay operator and certain core knowledge therewith are firstly introduced and an extensive result containing numerous (analytic and) geometric properties (of possible applications of the related operator) along with a number of special implications are then constituted. As method for proving, the well-known assertion proposed by [8] is also considered there.

In this paper we obtain some bounds in terms of polynomials for the function sinxx{{\sin x} \over x}, x ∈ [0, π].