Tom 29 (2021): Zeszyt 1 (June 2021)

We are concerned with a family of Markov operators and some modifications of them. Differences involving such operators are studied. We compare their Voronovskaya formulas and determine the limits of their iterates.

A new continuous distribution is proposed using Epanechnikov kernel function and the exponential distribution. This distribution is called the Epanechnikov-exponential distribution. Some properties of this distribution are studied. A simulation study is conducted to calculate the mean and the standard deviation of this distribution and to investigate the behavior of MLE to conserve the consistency property. An application to a real data set is conducted, it showed that he new distribution is more flexible than the exponential distribution.

The purpose of this paper is to prove a common fixed point theorem for a pair of mappings satisfying an implicit relation, generalizing the main results from [6], [10], [11], [13] and other papers.

In this current study, we introduce and investigate a new subclass of holormorphic and bi-univalent functions 𝕰 ^η,ϕ_q(ϑ) in the unit disk λ associated with q-derivative operator. The coefficient estimates |b₂| and |b₃| on the new subclass are obtained and important results are indicated.

In this paper, we consider the ruled surfaces obtained the lightlike curve in the 2-dimensional lightlike cone according to the frame given in [7]. We obtain necessary and sufficient conditions for the ruled surfaces to be minimal and to have a harmonic Gauss map. Then we see that the ruled surface is minimal if and only if it has a harmonic Gauss map.

Via Hirota bilinear method and perturbation technique, a more general N-soliton solution with a parameter p for a (3+1)-dimensional nonlinear evolution equation is obtained. And two N-soliton solutions in terms of Wronskian determinant are also presented in the case of p = 1 and p = 3.

The main purpose of this paper is to establish some common fixed point theorems for single and set-valued mappings, under strict contractive conditions with no continuity, no completeness, no inclusions and without using neither compactness nor closeness. These theorems improve the results of Fisher [8], Ahmed [1] and [2], and others. Also, common fixed point theorems for two hybrid pairs satisfying a contractive condition of integral type are given improving the results of [3], [4] and [6].

In this paper, we suggest and analyze a new approximation schemes (3) to solve the extended general variational inequalities (2), which were introduced by Muhammad Aslam Noor (see[7, 9]). Using the projection operator technique, we establish the equivalence between the extended general variational inequalities and the fixed-point problem. This equivalent formulation is used to discuss the existence of a solution of the extended general variational inequalities. Several special cases are also discussed.

In this article, by making use of Horadam polynomials, we introduce and investigate a certain family 𝔗_Σ (λ, α, β, k, γ; x) of analytic and biunivalent functions associated with Wanas operator which defined in the open unit disk 𝕌. We establish upper bounds for the initial Taylor-Maclaurin coefficients and obtain the Fekete-Szegö inequality of functions belonging to this family. We also point out several certain special cases for our results.

This paper is dealing with a class of operators fixing exponential functions. We study its convergence and an asymptotic formula is obtained. Finally, a comparison is stated, that shows that in a certain particular cases the new sequence approximates better than the classical ones.