<abstract xmlns="http://www.w3.org/1999/xhtml">

The purpose of the present paper is to introduce and study new subclasses of analytic functions which generalize the classes of Janowski functions with q-derivative. We also study certain a convolution conditions, and apply the convolution conditions to get sufficient condition and the neighborhood results related to the functions in the class 𝒮q(A, B, α).
</abstract>

A note on convolution of Janowski type functions with q-derivative

<abstract xmlns="http://www.w3.org/1999/xhtml">

In the present work, we establish the strong approximations of the empirical k-spacings process {αn(x): 0 ≤ x&lt; ∞} (cf. (3)). We state the moment convergence rates results for this process.
</abstract>

Laboratoire de Mathématiques Appliquées

On the strong approximation of the non-overlapping k-spacings process with application to the moment convergence rates

<abstract xmlns="http://www.w3.org/1999/xhtml">

In this paper, we study the prime order Cayley graph assigned to the group ℤn for different values of n. We specify some of the graph theoretical properties such as chromatic and perfect matching numbers. Furthermore, we determine the adjacency matrices and eigenvalues of the prime order Cayley graph associated with groups ℤn and 𝒟2n.
</abstract>

Some new results on the prime order Cayley graph of given groups

<abstract xmlns="http://www.w3.org/1999/xhtml">

In this paper, singularly perturbed differential equations having both small and large delay are considered. The considered problem contains large delay parameter on the reaction term and small delay parameter on the convection term. The solution of the problem exhibits interior layer due to the delay parameter and strong right boundary layer due to the small perturbation parameter ε. The resulting singularly perturbed problem is solved using exponential fitted operator method. The stability and parameter uniform convergence of the proposed method are proved. To validate the applicability of the scheme, one model problem is considered for numerical experimentation.
</abstract>

Parametric uniform numerical method for singularly perturbed differential equations having both small and large delay

<abstract xmlns="http://www.w3.org/1999/xhtml">

In this paper we introduce the concept of pre-Schur convex functions defined on general domains from plane. Then, by making use of Green’s identity for double integrals, we establish some integral inequalities for this class of functions that naturally generalize the case of Schur convex functions. Some exmples for rectangles and disks are also provided.
</abstract>

Pre-Schur convex functions and some integral inequalities on domains from plane

<abstract xmlns="http://www.w3.org/1999/xhtml">

In this paper we study a Neumann boundary value problem of a new p(x)-Kirchhoff type problems driven by p(x)-Laplacian-like operators. Using the theory of variable exponent Sobolev spaces and the method of the topological degree for a class of demicontinuous operators of generalized (S+) type,weprove theexistenceofaweak solutionsof this problem. Our results are a natural generalisation of some existing ones in the context of p(x)-Kirchhoff type problems.
</abstract>

Laboratory LMACS, Faculty of Science and Technology of Beni Mellal

On a new p(x)-Kirchhoff type problems with p(x)-Laplacian-like operators and Neumann boundary conditions

<abstract xmlns="http://www.w3.org/1999/xhtml">

The purpose of the present paper is to find a necessary and sufficient condition for Miller-Ross-type Poisson distribution series to be in the class 𝒲δ(α, γ, β) of analytic functions with negative coefficients .Also, we investigate several inclusion properties of the classes 𝒮∗, 𝒦 and ℝτ(A, B) associated of the operator 𝕀ν,cm defined by this distribution. Further, we consider an integral operator related to Miller-Ross-type Poisson distribution series. Several corollaries and consequences of the main results are also considered.
</abstract>

Subclass of analytic functions with negative coefficients related with Miller-Ross-type Poisson distribution series

<abstract xmlns="http://www.w3.org/1999/xhtml">

In this paper we deal with <bold>Nil</bold> geometry, which is one of the homogeneous Thurston 3-geometries. We define the “surface of a geodesic triangle” using generalized Apollonius surfaces. Moreover, we show that the “lines” on the surface of a geodesic triangle can be defined by the famous Menelaus’ condition and prove that Ceva’s theorem for geodesic trianglesistruein <bold>Nil</bold> space. In our work we will use the projective model of <bold>Nil</bold> geometry described by E. Molnár in [<xref ref-type="bibr" rid="j_ausm-2023-0008_ref_006">6</xref>].
</abstract>

On Menelaus’ and Ceva’s theorems in Nil geometry

<abstract xmlns="http://www.w3.org/1999/xhtml">

Menon’s identity states that for every positive integer n one has ∑ (a − 1, n) = φ (n)τ(n), where a runs through a reduced residue system (mod n), (a − 1, n) stands for the greatest common divisor of a − 1 and n, φ(n) is Euler’s totient function, and τ(n) is the number of divisors of n. Menon’s identity has been the subject of many research papers, also in the last years. We present detailed, self contained proofs of this identity by using different methods, and point out those that we could not identify in the literature. We survey the generalizations and analogs, and overview the results and proofs given by Menon in his original paper. Some historical remarks and an updated list of references are included as well.
</abstract>

Proofs, generalizations and analogs of Menon’s identity: a survey

<abstract xmlns="http://www.w3.org/1999/xhtml">

In this paper, we introduce and investigate a new family, denoted by 𝒲Σsc (λ, η, δ, r), of normalized holomorphic and bi-univalent functions with respect to symmetric conjugate points, defined in 𝕌, by making use the Borel distribution series, which is associated with the Horadam polynomials. We derive estimates on the initial Taylor-Maclaurin coefficients and solve the Fekete-Szeg˝o type inequalities for functions in this family.
</abstract>

College of Science University of Al-Qadisiyah

New family of bi-univalent functions with respect to symmetric conjugate points associated with Borel distribution

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Acta Universitatis Sapientiae, Mathematica

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