# Arabian Journal of Mathematics

## List of Papers (Total 204)

#### Best proximity points in modular function spaces

We generalize the notion of best proximity points in the context of modular function spaces. We have found sufficient conditions for the existence and uniqueness of best proximity points for cyclic maps in modular function spaces. We present an application of the main result for cyclic integral operators in Orlicz function spaces, endowed with an Orlicz function modular.

#### Some Grüss-type results via Pompeiu’s-like inequalities

In this paper, some Grüss-type results via Pompeiu’s-like inequalities are proved.

#### An algorithm for finding a common point of the solutions of fixed point and variational inequality problems in Banach spaces

Let C be a nonempty, closed and convex subset of a 2-uniformly convex and uniformly smooth real Banach space E. Let T: C→ C be relatively nonexpansive mapping and let A i : C→ E* be L i -Lipschitz monotone mappings, for i = 1,2. In this paper, we introduce and study an iterative process for finding a common point of the fixed point set of a relatively nonexpansive mapping and the...

#### On weakly $${\mathfrak{Z}}$$ -permutable subgroups of finite groups II

Let G be a finite group. We say that $${\mathfrak{Z}}$$ is a complete set of Sylow subgroups of G if for each prime p dividing the order of $${G, \mathfrak{Z}}$$ contains exactly one Sylow p-subgroup of G, G p say. A subgroup of G is said to be $${\mathfrak{Z}}$$-permutable in G if it permutes with every member of $${\mathfrak{Z}}$$. A subgroup H of G is said to be weakly...

#### Heat transfer near the stagnation point of an unsteady three-dimensional flow

In this paper, the unsteady laminar three-dimensional flow of an incompressible viscous fluid in the neighbourhood of a stagnation point is studied. The magnetic field is applied normal to the surface and the effects of viscous dissipation and Ohmic heating are taken into account. The unsteadiness in the flow is caused by the external free stream varying arbitrarily with time...

#### Ball convergence theorems for eighth-order variants of Newton’s method under weak conditions

We present a local convergence analysis for eighth-order variants of Newton’s method in order to approximate a solution of a nonlinear equation. We use hypotheses up to the first derivative in contrast to earlier studies such as Amat et al. (Appl Math Comput 206(1):164–174, 2008), Amat et al. (Aequationes Math 69:212–213, 2005), Chun et al. (Appl Math Comput. 227:567–592, 2014...

#### Inferences using type-II progressively censored data with binomial removals

This paper considers the estimation problem for Burr type-X model, when the lifetimes are collected under type-II progressive censoring with random removals, where the number of units removed at each failure time follows a binomial distribution. The methods of maximum likelihood as well as the Bayes procedure to derive both point and interval estimates of the parameters are used...

#### Categorical frameworks for generalized functions

We tackle the problem of finding a suitable categorical framework for generalized functions used in mathematical physics for linear and non-linear PDEs. We are looking for a Cartesian closed category which contains both Schwartz distributions and Colombeau generalized functions as natural objects. We study Frölicher spaces, diffeological spaces and functionally generated spaces...

#### Hermite–Hadamard type inequalities for differentiable $${h_{\varphi}}$$ -preinvex functions

In this paper, we introduce a new class of convex functions which is called $${h_{\varphi}}$$-preinvex functions. We prove several Hermite–Hadamard inequalities for $${h_{\varphi}}$$-preinvex functions. Some special cases are also discussed. Results proved in this paper continue to hold for these special cases. Our results may stimulate further investigation regarding variant...

#### On an integral equation under Henstock–Kurzweil–Pettis integrability

In this paper, we investigate the set of solutions for nonlinear Volterra type integral equations in Banach spaces in the weak sense and under Henstock–Kurzweil–Pettis integrability. Moreover, a fixed point result is presented for weakly sequentially continuous mappings defined on the function space C(K, X), where K is compact Hausdorff and X is a Banach space. The main condition...

#### Fuzzy $${k_{\circ}}$$ -preproximities related to fuzzy closure spaces

The aim of this paper is to define the concept of fuzzy k 0-preproximity and show how a fuzzy closure space is induced by a fuzzy k 0-preproximity and vice versa. Also, we introduce the notion of fuzzy k 0-preproximal neighborhood system.

#### Ulam stability of a generalized reciprocal type functional equation in non-Archimedean fields

In this paper, we obtain the solution of a new generalized reciprocal type functional equation in two variables and investigate its generalized Hyers–Ulam stability in non-Archimedean fields. We also present the pertinent stability results of Hyers–Ulam–Rassias stability, Ulam–Gavruta–Rassias stability and J. M. Rassias stability controlled by the mixed product-sum of powers of...

#### A regularity criterion for the 3D MHD equations in terms of the gradient of the pressure in the multiplier spaces

In this paper, we consider the regularity criterion for the 3D MHD equations and prove that if the gradient of the pressure belongs to $${L^\frac{2}{2-r}(0,T;\dot X_r(\mathbb{R}^{3}))}$$ with $${0\leq r\leq 1}$$ , then the solution is smooth. Notice that we extend the result given by Gala (Appl Anal 92:96–103, 2013).

#### Comparison of deterministic and stochastic SIRS epidemic model with saturating incidence and immigration

The purpose of this work is to compare the stochastic and deterministic versions of an SIRS epidemic model. The SIRS models studied here include constant inflows of new susceptibles, infectives and removeds. These models also incorporate saturation incidence rate and disease-related death. First, we study the global stability of deterministic model with and without the presence...

#### Studying monoids is not enough to study multiplicative properties of rings: an elementary approach

The aim of these notes is to indicate, using very simple examples, that not all results in ring theory can be derived from monoids and that there are results that deeply depend on the interplay between “ + ” and “·”.

#### Statistical dynamics of continuous systems: perturbative and approximative approaches

We discuss general concept of Markov statistical dynamics in the continuum. For a class of spatial birth-and-death models, we develop a perturbative technique for the construction of statistical dynamics. Particular examples of such systems are considered. For the case of Glauber type dynamics in the continuum we describe a Markov chain approximation approach that gives more...

#### Generalized functions beyond distributions

Ultrafunctions are a particular class of functions defined on a non-Archimedean field $${\mathbb{R}^{\ast } \supset \mathbb{R}}$$. They have been introduced and studied in some previous works (Benci, Adv Nonlinear Stud 13:461–486, 2013; Benci and Luperi Baglini, EJDE, Conf 21:11–21, 2014; Benci, Basic Properties of ultrafunctions, to appear in the WNDE2012 Conference Proceedings...

#### Note on valuative dimension in power series rings

We give necessary and sufficient conditions for the power series ring $${R{[[x_1,\ldots,x_n]]}}$$ to be a Jaffard domain, where R is an almost pseudo-valuation domain.

#### Existence results for a class of nonlocal problems involving p(x)-Laplacian

We study the existence of weak solutions for a p(x)-Kirchhoff problem. The main tool used is the variational method, more precisely, the Mountain Pass Theorem.

#### Non-linear differential polynomials sharing small function with finite weight

The purpose of the paper is to study the uniqueness of meromorphic functions sharing a small function with weight. The results of the paper improve and extend some recent results due to Banerjee and Sahoo (Sarajevo J Math 20:69–89, 2012), which in turn radically improve, extend and supplement some results of Dyavanal (J Math Anal Appl 372(1):252–261, 2010; 374(1):334, 2011; 374(1...

#### Hydrodynamic limit in a particle system with topological interactions

We study a system of particles in the interval [ 0 , ϵ - 1 ] ∩ Z , ϵ - 1 a positive integer. The particles move as symmetric independent random walks (with reflections at the endpoints); simultaneously new particles are injected at site 0 at rate j ϵ (j > 0) and removed at same rate from the rightmost occupied site. The removal mechanism is, therefore, of topological rather than...

#### Direct sums of trace maps and self-adjoint extensions

We give a simple criterion so that a countable infinite direct sum of trace (evaluation) maps is a trace map. An application to the theory of self-adjoint extensions of direct sums of symmetric operators is provided; this gives an alternative approach to results recently obtained by Malamud–Neidhardt and Kostenko–Malamud using regularized direct sums of boundary triplets.

#### Asymptotics of semigroups generated by operator matrices

We survey some known results about operator semigroup generated by operator matrices with diagonal or coupled domain. These abstract results are applied to the characterization of well-/ill-posedness for a class of evolution equations with dynamic boundary conditions on domains or metric graphs. In particular, our results on the heat equation with general Wentzell-type boundary...