Search

In this paper, we introduce and study a new kind of graph related to a unitary module [Formula: see text] on a commutative ring [Formula: see text] with identity, namely the annihilators comaximal graph of submodules of [Formula: see text], denoted by [Formula: see text]. The (undirected) graph [Formula: see text] is with vertices of all non-trivial submodules of [Formula: see text] and two vertices [Formula: see text] of [Formula: see text] are adjacent if and only if their annihilators are comaximal ideals of [Formula: see text], i.e. [Formula: see text]. The main purpose of this paper is to investigate the interplay between the graph-theoretic properties of [Formula: see text] and the module-theoretic properties of [Formula: see text]. We study the annihilators comaximal graph [Formula: see text] in terms of the powers of the decomposition of [Formula: see text] to product distinct prime numbers in some special cases.

In this paper, we propose and study a new algorithm for finding a common element of the sets of solutions of split equality pseudomonotone equilibrium, split equality monotone variational inclusion and fixed point problems for Bregman relatively nonexpansive mappings in [Formula: see text]-uniformly convex and uniformly smooth Banach spaces. Our iterative method uses stepsizes which do not require prior knowledge of the operator norm. We apply our result to solve split equality variational inequality and split equality convex minimization problems. The result present in this paper unifies and extends several existing results in the literature.

Let [Formula: see text] be a graph with edge set [Formula: see text]. For an edge [Formula: see text] in [Formula: see text], we define [Formula: see text], where [Formula: see text] and [Formula: see text] are degrees of vertices [Formula: see text] and [Formula: see text] in [Formula: see text], respectively. For [Formula: see text], the graph invariants [Formula: see text], [Formula: see text] and [Formula: see text] are defined as [Formula: see text], [Formula: see text] and [Formula: see text], where [Formula: see text] means that the edges [Formula: see text] and [Formula: see text] are incident. In this paper, some relationship between these graph invariants and some classical topological indices were presented. Moreover, some bounds for [Formula: see text], [Formula: see text] and [Formula: see text] are obtained and trees with the first through the third smallest [Formula: see text] and [Formula: see text], as well as the trees with the first through the forth smallest [Formula: see text] are also characterized.

In this paper, we prove that the dominion of any full orthodox subsemigroup of a medial orthodox semigroup is described by the Isbell zigzag theorem in the category of medial orthodox semigroups. As a consequence, the dominions of any full completely regular subsemigroup of a medial completely regular semigroup as well as that of any full Clifford subsemigroup of a medial Clifford semigroup are also described by the Isbell zigzag theorem in the categories of all medial completely regular semigroups and of all medial Clifford semigroups, respectively.

Finding the solution of the absolute value equations (AVEs) has attracted much attention in recent years. In this paper, we propose and analyze two generalized accelerated overrelaxation (AOR) methods for solving AVEs [Formula: see text], where [Formula: see text] is an [Formula: see text]-matrix. Furthermore, we discuss the convergence of the methods under some suitable assumptions. Numerical results are given to verify the effectiveness of our methods.

In this paper, our objective is to study numerous fundamental properties of the algebra of generalized derivations on a multiplicative BiHom-Poisson superalgebra [Formula: see text]. First, we present a description of some generalized derivations, central derivations, quasiderivations, centroid and quasicentroid of the multiplicative BiHom-Poisson superalgebra [Formula: see text] More specifically, we obtain some important connections and properties of these derivations. We prove that in a larger multiplicative BiHom-Poisson superalgebra, [Formula: see text] can be embedded as a derivations algebra. Finally, we show that when [Formula: see text] is centerless, the derivations of the larger multiplicative BiHom-Poisson superalgebras have direct sum decompositions.

The domatic number [Formula: see text] of a graph [Formula: see text] is the maximum number of disjoint dominating sets in a dominating set partition of a graph [Formula: see text]. For any graph [Formula: see text], [Formula: see text] where [Formula: see text] is the minimum degree of [Formula: see text], and [Formula: see text] is domatically full if the equality holds, i.e., [Formula: see text]. In this paper, we characterize domatically full Cartesian products of a path of order 2 and a tree of order at least 3. Moreover, we show a characterization of the Cartesian product of a longer path and a tree of order at least 3. By using these results, we also show that for any two trees of order at least 3, the Cartesian product of them is domatically full.

In this paper, we study the solvability of a very general class of integral equations whose kernel depends on four different functions. Necessary and sufficient conditions for the unique solvability of such integral equations are obtained. To achieve such a goal, the main technique consists in introducing eight new convolutions weighted by multi-dimensional Hermite functions and using them as convolutions somehow associated with our integral equations. In this way, two Young-type inequalities are also obtained.

In this paper, we study the existence and uniqueness of solutions for Riemann–Stieltjes integral boundary value problems of nonlinear implicit Hadamard fractional differential equations. The investigation of the main results depends on Schauder’s fixed point theorem and Banach’s contraction principle. An illustrative example is given to show the applicability of theoretical results.

The subjectivity domain of a module allows us to evaluate how close (or far) a module is from being injective. In this paper, we consider three families of rings characterized by their RD-injective left [Formula: see text]-modules via the subinjective domain: those whose noninjective RD-injective left [Formula: see text]-modules are subinjective relatively only to divisible modules, those whose noninjective RD-injective left [Formula: see text]-modules are subinjective relatively only to fp-injective modules and those whose noninjective RD-injective left [Formula: see text]-modules are subinjective relatively only to injective modules.

Let [Formula: see text] be a lattice, [Formula: see text] an ideal of [Formula: see text] and [Formula: see text] the set of all elements of [Formula: see text] which are not prime to [Formula: see text]. In this paper, we investigate some interesting properties of [Formula: see text] and introduce the total graph of a lattice [Formula: see text] with respect to an ideal [Formula: see text]. It is the graph with all elements of [Formula: see text] as vertices and for distinct [Formula: see text], the vertices [Formula: see text] and [Formula: see text] are adjacent if and only if [Formula: see text]. We investigated the basic properties of this graph and its induced subgraphs as diameter, girth, clique number, cut vertex and independence number.

This paper deals with the Ulam–Hyers stability of the following additive-quadratic mixed type functional equation: [Formula: see text] [Formula: see text] [Formula: see text] in modular spaces using the direct method.

The aim of this paper is to introduce new notions called generalized [Formula: see text] contraction and rational type [Formula: see text] contraction for hybrid maps in complete G-metric spaces. First, using new concept of generalized [Formula: see text] contraction we establish a common fixed point theorem for a hybrid pair of weakly compatible maps. Second, we prove a common fixed point theorem for occasionally coincidentally idempotent mappings satisfying another new concept of rational type [Formula: see text] contraction under common limit range property. Our results generalize and improve several known results of the existing literature. Also, we give an example to indicate the usefulness of our main results.

In this paper, on using a left exact preradical, we define a module [Formula: see text] to be EPD (EPG) if and only if each ep-submodule [Formula: see text] of [Formula: see text] is a direct summand (there exists a direct summand [Formula: see text] such that [Formula: see text] is essential in both [Formula: see text] and [Formula: see text]). We investigate structural properties of former new classes of modules and locate the implications between the other extending properties. We deal with decomposition theory as well as ring and module extensions for EPD and EPG-modules. We show that the EPD property is inherited by finite direct sums however we provide algebraic topological examples which show that direct summands do not enjoy the property. Moreover, we obtain that EPG property is closed under right essential overring and rational hull. We provide examples to illustrate some of the results by making special choices of left exact preradicals.

In this paper, we prove that if [Formula: see text] is a partitioning ideal of an [Formula: see text]-semiring [Formula: see text] with respect to two subsets [Formula: see text] and [Formula: see text] of [Formula: see text], then the quotient [Formula: see text]-semirings [Formula: see text] and [Formula: see text] are isomorphic. Also, the concepts of maximal homomorphism, steady homomorphism, one-one homomorphism and [Formula: see text]-homomorphism are generalized for [Formula: see text]-semirings and obtained relation between them. Finally, the fundamental theorem of semiring homomorphism is generalized for [Formula: see text]-semirings.

A collection of matrices is not always reducible, but it is beneficial for further analysis if it is. Some criteria for the algebraic reducibility have been considered in literature and, indeed, in some cases we are able to compute the reduced forms explicitly. We will review these methods in this paper. As their applications, we will consider the reductions (simplifications) of matrix continued fractions and discuss the convergence problems.

Roopaei [J. Inequal. Appl. 2020 (2020) 120] introduced the sequence space [Formula: see text] which is a matrix domain of Copson matrix in the space [Formula: see text] [Formula: see text] In this paper, we characterize the matrix classes [Formula: see text], [Formula: see text] and [Formula: see text] [Formula: see text]. Moreover, we characterize compact operators associated with matrices belonging to these classes via the techniques of measures of noncompactness.

In this paper, we consider mixed approximation operators based on second-kind beta transform using Szász–Mirakjan operators. For the proposed operators, we establish some direct results, Voronovskaya-type theorem, quantitative Voronovskaya-type theorem, Grüss–Voronovskaya-type theorem, weighted approximation and functions of bounded variation.

All groups under consideration are finite. Let [Formula: see text] be some partition of the set of all primes [Formula: see text], [Formula: see text] be a group, and [Formula: see text] be a class of groups. Then, [Formula: see text] and [Formula: see text] A function [Formula: see text] of the form [Formula: see text] is called a formation [Formula: see text]-function. For any formation [Formula: see text]-function [Formula: see text] the class [Formula: see text] is defined as follows: [Formula: see text] [Formula: see text] If for some formation [Formula: see text]-function [Formula: see text] we have [Formula: see text] then the class [Formula: see text] is called [Formula: see text]-local and [Formula: see text] is called a [Formula: see text]-local definition of [Formula: see text] Every formation is called 0-multiply [Formula: see text]-local. For [Formula: see text] a formation [Formula: see text] is called [Formula: see text]-multiply [Formula: see text]-local provided either [Formula: see text] is the class of all identity groups or [Formula: see text] where [Formula: see text] is [Formula: see text]-multiply [Formula: see text]-local for all [Formula: see text] Let [Formula: see text] be a set of subgroups of [Formula: see text] such that [Formula: see text]. Then, [Formula: see text] is called a subgroup functor if for every epimorphism [Formula: see text] : [Formula: see text] and any groups [Formula: see text] and [Formula: see text] we have [Formula: see text] and [Formula: see text]. A class of groups [Formula: see text] is called [Formula: see text]-closed if [Formula: see text] for all [Formula: see text]. In this paper, we study the properties of [Formula: see text]-closed [Formula: see text]-multiply [Formula: see text]-local formations generated by some set of groups. In particular, we obtained a description of the smallest [Formula: see text]-local definition of such formation, we also prove that [Formula: see text]-closed [Formula: see text]-multiply [Formula: see text]-local formation [Formula: see text] is one-generated if and only if [Formula: see text] is finite and [Formula: see text] have a integrated [Formula: see text]-local definition [Formula: see text] such that [Formula: see text] is a one-generated [Formula: see text]-closed [Formula: see text]-multiply [Formula: see text]-local formation for all [Formula: see text]. In addition, we prove that the class of all [Formula: see text]-closed one-generated [Formula: see text]-multiply [Formula: see text]-local formations coincides with the class of all one-generated [Formula: see text]-closed [Formula: see text]-multiply [Formula: see text]-local formations.

The irregularity of a simple undirected graph G is defined as irr(G) = Sigma(uv is an element of E(G)) vertical bar d(G)(u) - d(G) (v) vertical bar, where d(G) (u) denotes the degree of a vertex u is an element of V (G). The total irregularity of a graph as a new measure of graph irregularity is defined as irr(t) (G) = 1/2 Sigma(u,v is an element of V (G) )vertical bar d(G) (u) - d(G) (v) vertical bar. In this paper, the irregularity and the total irregularity of fractal graphs and the derived graphs from a class of fractal graphs are investigated. Exact formulae are presented for the computation of the irregularity and total irregularity of fractal-type graphs in terms of the parameters of the underlying graphs.

In this paper, one-dimensional time fractional telegraph equation is deduced using fractional Ohm’s law in transmission lines. The nonlocal behavior, arising from the time fractality, is discussed via fractional calculus. Here, the time fractional differential equation related to electrical GLRC circuit is proposed in terms of the Liouville–Caputo fractional derivative. To keep the dimensionality of the physical parameters [Formula: see text] the new parameter [Formula: see text] is introduced. This parameter ([Formula: see text]) characterizes the existence of fractional structure in the system. The analytical solution of the proposed equation is obtained by using Laplace transform method in terms of Mittag-Leffler function which describes physical system with memory. The order of the time derivative being considered is [Formula: see text]. The result of an example shows that the behavior of voltage depends on the value of the fractional order of the proposed equation.

This paper studies the bi-compact-[Formula: see text]-open topology on the family [Formula: see text] of all continuous functions from a completely regular space [Formula: see text] to the space [Formula: see text]. We compare this topology with open-point topology, bi-point-open topology and bi-compact-open topology and mention an example of a space asked in [P. Garg and S. Kundu, The compact-[Formula: see text]-open topology on [Formula: see text], Topology Appl. 159(8) (2012) 2082–2089] which satisfies [Formula: see text]. We also investigate submertrizability, mertrizability, separability, [Formula: see text]ech-completeness and Baire property of bi-compact-[Formula: see text]-open topology on [Formula: see text].

For a graph [Formula: see text], a double Roman dominating function is a function [Formula: see text] having the property that if [Formula: see text], then vertex [Formula: see text] must have at least two neighbors assigned [Formula: see text] under [Formula: see text] or one neighbor with [Formula: see text], and if [Formula: see text], then vertex [Formula: see text] must have at least one neighbor with [Formula: see text]. The weight of a double Roman dominating function [Formula: see text] is the value [Formula: see text]. The double Roman domination number of a graph [Formula: see text], denoted by [Formula: see text], equals the minimum weight of a double Roman dominating function on [Formula: see text]. The double Roman domination subdivision number [Formula: see text] of a graph [Formula: see text] is the minimum number of edges that must be subdivided (each edge in [Formula: see text] can be subdivided at most once) in order to increase the double Roman domination number. In this paper, we first show that the decision problem associated with sd[Formula: see text] is NP-hard and then establish upper bounds on the double Roman domination subdivision number for arbitrary graphs.

The concept of Sombor indices (SO) of a graph was recently introduced by Gutman and the reduced Sombor index [Formula: see text] of a graph [Formula: see text] is defined by [Formula: see text] where [Formula: see text] is the degree of the vertex [Formula: see text]. In this paper, we study the extremal properties of the reduced Sombor index and characterize the bicyclic graphs with extremal [Formula: see text]-value.

This paper’s purpose is to study the nonlinear Fredholm implicit integro-differential equation in the complex plane, where the term implicit integro-differential means that the derivative of unknown function is founded inside of the integral operator. Initially, according to Banach fixed point theory, we ensure that the equation has a unique solution under particular conditions. However, we exhibit a numerical process based on the conjunction between Nyström and Picard methods, for the sake of approximating solutions of this equation. In addition to that, the convergence analysis of this numerical process is demonstrated, and some illustrated numerical examples are presented.

The Young type inequality asserts that if [Formula: see text] are two positive real numbers, then for each [Formula: see text], we have [Formula: see text] In this paper, we obtain some new inequalities using two different weights. For example, if [Formula: see text], then [Formula: see text] [Formula: see text] where [Formula: see text] In addition, we refine some matrix inequalities for Unitarily invariant norms by applying the deduced numerical inequalities.

The main purpose of this work is to study the existence of solutions for a perturbed second-order evolution inclusion involving time-dependent subdifferential operators. Under suitable conditions on the set-valued perturbation, the main result of the paper is proved in the context of a separable Hilbert space. A second-order evolution quasi-variational inequality is also investigated.

In this paper, the inverse problem of reconstructing the right-hand side from integral observation is studied by using variational method to minimizing objective functional combining with Tikhonov regularization. The L-curve method is suggested for choosing the regularization parameter.

In this paper, we define a module [Formula: see text] to be [Formula: see text] if and only if intersection of each pair of [Formula: see text]-closed direct summands is also a direct summand of [Formula: see text]. We investigate structural properties of [Formula: see text]-modules and locate the implications between the other module properties which are essentially based on direct summands. We deal with decomposition theory as well as direct summands of [Formula: see text]-modules. We apply our results to matrix rings. To this end, it is obtained that the [Formula: see text] property is not Morita invariant.

The power graph of a finite group G is a special type of undirected simple graph whose vertex set is set of elements of G, in which two distinct vertices of G are adjacent if one is the power of other. Let [Formula: see text] be a finite abelian 2-group of order [Formula: see text] where [Formula: see text]. In this paper, we establish that the power graph of finite abelian group G always has graceful labeling without any condition on [Formula: see text].

In this paper, we introduce Fibonacci backward difference operator [Formula: see text] of fractional order l by the composition of Fibonacci band matrix [Formula: see text] and difference operator [Formula: see text] of fractional order l, defined by [Formula: see text] and introduce sequence spaces [Formula: see text] and [Formula: see text] We present some topological properties, obtain Schauder basis and determine [Formula: see text]-, [Formula: see text]- and [Formula: see text]-duals of the spaces [Formula: see text] and [Formula: see text] We characterize certain classes of matrix mappings from the spaces [Formula: see text] and [Formula: see text] to any of the space [Formula: see text] [Formula: see text] [Formula: see text] or [Formula: see text] Finally we compute necessary and sufficient conditions for a matrix operator to be compact on the spaces [Formula: see text] and [Formula: see text]

In this paper, we introduce a new explicit extragradient algorithm for solving Variational Inequality Problem (VIP) in Banach spaces. The proposed algorithm uses a linesearch method whose inner iterations are independent of any projection onto feasible sets. Under standard and mild assumption of pseudomonotonicity and uniform continuity of the VIP associated operator, we establish the strong convergence of the scheme. Further, we apply our algorithm to find an equilibrium point with minimal environmental cost for a model in electricity production. Finally, a numerical result is presented to illustrate the given model. Our result extends, improves and unifies other related results in the literature.

This paper discusses the existence and multiplicity of positive solutions for fractional differential equations with nonlocal fractional integro-differential boundary conditions set on an unbounded domain. Using properties of Green’s function and the fixed point theory, some existence results were obtained. Three examples illustrate the existence theorems.

In this work, we introduce a modified inertial algorithm for solving the split common null point problem without the prior knowledge of the operator norms in Banach spaces. The strong convergence theorem of our method is proved under suitable assumptions. We apply our result to the split feasibility problem, split equilibrium problem and split minimization problem. Finally, we provide some numerical experiments including compressed sensing to illustrate the performances of the proposed method. The result presented in this paper improves and generalizes many recent important results in the literature.