# Showing papers in "Asian-european Journal of Mathematics in 2017"

••

TL;DR: In this paper, the authors investigated the radius ρ such that, for the function F(z) = f(ρz)/ρ, zF′(z)/F(z), lies in the lune defined by w ∈ ℂ : |w2 − 1| < 2|w|} for all z ∈ 𝔻.

Abstract: Several subclasses of starlike functions are associated with regions in the right half plane of the complex plane, like half-plane, disks, sectors, parabolas and lemniscate of Bernoulli. For a normalized analytic function f defined on the open unit disk 𝔻 belonging to certain well-known classes of functions associated with the above regions, we investigate the radius ρ such that, for the function F(z) = f(ρz)/ρ, zF′(z)/F(z) lies in the lune defined by {w ∈ ℂ : |w2 − 1| < 2|w|} for all z ∈ 𝔻.

46 citations

••

TL;DR: In this article, sufficient conditions for approximate controllability of a semilinear fractional stochastic control system with delay were presented for Lipschitz continuous nonlinear functions.

Abstract: The objective of this paper is to present some sufficient conditions for approximate controllability of semilinear fractional stochastic control system with delay. The results hold when the nonlinear function is Lipschitz continuous. Sufficient conditions are obtained by separating the given fractional semilinear stochastic system into two systems namely a semilinear fractional system and a fractional linear stochastic system. To prove our results, the Schauder fixed point theorem is applied. At the end, one example is given to illustrate the results.

28 citations

••

TL;DR: In this paper, the authors presented the formulation of a corruption control model and its analysis using the theory of differential equations and found the equilibrium of the model and stability of these equilibria are discussed in detail.

Abstract: The problem of corruption is of serious concern in all the nations, more so in the developing countries. This paper presents the formulation of a corruption control model and its analysis using the theory of differential equations. We found the equilibria of the model and stability of these equilibria are discussed in detail. The threshold quantity R0 which has a similar implication here as in the epidemiological modeling is obtained for the present model. The corruption free equilibrium is found to be stable when R0 is less than 1 and unstable for R0 > 1. The endemic equilibrium which signifies the presence of corrupted individuals in the society exists only when R0 > 1. This equilibrium point is locally asymptotically stable whenever it exists. We perform extensive numerical simulations to support the analytical findings. Furthermore, we extend the model to include optimal control and the optimal control profile is obtained to get the maximum control within a stipulated period of time. Our presented results show that the level of corruption in the society can be reduced if corruption control efforts through media/punishments etc. are increased and put in place.

24 citations

••

TL;DR: In this paper, Pachpatte's inequality is employed to discuss the Ulam-Hyers stabilities of Volterra integrodifferential equations and delay integro-differential equations in Banach spaces on both finite and infinite intervals.

Abstract: In this paper, Pachpatte’s inequality is employed to discuss the Ulam–Hyers stabilities for Volterra integrodifferential equations and Volterra delay integrodifferential equations in Banach spaces on both finite and infinite intervals. Examples are given to show the applicability of our obtained results.

20 citations

••

TL;DR: In this article, the authors investigate commutativity of a ring with involution (R, ∗) which admits a generalized derivation satisfying certain algebraic identities, and provide examples to show that the assumed restrictions cannot be relaxed.

Abstract: Our purpose in this paper is to investigate commutativity of a ring with involution (R,∗) which admits a generalized derivation satisfying certain algebraic identities. Some well-known results characterizing commutativity of prime rings have been generalized. Moreover, we provide examples to show that the assumed restrictions cannot be relaxed.

19 citations

••

TL;DR: In this article, the exact solutions of nonlinear KdV-like equations using Lie point symmetry and λ-symmetry methods were obtained in the form of doubly periodic, bright and dark soliton solutions.

Abstract: In this paper, we obtained some new exact solutions of some nonlinear KdV-like equations using Lie point symmetry and λ-symmetry methods. The obtained solutions are in the form of doubly periodic, bright and dark soliton solutions.

18 citations

••

TL;DR: In this article, an approximate solution for solving weakly singular kernel partial integro-differential equations with time fractional order is proposed, based on using a second-order time difference approximation followed by applying the fractional integral operator and piecewise linear interpolation to compute the singularity of the kernel that appear in the discretization process.

Abstract: In this paper, an approximate solution for solving weakly singular kernel partial integro-differential equations with time fractional order is proposed. The method is based on using a second-order time difference approximation followed by applying the fractional integral operator and piecewise linear interpolation to compute the singularity of the kernel that appear in the discretization process. The stability of the method is also considered in the sense of von Neumann analysis. Numerical examples are solved to demonstrate the validity and applicability of the presented technique.

17 citations

••

TL;DR: For non-abelian nilpotent Lie algebras with dimension n, the authors showed that s(L) = 3 is a sufficient condition that L ≤ H(1) ⊕ F(n − 3).

Abstract: Let L be a non-abelian nilpotent Lie algebra of dimension n and put s(L) = 1 2(n − 1)(n − 2) + 1 −dimℳ(L), where ℳ(L) denotes the Schur multiplier of L. Niroomand and Russo in 2011 proved that s(L) ≥ 0 and that s(L) = 0 if and only if L≅H(1) ⊕ F(n − 3), in which H(1) is the Heisenberg algebra of dimension 3 and F(n − 3) is the abelian (n − 3)-dimensional Lie algebra. In the same year, they also classified all nilpotent Lie algebras L satisfying s(L) = 1 or 2. In this paper, we obtain all nilpotent Lie algebras L provided that s(L) = 3.

16 citations

••

TL;DR: In this paper, the authors construct Kantorovich type Szasz-Mirakjan operators generated by Dunkl generalization of the exponential function via q-integers and obtain some approximation results via well-kno...

Abstract: In this paper, we construct Kantorovich type Szasz–Mirakjan operators generated by Dunkl generalization of the exponential function via q-integers. We obtain some approximation results via well-kno...

14 citations

••

TL;DR: The structural properties of skew cyclic codes over the ring are investigated using decomposition method and the idempotent generators of skew cycling codes over [Formula: see text] have been discussed.

Abstract: In this paper, we study skew cyclic codes over the ring Fq + uFq + vFq, where u2 = u, v2 = v, uv = vu = 0, q = pm and p is a prime. We define a Gray map from Fq + uFq + vFq to Fq3 and investigate t...

14 citations

••

TL;DR: In this article, the authors define two n × n matrices An and Bn with ai,j = Hi,jr and bi,j= Hi,mj, respectively, where Hn,mr are a generalized hyperharmonic numbers of order r.

Abstract: In this paper, we define two n × n matrices An and Bn with ai,j = Hi,jr and bi,j = Hi,mj, respectively, where Hn,mr are a generalized hyperharmonic numbers of order r. We give some new factorizations and determinants of the matrices An and Bn.

••

Düzce University

^{1}TL;DR: In this article, some generalization of weighted Ostrowski type integral inequalities for mappings of bounded variation are obtained and some interesting inequalities as special cases are given, and the generalization is shown to be applicable to the case of bounded variations.

Abstract: In this paper, some generalization of weighted Ostrowski type integral inequalities for mappings of bounded variation are obtained and some interesting inequalities as special cases are given.

••

TL;DR: In this article, the existence of fixed points of mapping defined on generalized metric spaces satisfying a nonlinear contraction condition was proved. But the results were generalized to generalized and ordinary metric spaces.

Abstract: In the paper, we shall prove the results on the existence of fixed points of mapping defined on generalized metric space satisfying a nonlinear contraction condition, which is a generalization of Diaz and Margolis theorem (see [A fixed point theorem of the alternative, for contractions on a generalized complete metric space, Bull. Amer. Math. Soc. 74 (1968) 305–309]). We also present local fixed point theorems both in generalized and ordinary metric spaces. Our results are generalizations of Banach fixed point theorem and many other results.

••

TL;DR: In this paper, the authors generalize the concept of residuated posets by replacing the usual partial ordering by a generic binary relation, giving rise to relational systems which are residuated, and modify the definition of adjointness in such a way that the ordering relation can be harmlessly replaced by a binary relation.

Abstract: The aim of the present paper is to generalize the concept of residuated poset, by replacing the usual partial ordering by a generic binary relation, giving rise to relational systems which are residuated. In particular, we modify the definition of adjointness in such a way that the ordering relation can be harmlessly replaced by a binary relation. By enriching such binary relation with additional properties, we get interesting properties of residuated relational systems which are analogical to those of residuated posets and lattices.

••

TL;DR: In this article, the authors introduced and studied strongly almost convergent double sequence spaces by Riesz mean associated with a four-dimensional bounded regular matrix and a Musielak-Orlicz function.

Abstract: In this paper, we introduce and study some strongly almost convergent double sequence spaces by Riesz mean associated with four-dimensional bounded regular matrix and a Musielak–Orlicz function ove...

••

TL;DR: In this paper, an alternative but considerable short approach is proposed for determining the aforementioned tricyclic graphs, which is based on the maximum general sum-connectivity index among all n-vertex tricycle graphs.

Abstract: Recently, Zhu and Lu, [On the general sum-connectivity index of tricyclic graphs, J. Appl. Math. Comput. 51(1) (2016) 177–188] determined the graphs having maximum general sum-connectivity index among all n-vertex tricyclic graphs. In this short note, an alternative but considerable short approach is proposed for determining the aforementioned graphs.

••

TL;DR: In this paper, the authors considered the regularity problem for weak Navier-Stokes equations in ℝ3 and showed that, if the velocity u satisfies ∂3u ∈ L2(0,T; BMO(ℝ 3)) then the solution actually is smooth on ( 0,T).

Abstract: In this note, we consider the regularity problem for the weak solutions, under the critical condition to the Navier–Stokes equations in ℝ3. We show that, if the velocity u satisfies ∂3u ∈ L2(0,T; BMO(ℝ3)) then the solution actually is smooth on (0,T). This improves a result established in a recent work by Liu [Q. Liu, A regularity criterion for the Navier–Stokes equations in terms of one directional derivative of the velocity, Acta Appl. Math. 140 (2015) 1–9].

••

TL;DR: In this paper, the authors characterized the connected hop dominating sets in the join, corona and lexicographic product of graphs and determined the corresponding connected hop domination number of these graphs.

Abstract: Let G = (V (G),E(G)) be a simple graph. A hop dominating set S ⊆ V (G) is called a connected hop dominating set of G if the induced subgraph 〈S〉 of S is connected. The smallest cardinality of a connected hop dominating set of G, denoted by γch(G), is called the connected hop domination number of G. In this paper, we characterize the connected hop dominating sets in the join, corona and lexicographic product of graphs and determine the corresponding connected hop domination number of these graphs. The study of these concepts is motivated with a social network application.

••

TL;DR: The study of the essential ideal graph of a commutative ring with identity was initiated in this article, where the authors investigated its properties and showed that it is a graph whose vertex set is the set of all nonzero proper ideals of R and two vertices I and J are adjacent whenever I + J is an essential ideal.

Abstract: Let R be a commutative ring with identity The essential ideal graph of R, denoted by ℰR, is a graph whose vertex set is the set of all nonzero proper ideals of R and two vertices I and J are adjacent whenever I + J is an essential ideal In this paper, we initiate the study of the essential ideal graph of a commutative ring and we investigate its properties

••

TL;DR: In this article, it was shown that ID*(L) and ID*M are isomorphic for any two isoclinic Filippov algebras L and M.

Abstract: Let L be a Filippov algebra. A derivation of L is called an ID-derivation if its image is contained in the derived algebra of L. Let ID*(L) be the set of all ID-derivations which map central elements to 0. We prove that ID*(L) and ID*(M) are isomorphic for any two isoclinic Filippov algebras L and M.

••

TL;DR: For a group algebra KG of a group G over a field K of characteristic p > 0, it is well known that p + 1 is the minimal upper as well as the minimal lower Lie nilpotency index as mentioned in this paper.

Abstract: For a group algebra KG of a group G over a field K of characteristic p > 0, it is well known that p + 1 is the minimal upper as well as the minimal lower Lie nilpotency index. Group algebras of upper Lie nilpotency index upto 7p − 5 have already been characterized completely. In this paper, we classify the modular group algebra KG having upper Lie nilpotency index 8p − 6 which is the possible next higher Lie nilpotency index.

••

TL;DR: In this article, the traveling fronts of curvature flow and constant φ-curvature curves were shown to have the same properties as Fenchel's type theorem in the plane with density eφ satisfying Δφ = 0.

Abstract: In this paper, we show some relations between traveling fronts of curvature flow and constant φ-curvature curves. In the plane with density eφ satisfying Δφ = 0, we prove a Fenchel’s type theorem f...

••

TL;DR: In this paper, an alternative but relatively simple approach is used for characterizing the aforementioned graph, which is a tetracyclic graph with respect to the first and second Zagreb indices.

Abstract: In the chemical graph theory, graph invariants are usually referred to as topological indices. The second Zagreb index (denoted by M2) is one of the most studied topological indices. For n ≥ 5, let 𝕋𝔼𝕋n be the collection of all non-isomorphic connected graphs with n vertices and n + 3 edges (such graphs are known as tetracyclic graphs). Recently, Habibi et al. [Extremal tetracyclic graphs with respect to the first and second Zagreb indices, Trans. on Combin. 5(4) (2016) 35–55.] characterized the graph having maximum M2 value among all members of the collection 𝕋𝔼𝕋n. In this short note, an alternative but relatively simple approach is used for characterizing the aforementioned graph.

••

TL;DR: In this paper, an attempt has been made to understand the complex dynamics of a spatial predator-prey system with Beddington-DeAngelis type functional response in the presence of prey-taxis and subjected to homogonality.

Abstract: An attempt has been made to understand the complex dynamics of a spatial predator–prey system with Beddington–DeAngelis type functional response in the presence of prey-taxis and subjected to homog...

••

TL;DR: The distance signless Laplacian matrix of a connected graph G is defined as DQ(G) = Tr(G + D(G), where D is the distance matrix of G and Tr is the diagonal matrix whose main entries are the vertex transmissions of G as mentioned in this paper.

Abstract: The distance signless Laplacian matrix DQ(G) of a connected graph G is defined as DQ(G) = Tr(G) + D(G), where D(G) is the distance matrix of G and Tr(G) is the diagonal matrix whose main entries are the vertex transmissions of G, and the spectral radius of a connected graph G is the largest eigenvalue of DQ(G). In this paper, first we obtain the DQ(G)-eigenvalues of the join of certain regular graphs. Next, we give some new bounds on the distance signless Laplacian spectral radius of a graph G in terms of graph parameters and characterize the extremal graphs. Utilizing these results we present some upper and lower bounds on the distance signless Laplacian energy of a graph G.

••

TL;DR: In this article, the authors investigated the trees which maximize or minimize the reduced second Zagreb index among all n-vertex trees with fixed number of segments, and developed some results, which may be used to characterize the extremal trees with respect to the aforementioned index.

Abstract: The current note is devoted to investigate the trees, which maximize or minimize the reduced second Zagreb index among all n-vertex trees with fixed number of segments. This note also involves development of some results, which may be used to characterize the extremal trees with respect to the aforementioned index among all n-vertex trees having fixed number of branching vertices.

••

TL;DR: In this article, the authors give algebraic dependences theorems for meromorphic mappings sharing moving hyperplanes without counting multiplicity, where all zeros with multiplicities more than a certain number are omitted.

Abstract: This paper deals with the multiple values and algebraic dependences problem of meromorphic mappings sharing moving hyperplanes in projective space. We give some algebraic dependences theorems for meromorphic mappings sharing moving hyperplanes without counting multiplicity, where all zeros with multiplicities more than a certain number are omitted. Basing on these results, some unicity theorems regardless of multiplicity for meromorphic mappings in several complex variables are given. These results are extensions and strong improvements of some recent results.

••

TL;DR: In this article, the authors characterize ordered k-regular semirings using their ordered kideals and investigate the characterizations of left and right ordered K-regular semiirings.

Abstract: An ordered semiring (S, +,⋅,≤) is called ordered k-regular if for every element a of S there exist x,y,s,t ∈ S with x ≤ asa,y ≤ ata such that a + x ≤ y. An ordered ideal A of S is called an ordered k-ideal, if x ∈ S and x + a = b for some a,b ∈ A then x ∈ A. In this work, we characterize ordered k-regular semirings using their ordered k-ideals. Moreover, characterizations of left(right) ordered k-regular semirings and left(right) ordered k-weakly regular semirings are investigated.

••

TL;DR: In this article, the authors introduce the concept of set-valued Presic-Reich type contractive condition in ultrametric spaces and establish the existence and uniqueness of coincidence and common fixed point of a setvalued and a single-valued mapping besides furnishing illustrative examples.

Abstract: In this paper, we introduce the concept of set-valued Presic–Reich type contractive condition in ultrametric spaces and establish the existence and uniqueness of coincidence and common fixed point of a set-valued and a single-valued mapping besides furnishing illustrative examples to highlight the realized improvements in the context of ultrametric spaces. Our results generalize and extend some known results in the literature.

••

TL;DR: In this article, the generalized Srivastava-Attiya operator is studied and a set of subordination results are obtained and some special cases connected with the Hurwitz-Lerch zeta function and their relevances with known results are also pointed out.

Abstract: In this paper, we study certain properties involving the generalized Srivastava–Attiya operator. A set of subordination results are obtained and some special cases connected with the Hurwitz–Lerch zeta function and their relevances with known results are also pointed out.