Abstract: Publication date: Available online 15 March 2019Source: Arab Journal of Mathematical SciencesAuthor(s): Tarek Saanouni The initial value problem for a semilinear highorder heat equation is investigated. In the focusing case, global wellposedness and exponential decay are obtained. In the focusing sign, global and non global existence of solutions are discussed via the potential well method.
Abstract: Publication date: Available online 14 March 2019Source: Arab Journal of Mathematical SciencesAuthor(s): Sabri T.M. Thabet, Bashir Ahmad, Ravi P. Agarwal In this paper, we study a Cauchytype problem for Hilfer fractional integrodifferential equations with boundary conditions. The existence of solutions for the given problem is proved by applying measure of noncompactness technique in an abstract weighted space. Moreover, we use generalized Gronwall inequality with singularity to establish continuous dependence and uniqueness of ϵapproximate solutions.
S
strong+
Abstract: Publication date: Available online 5 March 2019Source: Arab Journal of Mathematical SciencesAuthor(s): S. Visweswaran, Premkumar T. Lalchandani The rings considered in this article are commutative with identity. Modules are assumed to be unitary. Let R be a ring and let S be a multiplicatively closed subset of R. We say that a module M over R satisfiesS strongaccr∗ if for every submodule N of M and for every sequence of elements of R, the ascending sequence of submodules (N:Mr1)⊆(N:Mr1r2)⊆(N:Mr1r2r3)⊆⋯ is Sstationary. That is, there exist k∈N and s∈S such that s(N:Mr1⋯rn)⊆(N:Mr1⋯rk) for all n≥k. We say that a ring R satisfies S strong accr∗ if R regarded as a module over R satisfies Sstrong
Abstract: Publication date: Available online 25 February 2019Source: Arab Journal of Mathematical SciencesAuthor(s): Munmun Hazarika, Sougata Marik For n≥1, let Dn be the polydisk in ℂn, and let Tn be the ntorus. L2(Tn) denotes the space of Lebesgue square integrable functions on Tn. In this paper we define slant Toeplitz operators on L2(Tn). Besides giving a necessary and sufficient condition for an operator on L2(Tn) to be slant Toeplitz, we also establish several properties of slant Toeplitz operators.
Abstract: Publication date: Available online 22 February 2019Source: Arab Journal of Mathematical SciencesAuthor(s): H. Fukharuddin, A.R. Khan The purpose of this paper is to introduce the implicit midpoint rule (IMR) of nonexpansive mappings in 2 uniformly convex hyperbolic spaces and study its convergence. Strong and △convergence theorems based on this algorithm are proved in this new setting. The results obtained hold concurrently in uniformly convex Banach spaces, CAT0 spaces and Hilbert spaces as special cases.
Abstract: Publication date: Available online 19 February 2019Source: Arab Journal of Mathematical SciencesAuthor(s): Rakesh Kumar, Anuj Kumar Sharma, Kulbhushan Agnihotri A nonlinear modified form of Bass model involving the interactions of nonadopter and adopter populations has been proposed to describe the process of diffusion of a new technology in the presence of evaluation period (time delay). The basic aim is to model the diffusion of those technologies which require higher investments, and which require government subsidies for promotions in the various markets. We use government incentives and the costs in the form of external factors, as well as the internal word of mouth that considerably influence the nonadopters decisions. A qualitative analysis has been performed to determine the stability of the various equilibria. The Hopf bifurcation occurs near the positive equilibrium when the time delay passes some critical values. By applying the normal form theory and the center manifold reduction for functional differential equations, explicit formulae presenting stability properties of bifurcating periodic solutions have been computed. Moreover, the intraspecific competition has played an important role in establishing the maturity stage in the innovation diffusion model. Numerical analysis has been carried out to justify the correctness of our analytical findings.
Abstract: Publication date: Available online 8 February 2019Source: Arab Journal of Mathematical SciencesAuthor(s): Godwin Amechi Okeke, Safeer Hussain Khan The purpose of this paper is to extend the recent results of Okeke et al. (2018) to the class of multivalued ρquasicontractive mappings in modular function spaces. We approximate fixed points of this class of nonlinear multivalued mappings in modular function spaces. Moreover, we extend the concepts of Tstability, almost Tstability and summably almost Tstability to modular function spaces and give some results.
Abstract: Publication date: Available online 11 January 2019Source: Arab Journal of Mathematical SciencesAuthor(s): Aguech Rafik, Selmi Olfa In this paper, we consider a two color multidrawing urn model. At each discrete time step, we draw uniformly at random a sample of m balls (m≥1) and note their color, they will be returned to the urn together with a random number of balls depending on the sample’s composition. The replacement rule is a 2 × 2 matrix depending on bounded discrete positive random variables. Using a stochastic approximation algorithm and martingales methods, we investigate the asymptotic behavior of the urn after many draws.
m

Abstract: Publication date: Available online 2 January 2019Source: Arab Journal of Mathematical SciencesAuthor(s): Artion Kashuri, Rozana Liko The authors discover a new identity concerning differentiable mappings defined on minvex set via fractional integrals. By using the obtained identity as an auxiliary result, some fractional integral inequalities for generalized relative semi m(r;h1,h2)preinvex mappings by involving generalized MittagLeffler function are presented. It is pointed out that some new special cases can be deduced from main results of the paper. Also these inequalities have some connections with known integral inequalities. At the end, some applications to special means for different positive real numbers are provided as well.
Abstract: Publication date: January 2019Source: Arab Journal of Mathematical Sciences, Volume 25, Issue 1Author(s): J.B. Gatsinzi Let f:X→Y be a map between simply connected spaces having the homotopy of finite type CWcomplexes, where H∗(Y,Q) is finite dimensional and ϕ:(∧V,d)→(B,d) a Sullivan model of f. We consider (B,d) as a module over ∧V via the mapping ϕ. Let map(X,Y;f) denote the component of f in the space of mappings from X to Y. In this paper we show that there is a canonical injection π∗(Ωmap(X,Y;f))⊗Q→HH∗(∧V;B).
Abstract: Publication date: January 2019Source: Arab Journal of Mathematical Sciences, Volume 25, Issue 1Author(s): Rafik Aguech, Wissem Jedidi We give several new characterizations of completely monotone functions and Bernstein functions via two approaches: the first one is driven algebraically via elementary preserving mappings and the second one is developed in terms of the behavior of their restriction on N0. We give a complete answer to the following question: Can we affirm that a function f is completely monotone (resp. a Bernstein function) if we know that the sequence f(k)k is completely monotone (resp. alternating)' This approach constitutes a kind of converse to Hausdorff’s moment characterization theorem in the context of completely monotone sequences.
Abstract: Publication date: January 2019Source: Arab Journal of Mathematical Sciences, Volume 25, Issue 1Author(s): Hongwu Wu, Julio G. Dix By using iterated estimates involving all delay arguments, we establish an oscillation criterion for firstorder linear differential equations with several delay arguments. This criterion is focused on the interaction among the delay arguments, instead of converting the original equation into a single delay equation and using existing results. Several examples illustrate the results obtained.
Abstract: Publication date: January 2019Source: Arab Journal of Mathematical Sciences, Volume 25, Issue 1Author(s): Godwin Amechi Okeke We approximate the fixed points of contraction mappings using the Picard–Krasnoselskii hybrid iterative process, which is known to converge faster than all of Picard, Mann and Ishikawa iterations in complex valued Banach spaces. Moreover, we prove analytically and with a numerical example that the Picard–Mann hybrid iteration and the Picard–Krasnoselskii hybrid iteration have the same rate of convergence. Furthermore, we apply our results in finding solutions of delay differential equations in complex valued Banach spaces.
Abstract: Publication date: January 2019Source: Arab Journal of Mathematical Sciences, Volume 25, Issue 1Author(s): Emmanuel Fouotsa This paper considers the computation of the Ate pairing on the Hessian model of elliptic curves. Due to the many important properties making the model attractive in cryptography, we compute for the first time the Ate pairing on this model and show how both the Tate and the Ate pairings can be parallelized on this curve. We wrote codes in the Sage software to ensure the correctness of formulas in this work.
q
integral+equations+in+fractional+
Abstract: Publication date: January 2019Source: Arab Journal of Mathematical Sciences, Volume 25, Issue 1Author(s): M.A. ALTowailb In this paper, we consider a certain system of triple qintegral equations, where the kernel is the third Jackson qBessel functions. We give two solutions by using the fractional qcalculus approach. We study also the system with general kernel. A qanalogue of the result by Cooke and by Williams of 1963 is included.
Abstract: Publication date: January 2019Source: Arab Journal of Mathematical Sciences, Volume 25, Issue 1Author(s): Aymen Ben Amira, Bechir Chaari, Jamel Dammak, Hamza Si Kaddour Two digraphs G=(V,E) and G′=(V,E′) are isomorphic up to complementation if G′ is isomorphic to G or to the complement G¯≔(V,{(x,y)∈V2:x≠y,(x,y)∉E}) of G. The Boolean sum G+̇G′ is the symmetric digraph U=(V,E(U)) defined by {x,y}∈E(U) if and only if (x,y)∈E and (x,y)∉E′, or (x,y)∉E and (x,y)∈E′. Let k be a nonnegative integer. The digraphs G and G′ are (≤k)hypomorphic up to complementation if for every telement subset X of V, with t≤k, the induced subdigraphs G↾X and G↾X...
Abstract: Publication date: January 2019Source: Arab Journal of Mathematical Sciences, Volume 25, Issue 1Author(s): Bouharket Bendouma, Ahmed Hammoudi In this article, we study the existence of solutions to systems of firstorder ∇dynamic inclusions on time scales with terminal or periodic boundary conditions. We employ the method of solutiontube and Kakutani fixed point theorem.
Abstract: Publication date: Available online 31 December 2018Source: Arab Journal of Mathematical SciencesAuthor(s): Khuram Ali Khan, Tasadduq Niaz, Đilda Pečarić, Josip Pečarić In this work, we estimated the different entropies like Shannon entropy, Rényi divergences, Csiszár divergence by using Jensen’s type functionals. The Zipf’s–Mandelbrot law and hybrid Zipf’s–Mandelbrot law are used to estimate the Shannon entropy. The Abel–Gontscharoff Green functions and Fink’s Identity are used to construct new inequalities and generalized them for mconvex function.
Abstract: Publication date: Available online 4 December 2018Source: Arab Journal of Mathematical SciencesAuthor(s): M.M. Elborai, M.I. Youssef In this paper, we use Schauder’s fixed point to establish the existence of at least one solution for a functional nonlocal stochastic differential equation under sufficient conditions in the space of all square integrable stochastic processes with a finite second moment. We state and prove the conditions which guarantee the uniqueness of the solution. We solve a nonlinear example analytically and obtain the initial condition which makes the solution passes through a random position with a given normal distribution at a specified time. Also, the Milstein scheme to this example is studied.
Abstract: Publication date: Available online 27 November 2018Source: Arab Journal of Mathematical SciencesAuthor(s): Arshi Meraj, Dwijendra N. Pandey This paper is concerned with the existence of mild solutions for a class of fractional semilinear integrodifferential equations having noninstantaneous impulses. The result is obtained by using noncompact semigroup theory and fixed point theorem. The obtained result is illustrated by an example at the end.
Abstract: Publication date: Available online 22 November 2018Source: Arab Journal of Mathematical SciencesAuthor(s): Arnab Bhattacharjee Mason introduced the notion of reflexive property of rings as a generalization of reduced rings. For a ring endomorphism α, Krempa studied αrigid rings as an extension of reduced rings. In this note, we introduce the notion of αquasi reflexive rings as a generalization of αrigid rings and a natural extension of the reflexive property to ring endomorphisms. We investigate various properties of these rings and also study ring theoretic extensions such as polynomial rings, trivial extensions, right (left) quotient rings, Dorroh extensions etc. over these rings.
Abstract: Publication date: Available online 12 November 2018Source: Arab Journal of Mathematical SciencesAuthor(s): Velusamy Raja, Ayyadurai Tamilselvan A class of third order singularly perturbed convection diffusion type equations with integral boundary condition is considered. A numerical method based on a finite difference scheme on a Shishkin mesh is presented. The method suggested is of almost first order convergent. An error estimate is derived in the discrete norm. Numerical examples are presented, which validate the theoretical estimates.
Abstract: Publication date: Available online 23 July 2018Source: Arab Journal of Mathematical SciencesAuthor(s): A.M. Jarrah, Nikhil Khanna A formula for calculating moments for wavelet packets is derived and a sufficient condition for moments of wavelet packets to be vanishing is obtained. Also, the convolution and crosscorrelation theorems for Hilbert transform of wavelets are proved. Finally, using MRA of L2(R), some results on the vanishing moments of the scaling functions, wavelets and their convolution in two dimension are given.
Abstract: Publication date: July 2018Source: Arab Journal of Mathematical Sciences, Volume 24, Issue 2Author(s): Karim Chaira, Samih Lazaiz In this paper, we formulate best proximity pair theorems for noncyclic relatively ρnonexpansive mappings in modular spaces in the setting of proximal ρadmissible sets. As a companion result, we establish a best proximity pair theorem for pointwise noncyclic contractions in modular spaces. To that end, we provide some examples throughout the paper to illustrate the validity of the obtained results.
Abstract: Publication date: July 2018Source: Arab Journal of Mathematical Sciences, Volume 24, Issue 2Author(s): Kawtar Attas, Abderrahim Boussaïri, Mohamed Zaidi An arcweighted digraph is a pair (D,ω) where D is a digraph and ω is an arcweight function that assigns to each arc uv of D a nonzero real number ω(uv). Given an arcweighted digraph (D,ω) with vertices v1,…,vn, the weighted adjacency matrix of (D,ω) is defined as the n×n matrix A(D,ω)=[aij] where aij=ω(vivj) if vivj is an arc of D, and 0otherwise. Let (D,ω) be a positive arcweighted digraph and assume that D is loopless and symmetric. A skewsigning of (D,ω) is an arcweight function ω′ such that ω′(uv)=±ω(uv) and ω′(uv)ω′(vu)
Abstract: Publication date: July 2018Source: Arab Journal of Mathematical Sciences, Volume 24, Issue 2Author(s): B. Radhakrishnan, M. Tamilarasi This paper deals with the existence of solutions for quasilinear random impulsive neutral functional differential evolution equation in Banach spaces and the results are derived by using the analytic semigroup theory, fractional powers of operators and the Schauder fixed point approach. An application is provided to illustrate the theory.
Abstract: Publication date: July 2018Source: Arab Journal of Mathematical Sciences, Volume 24, Issue 2Author(s): Samuel Azubuike Iyase, Olawale Joshua Adeleke This paper investigates the existence of solutions for higherorder multipoint boundary value problems at resonance. We obtain existence results by using coincidence degree arguments.
Abstract: Publication date: July 2018Source: Arab Journal of Mathematical Sciences, Volume 24, Issue 2Author(s): S. Reza Hejazi, Elham Lashkarian In this paper, a (3+1)dimensional wave equation is studied from the point of view of Lie’s theory in partial differential equations including conservation laws. The symmetry operators are determined to find the reduced form of the considered equation. The nonlocal conservation theorems and multipliers approach are performed on the (3+1)dimensional wave equation. We obtain conservation laws by using five methods, such as direct method, Noether’s method, extended Noether’s method, Ibragimov’s method; and finally we can derive infinitely many conservation laws from a known conservation law viewed as the last method. We also derive some exact solutions using some conservation laws Anco and Bluman (2002).
Abstract: Publication date: July 2018Source: Arab Journal of Mathematical Sciences, Volume 24, Issue 2Author(s): Abdelkader Zagane, Seddik Ouakkas In this paper, we will study the class of biharmonic maps with potential, in the particular case represented by conformal maps between equidimensional manifolds. Some examples are constructed in particular cases (Euclidean space and sphere).
Abstract: Publication date: July 2018Source: Arab Journal of Mathematical Sciences, Volume 24, Issue 2Author(s): Anupam Sharma In this paper we approximate common fixed points of nearly asymptotically nonexpansive mappings under modified SPiteration process in the setting of CAT(k) spaces and establish strong and Δconvergence theorems. Our results generalize and improve the corresponding known results of the existing literature.