Authors:P. Titus; P. Balakrishnan; K. Ganesamoorthy Pages: 311 - 320 Abstract: For any vertex x in a connected graph G of order \(n \ge 2\) , a set \(S \subseteq V(G)\) is an x-detour monophonic set of G if each vertex \(v \in V(G)\) lies on an x-y detour monophonic path for some element y in S. The minimum cardinality of an x-detour monophonic set of G is the x-detour monophonic number of G, denoted by \(dm_x(G)\) . A connected x-detour monophonic set of G is an x-detour monophonic set S such that the subgraph induced by S is connected. The minimum cardinality of a connected x-detour monophonic set of G is the connected x-detour monophonic number of G, denoted by \(cdm_x(G)\) . We determine bounds for it and find the value of \(cdm_x(G)\) for some special classes of graphs. For positive integers r, d and k with \(2 \le r \le d\) and \(k \ge 2\) , there exists a connected graph G with monophonic radius r, monophonic diameter d and connected x-detour monophonic number k for some vertex x in G. Also, it is shown that for positive integers j, k, l and n with \(2 \le j \le k \le l \le n-4\) , there is a connected graph G of order n with \(m_x(G) = j, dm_x(G) = k\) and \(cdm_x(G) = l\) for some vertex x in G, where \(m_x(G)\) is the x-monophonic number of G. PubDate: 2017-06-01 DOI: 10.1007/s13370-016-0452-x Issue No:Vol. 28, No. 3-4 (2017)

Authors:Oganeditse A. Boikanyo Pages: 321 - 332 Abstract: Let \((x_n)\) be a sequence generated by \(x_{n+1}=\alpha _nu+\gamma _nx_n+\delta _nJ_{\beta _n}x_n+e_n\) for \(n\ge 0\) , where \(J_{\beta _n}\) is the resolvent of a maximal monotone operator A with \(\beta _n\in (0,\infty )\) , \(u,x_0\in H\) , \((e_n)\) is a sequence of errors and \(\alpha _n\in (0,1)\) , \(\gamma _n\in (-1,1)\) , \(\delta _n\in (0,2)\) are real numbers such that \(\alpha _n+\gamma _n+\delta _n=1\) for all \(n\ge 0\) . We present strong convergence results for the sequence generated by the generalized contraction proximal point algorithm defined above under weaker accuracy conditions and mild conditions on the parameters \(\alpha _n, \beta _n\) and \(\delta _n\) . Our results generalize and unify many known results in the literature. PubDate: 2017-06-01 DOI: 10.1007/s13370-016-0453-9 Issue No:Vol. 28, No. 3-4 (2017)

Authors:Hadi Nosratipour; Omid Solaymani Fard; Akbar Hashemi Borzabadi; Farhad Sarani Pages: 333 - 356 Abstract: The stable equilibrium configuration of structures is a main goal in structural optimization. This goal may be achieved through minimizing the potential energy function. In the real world, sometimes, the input data and parameters of structural engineering design problems may be considered as fuzzy numbers which lead us to develop structural optimization methods in a fuzzy environment. In this regard, the present paper is intended to propose a fuzzy optimization scheme according to the nonmonotone globalization technique, the Barzilai–Borwein (BB) gradient method and the generalized Hukuhara differentiability (gH-differentiability). In fact, using the best benefits of BB-like methods i.e., simplicity, efficiency and low memory requirements, a modified global Barzilai–Borwein (GBB) gradient method is proposed for obtaining a non-dominated solution of the unconstrained fuzzy optimization related to the two bar asymmetric shallow truss in a fuzzy environment. The global convergence to first-order stationary points is also proved and the R-linear convergence rate is established under suitable assumptions. Furthermore, some numerical examples are given to illustrate the main results. PubDate: 2017-06-01 DOI: 10.1007/s13370-016-0451-y Issue No:Vol. 28, No. 3-4 (2017)

Authors:Mohammed Al-Hawmi; Elhoussine Azroul; Hassane Hjiaj; Abdelfattah Touzani Pages: 357 - 378 Abstract: In this work, we consider the following quasilinear elliptic unilateral equations of the type $$\begin{aligned} -\sum _{i=1}^{N}\frac{\partial }{\partial x_{i}}a_{i}(x,u,\nabla u) = \mu - \text{ div } \phi (u)\quad \text{ in } \Omega . \end{aligned}$$ In the anisotropic Sobolev space, we prove the existence of entropy solutions for our unilateral problem, where \(\mu = f-\text{ div } F\) belongs to \(L^{1}(\Omega ) + W^{-1,\mathbf {p'}}(\Omega )\) and \(\phi (\cdot ) \in C^{0}(\mathbb {R},\mathbb {R}^{N}).\) PubDate: 2017-06-01 DOI: 10.1007/s13370-016-0448-6 Issue No:Vol. 28, No. 3-4 (2017)

Authors:Vakkas Uluçay; Mehmet Şahin; Necati Olgun; Adem Kilicman Pages: 379 - 388 Abstract: In this study, using the neutrosophic soft definitions, we define some new concept such as the neutrosophic soft lattice, neutrosophic soft sublattice, complete neutrosophic soft lattice, modular neutrosophic soft lattice, distributive neutrosophic soft lattice, neutrosophic soft chain then we study the relationship and observe some common properties. PubDate: 2017-06-01 DOI: 10.1007/s13370-016-0447-7 Issue No:Vol. 28, No. 3-4 (2017)

Authors:B. Kheirfam Pages: 389 - 406 Abstract: Kernel functions play an important role in defining new search directions for primal-dual interior-point algorithms for solving symmetric optimization problems. In this paper we present a new kernel function for which interior point method yields iteration bounds \({\mathcal {O}}(\sqrt{r}\log r\log \frac{r}{\epsilon })\) and \({\mathcal {O}}(\sqrt{r}\log \frac{r}{\epsilon })\) for large-and small-update methods, respectively, which matches currently the best known bounds for such methods. PubDate: 2017-06-01 DOI: 10.1007/s13370-016-0455-7 Issue No:Vol. 28, No. 3-4 (2017)

Authors:Ghania Khenniche; Pierre Spiteri; Salah Bouhouche; Hocine Sissaoui Pages: 417 - 441 Abstract: The present study deals with the numerical simulation of steel solidification in continuous casting. We consider a semi-discretization with respect to the time of the studied evolution problem; then we have to solve a sequence of stationary coupled problems. So, due to the fact that the temperature is assumed to be positive, after reformulation of the problem into a variational inequality, we study under appropriate assumptions the existence and uniqueness of the solution of the stationary coupled problems. We also consider a multivalued formulation of the same problem which allows to analyze the behavior of the iterative relaxation algorithms used for the solution of the discretized problems. Finally the numerical experiments are presented. PubDate: 2017-06-01 DOI: 10.1007/s13370-016-0454-8 Issue No:Vol. 28, No. 3-4 (2017)

Authors:T. A. Biala; S. N. Jator; R. B. Adeniyi Pages: 443 - 450 Abstract: In this work, we study the performance of boundary value methods (BVMs) discussed in Biala [10] and Biala et al. [11] in combination with the method of lines on second order PDEs. The method of lines converts the PDEs into an equivalent system of second order ordinary differential equations. The performance of BVMs on the semi-discretized system is evidenced by a few numerical examples. PubDate: 2017-06-01 DOI: 10.1007/s13370-016-0458-4 Issue No:Vol. 28, No. 3-4 (2017)

Authors:Khaled Mehrez Pages: 451 - 457 Abstract: In this paper, by using Jensen’s inequality and Chebyshev integral inequality, some generalizations and new refined Hardy type integral inequalities are obtained. In addition, the corresponding reverse relation are also proved. PubDate: 2017-06-01 DOI: 10.1007/s13370-016-0461-9 Issue No:Vol. 28, No. 3-4 (2017)

Authors:Abdulhadi Aminu; Muhammad Aminu; M. Z. Ringim Pages: 481 - 491 Abstract: The permanent is a matrix function introduced (independently) by Cauchy and Binet and a number of results have so far been proved. In this paper, we extend the concept of permanent into rhotrix and also present a way of finding the permanent of a rhotrix and also establish some results. Rhotrix is an object that lies in some way between \(n\times n\) dimensional matrices and \(( {2n-1})\times (2n-1)\) dimensional matrices. PubDate: 2017-06-01 DOI: 10.1007/s13370-016-0457-5 Issue No:Vol. 28, No. 3-4 (2017)

Authors:Hamidou Dathe; Adamou Saidou Pages: 493 - 503 Abstract: We build a concrete pseudo-Anosov bundle on which there is no transversely projective foliation without compact leaf that is not transversely affine. PubDate: 2017-06-01 DOI: 10.1007/s13370-016-0462-8 Issue No:Vol. 28, No. 3-4 (2017)

Authors:Zahra Barati Pages: 505 - 514 Abstract: In this paper, we consider the problem of planarity and outerplanarity of iterated line graphs of the zero divisor graphs for finite commutative rings. We give a full characterization of all zero divisor graphs with respect to their planarity and outerplanarity indexes. PubDate: 2017-06-01 DOI: 10.1007/s13370-016-0460-x Issue No:Vol. 28, No. 3-4 (2017)

Authors:Maggie Aphane; Seithuti Moshokoa Pages: 549 - 553 Abstract: In the note we discuss partial metric type structures and present their basic properties as well as their relationship with metric type structures. As an application, fixed point theorems for a Lipschitzian map on this structures will be presented. PubDate: 2017-06-01 DOI: 10.1007/s13370-016-0467-3 Issue No:Vol. 28, No. 3-4 (2017)

Authors:Mohd Arif Raza; Nadeem Ur Rehman Pages: 555 - 561 Abstract: Let R be a prime ring of characteristic different from two with center Z(R). In the present paper we study the case when a generalized derivation F associated with a nonzero derivation d of R satisfies \([F([x, y]_k), [x, y]_k]\in Z(R)\) for all x, y in some appropriate subset of R, where k is a fixed positive integer. We obtain a description of the structure of R and information on the form of F in terms of the standard identity \(s_4\) and the multiplication by the specific element from the extended centroid. PubDate: 2017-06-01 DOI: 10.1007/s13370-016-0465-5 Issue No:Vol. 28, No. 3-4 (2017)

Authors:Appolinaire Dossavi-Yovo; Bo He; Alain Togbé Pages: 563 - 574 Abstract: In this paper, we consider the \(D(\pm k)\) -triple \(\{k\mp 1,k, 4k\mp 1\}\) and we prove that, if k is not a perfect square then: There is no d such that \(\{k-1,k, 4k-1, d\}\) is a D(k)-quadruple; If \(\{k,k+1,4k+1,d \}\) is a \(D(-k)\) -quadruple, then \(d=1\) . This extends a work done by Fujita [13]. PubDate: 2017-06-01 DOI: 10.1007/s13370-016-0466-4 Issue No:Vol. 28, No. 3-4 (2017)

Authors:A. Parsapour; Kh. Ahmad Javaheri Pages: 575 - 593 Abstract: The zero divisor graph of a partially ordered set (poset, briefly) \((P, \le )\) with the least element 0, which is denoted by \(G^*(P)\) , is an undirected graph with vertex set \(P^*= P{\setminus } \{0\}\) and, for two distinct vertices x and y, x is adjacent to y in \(G^*(P)\) if and only if \(\{x,y\}^l=\{0\}\) , where, for a subset S of P, \(S^l\) is the set of all elements \(x\in P\) with \(x\le s\) , for all \(s\in S\) . In this paper we completely characterize all posets P with projective zero divisor graphs \(G^*(P)\) . PubDate: 2017-06-01 DOI: 10.1007/s13370-016-0464-6 Issue No:Vol. 28, No. 3-4 (2017)

Authors:M. E. Okpala Pages: 595 - 604 Abstract: In this paper we introduce a new general class of multi-valued Lipschitz hemicontractive mappings. We then prove strong convergence theorems for finding a fixed point of the mapping using a new two steps averaged algorithm. The method used in the proof is new and enables us to systematically avoid so many strong assumptions in the contemporary literature. The theorems obtained generalize and improve many results in the literature. PubDate: 2017-06-01 DOI: 10.1007/s13370-016-0468-2 Issue No:Vol. 28, No. 3-4 (2017)

Authors:N. Subramanian Pages: 615 - 628 Abstract: Let X be a Banach lattice and \(\chi ^{2}_{f}\) be an double gai Orlicz sequence space associated to an Orlicz function with the \(\Delta _{2}\) - condition. In this paper we define the Ces \(\grave{\mathbf{a }}\) ro \(\chi ^{2}\) sequence space Ces \(_{p}^{q}\left( \chi ^{2}_{f}\right) \) generated by a Orlicz sequence space and exhibit some general properties of the spaces. PubDate: 2017-06-01 DOI: 10.1007/s13370-016-0469-1 Issue No:Vol. 28, No. 3-4 (2017)

Authors:Olusheye Akinfenwa Pages: 629 - 641 Abstract: A new third derivative hybrid block method is presented for the solution of first order stiff systems of initial value problems. The main method and additional methods are obtained from the same continuous scheme derived via interpolation and collocation procedures using power series as the basis function. The continuous representation of the scheme permits us to evaluate at both grid and off-grid points. The stability properties of the method is discussed. The block method is applied simultaneously to generate the numerical solutions of (1) over non-overlapping intervals. Numerical results obtained using the proposed third derivative hybrid method in block form reveal that it compares favorably well with existing methods in the literature. PubDate: 2017-06-01 DOI: 10.1007/s13370-016-0471-7 Issue No:Vol. 28, No. 3-4 (2017)

Authors:Julio C. Ramos-Fernández; Margot Salas-Brown Pages: 661 - 667 Abstract: We present some characterizations for the multiplication operators \(M_u\) with finite range when acts on any Köthe sequence spaces. we also characterize its compactness and Fredholmness. Our characterizations are presented in terms of certain properties of the zeros set and the support of the symbol u. PubDate: 2017-06-01 DOI: 10.1007/s13370-016-0475-3 Issue No:Vol. 28, No. 3-4 (2017)