Publication Date: 2025
Journal of Mathematical Analysis and Applications (0022247X)551(1)
In this article, we investigate μ-lineability of the set of non-absolutely p-summing operators between certain pairs of Banach spaces. Moreover, we prove that for many known Banach spaces E and F, K(E,F)∖⋃1≤p<∞Πp(E,F) is maximal lineable in L(E,F). Our results provide a more comprehensive answer to a question posed by Botelho, Diniz and Pellegrino [12]. © 2025 Elsevier Inc.
Publication Date: 2025
Optimization (2331934)
In this article, we obtain an extension of the Ekeland variational principle in quasi-uniform spaces. Since the Ekeland variational principle is a type of perturbed optimization problem, the perturbations do not need to satisfy the triangle property to obtain results. We also give some equivalent results of our main results. Moreover, we present a new version of the Ekeland variational principle and its equivalent results, in the setting of quasi-gage spaces. Finally, we establish the Ekeland variational principle in a (metric) modular space as an application of our results. © 2025 Informa UK Limited, trading as Taylor & Francis Group.
Publication Date: 2024
Journal of Computational Physics (219991)508
In this research article, we introduce a high-order and non-oscillatory finite volume method in combination with radial basis function approximations and use it for the solution of scalar conservation laws on unstructured meshes. This novel approach departs from conventional non-oscillatory techniques, which often require the use of multiple stencils to achieve smooth reconstructions. Instead, the new method uses a single central stencil and hinges on an approximate interpolation methodology called the weighted smoothed reconstruction (WSR), with a foundation on polyharmonic spline interpolation. Through some numerical experiments, we demonstrate the efficiency and accuracy of the new approach. It reduces the computational cost and performs well in capturing shocks and sharp solution fronts. © 2024 The Author(s)
Publication Date: 2024
Forum Mathematicum (9337741)37pp. 1185-1200
Let (S, n) be a commutative noetherian local ring and let ω ∈ n be non-zerodivisor. This paper is concerned with the two categories of monomorphisms between finitely generated (Gorenstein) projective S-modules, such that their cokernels are annihilated by ω. It is shown that these categories, which will be denoted by Mon(ω, P) and Mon(ω, G), are both Frobenius categories with the same projective objects. It is also proved that the stable category Mon(ω, P) is triangle equivalent to the category of D-branes of type B, DB(ω), which has been introduced by Kontsevich and studied by Orlov. Moreover, it will be observed that the stable categories Mon(ω, P) and Mon(ω, G) are closely related to the singularity category of the factor ring R = S/(ω). Precisely, there is a fully faithful triangle functor from the stable category Mon(ω, G) to Dsg(R), which is dense if and only if R (and so S) are Gorenstein rings. Particularly, it is proved that the density of the restriction of this functor to Mon(ω, P), guarantees the regularity of the ring S. © 2024 Walter de Gruyter GmbH. All rights reserved.
Publication Date: 2013
Statistics and Probability Letters (1677152)83(12)pp. 2664-2672
In this paper, we derive mixture representations for the reliability function of the conditional residual lifetime of a coherent system with n independent and identically distributed (i.i.d.) components under the condition that at least j and at most k - 1 (. j < k) components have failed by time t. Based on these mixture representations, we then discuss stochastic comparisons of the conditional residual lifetimes of two coherent systems with independent and identical components. © 2013 Elsevier B.V.
Publication Date: 2013
Bulletin Of The Iranian Mathematical Society (1017060X)39(3)pp. 529-557
We extend the method of adaptive two-stage sequen-tial sampling to include designs where there is more than one crite-ria used in deciding on the allocation of additional sampling effort. These criteria, or conditions, can be a measure of the target popula-tion, or a measure of some related population. We develop Murthy estimator for the design that is unbiased estimators for the pop-ulation mean, and propose another, more efficient, estimator. We investigate asymptotic properties of this estimator. We use a sim-ulation study to investigate design properties of the multi-criteria adaptive stratified sequential sampling scheme and also some esti-mator properties under the design. ©2013 Iranian Mathematical Society.
Publication Date: 2013
Applied Numerical Mathematics (1689274)68pp. 73-82
The Meshless Local Petrov–Galerkin (MLPG) method is one of the popular meshless methods that has been used very successfully to solve several types of boundary value problems since the late nineties. In this paper, using a generalized moving least squares (GMLS) approximation, a new direct MLPG technique, called DMLPG, is presented. Following the principle of meshless methods to express everything “entirely in terms of nodes” the generalized MLS recovers test functionals directly from values at nodes, without any detour via shape functions. This leads to a cheaper and even more accurate scheme. In particular, the complete absence of shape functions allows numerical integrations in the weak forms of the problem to be done over low-degree polynomials instead of complicated shape functions. Hence, the standard MLS shape function subroutines are not called at all. Numerical examples illustrate the superiority of the new technique over the classical MLPG. On the theoretical side, this paper discusses stability and convergence for the new discretizations that replace those of the standard MLPG. However, it does not treat stability, convergence, or error estimation for the MLPG as a whole. This should be taken from the literature on MLPG. © 2013 IMACS
Publication Date: 2012
Topology and its Applications (1668641)159(16)pp. 3453-3460
In this paper, we present some asymptotic stationary point results for topological contraction mappings by relaxing the compactness of the space. Moreover, some classes of topological contractions are characterized. © 2012 Elsevier B.V.
Publication Date: 2012
Engineering Analysis with Boundary Elements (9557997)36(4)pp. 511-519
The meshless local boundary integral equation (MLBIE) method with an efficient technique to deal with the time variable are presented in this article to analyze the transient heat conduction in continuously nonhomogeneous functionally graded materials (FGMs). In space, the method is based on the local boundary integral equations and the moving least squares (MLS) approximation of the temperature and heat flux. In time, again the MLS approximates the equivalent Volterra integral equation derived from the heat conduction problem. It means that, the MLS is used for approximation in both time and space domains, and we avoid using the finite difference discretization or Laplace transform methods to overcome the time variable. Finally the method leads to a single generalized Sylvester equation rather than some (many) linear systems of equations. The method is computationally attractive, which is shown in couple of numerical examples for a finite strip and a hollow cylinder with an exponential spatial variation of material parameters. © 2011 Elsevier Ltd. ALl Rights Reserved.
Publication Date: 2012
IMA Journal of Numerical Analysis (2724979)32(3)pp. 983-1000
The moving least squares (MLS) method provides an approximation û of a function u based solely on values u(xj) of u on scattered 'meshless' nodes xj. Derivatives of u are usually approximated by derivatives of û. In contrast to this, we directly estimate derivatives of u from the data, without any detour via derivatives of û. This is a generalized MLS technique, and we prove that it produces diffuse derivatives as introduced by Nyroles et al. (1992, Generalizing the finite element method: diffuse approximation and diffuse elements. Comput. Mech., 10, 307-318). Consequently, these turn out to be efficient direct estimates of the true derivatives, without anything 'diffuse' about them, and we prove optimal rates of convergence towards the true derivatives. Numerical examples confirm this, and we finally show how the use of shifted and scaled polynomials as basis functions in the generalized and standard MLS approximation stabilizes the algorithm. © 2010 The author. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved.
Publication Date: 2006
Theory of Probability and its Applications (0040585X)50(3)pp. 448-462
A simple random measure is a finite sum of random measures with disjoint supports. A type of simple random measure which is induced by a multivariate random measure (Φ1, . . . , Φm) and measurable mappings T1, . . . , Tm is introduced and studied. Interestingly it gives rise to introducing a class of processes, called simple, that include stationary processes and discrete time periodically correlated processes. This study involves spectral domain and time domain characterizations and simulation. The role of spectral kernels in analysis of nonstationary processes is also discussed. © 2006 Society for Industrial and Applied Mathematics.
Publication Date: 2005
Stochastic Processes and their Applications (3044149)115(11)pp. 1838-1859
The spectral structure of discrete time periodically correlated (as well as multivariate stationary) symmetric α-stable processes is identified by decomposing such a process uniquely in distribution into one sum of three mutually independent periodically correlated (multivariate stationary) stable processes that are classified as mixed moving average, harmonizable and of a third kind. The techniques are based on presenting the flow and its cocycle that govern the spectral representation of the process, using the Hopf decomposition and specifying the harmonizable component. © 2005 Elsevier B.V. All rights reserved.
Publication Date: 2005
Journal of Optimization Theory and Applications (223239)126(1)pp. 109-124
In this paper, we apply a new version of the Brézis, Nirenberg, and Stampacchia theorem; we use pseudomonotonicity and some coercivity conditions to establish some existence result for a solution of generalized vector equilibrium problems for multivalued bifunctions. The proper quasiconvexity of multivalued bifunctions is introduced and existence theorems for generalized vector equilibrium problems related to multivalued mappings with the KKM property are obtained. The new results extend and modify various existence theorems for similar problems. © 2005 Springer Science+Business Media, Inc.
Publication Date: 2005
Journal of Optimization Theory and Applications (223239)126(1)pp. 125-136
Existence results for quasimonotone vector equilibrium problems and quasimonotone vector variational inequalities are obtained starting from an existence result for a scalar equilibrium problem involving two quasimonotone bifunctions. These results are established under weaker conditions than in previous works. © 2005 Springer Science+Business Media, Inc.
Publication Date: 2004
Journal of Optimization Theory and Applications (223239)123(2)pp. 349-364
By using quasimonotone and pseudomonotone bifunctions, we derive sufficient conditions which include weak coercivity conditions for existence of equilibrium points. As a consequence, we improve some recent results on the existence of such solutions.
Publication Date: 2003
International Journal of Mathematics and Mathematical Sciences (1611712)2003(51)pp. 3267-3276
We give some new versions of KKM theorem for generalized convex spaces. As an application, we answer a question posed by Isac et al. (1999) for the lower and upper bounds equilibrium problem. © 2003 Hindawi Publishing Corporation. All rights reserved.
Publication Date: 2018
Acta Mechanica (15970)229(6)pp. 2657-2673
This paper concerns a new and fast meshfree method for the linear coupled thermoelasticity problem. The resulting algorithm provides an attractive alternative to existing mesh-based and meshfree methods. Compared with mesh-based methods, the proposed technique inherits the advantages of meshfree methods allowing the use of scattered points instead of a predefined mesh. Compared with the existing meshfree methods, the proposed technique is truly meshless, requiring no background mesh for both trial and test spaces and, more importantly, numerical integrations are done over low-degree polynomials rather than complicated shape functions. In fact, this method mimics the known advantages of both meshless and finite element methods, where in the former triangulation is not required for approximation and in the latter the stiffness and mass matrices are set up by integration against simple polynomials. The numerical results of the present work concern the thermal and mechanical shocks in a finite domain considering classical coupled theory of thermoelasticity. © 2018, Springer-Verlag GmbH Austria, part of Springer Nature.
Publication Date: 2018
Journal of Mathematical Analysis and Applications (0022247X)458(2)pp. 925-936
In this paper, we introduce the notion of the Bishop–Phelps–Bollobás property for numerical radius (BPBp-ν) for a subclass of the space of bounded linear operators. Then, we show that certain subspaces of L(L1(μ)) have the BPBp-ν for every finite measure μ. As a consequence we deduce that the subspaces of finite-rank operators, compact operators and weakly compact operators on L1(μ) have the BPBp-ν. © 2017 Elsevier Inc.
Publication Date: 2018
European Journal of Operational Research (3772217)265(1)pp. 39-48
We introduce a new concept of generalized convexity at a given point for a family of real-valued functions and deduce nonsmooth sufficient optimality conditions for robust (weakly) efficient solutions. In addition, we present a robust duality theory and Mond–Weir type duality for an uncertain multiobjective optimization problem. Furthermore, some nonsmooth saddle-point theorems are obtained under our generalized convexity assumption. Finally we show the viability of our new concept of generalized convexity for robust optimization and portfolio optimization. © 2017 Elsevier B.V.
Publication Date: 2018
Fixed Point Theory (15835022)19(1)pp. 211-218
In this paper the concept of set-valued cyclic Meir–Keeler contraction map is introduced. The existence of best proximity point for such maps on a metric space with the UC property is presented. © 2018, House of the Book of Science. All rights reserved.
Publication Date: 2018
SIAM Journal on Numerical Analysis (361429)56(1)pp. 274-295
In this paper, a numerical solution of partial differential equations on the unit sphere is given by using a kernel trial approximation in combination with a special Petrov–Galerkin test discretization. The solvability of the scheme is proved, and the error bounds are obtained for functions in appropriate Sobolev spaces. The condition number of the final system is estimated in terms of discretization parameters. The method is meshless because in the trial side the numerical solution parameterizes entirely in terms of scattered points and in the test side everything breaks down to simple numerical integrations over independent spherical caps. This means that no connected background mesh is required for either approximation or integration. © 2018 Society for Industrial and Applied Mathematics.
Publication Date: 2018
Journal of Nonlinear and Convex Analysis (13454773)19(7)pp. 1189-1198
In this paper, we study the existence of fixed point for asymptotic compact absorbing contraction map and generalized a-set contraction maps. Moreover, we present structure of fixed point set results for this maps. Also, the asymptotic version of the Meir-Keeler, Boyd-Wong, Nadler contractions for the KKM maps on metric space are given. © 2018 Yokohama Publications.
Publication Date: 2018
Nonlinear Studies (13598678)25(3)pp. 689-700
In this paper we show the stability of the Gelfand-Phillips property of order p under tak- ing injective tensor product, compact operators, and Bochner integrable functions. The concept of L-limited sets of order p; is introduced and some characterizations of limited p-convergent operators are given. Also we define the notion of L-limited property of order p and characterize this property in terms of weak compact operators. Furthermore, we give a new dual characterization of the class of weak* p-convergent operators through L-limited sets of order p: Moreover, some characterizations of the Gelfand-Phillips property of order p in terms of limited p-convergent operators are obtained. In addition by applying our results on the limited p-convergent operators, we obtain some characteriza- tions of the Dunford-Pettis* property of order p. © CSP - Cambridge, UK.
Publication Date: 2017
BIT Numerical Mathematics (63835)57(4)pp. 1041-1063
In this paper a direct approximation method on the sphere, constructed by generalized moving least squares, is presented and analyzed. It is motivated by numerical solution of partial differential equations on spheres and other manifolds. The new method generalizes the finite difference methods, someway, for scattered data points on each local subdomain. As an application, the Laplace–Beltrami equation is solved and the theoretical and experimental results are given. The new approach eliminates some drawbacks of the previous methods. © 2017, Springer Science+Business Media Dordrecht.
Publication Date: 2018
Filomat (3545180)32(6)pp. 2081-2089
In this paper, we study the existence and uniqueness of best proximity points for cyclic Meir– Keeler contraction mappings in metric spaces with the property W-WUC. Also, the existence of best proximity points for set-valued cyclic Meir-Keeler contraction mappings in metric spaces with the property WUC are obtained. © 2018, University of Nis. All rights reserved.
Publication Date: 2017
Journal of Mathematical Analysis and Applications (0022247X)449(1)pp. 756-768
We let B be a separable Banach space, and let {Zn} be a sequence of independent and identically distributed random elements in B. Then we prove that for a given strongly periodic sequence of bounded linear operators {ρn}, the order one autoregressive system equations Xn=ρnXn−1+Zn,n in set on integers, possesses a unique almost sure strictly periodically correlated solution; under E[log+‖Z0‖]<∞, which appears to be necessary as well. We proceed on to derive the limiting distribution of ∑n=1NXn that appears to be a Gaussian distribution on B. We also provide interesting examples and observations. © 2016 Elsevier Inc.
