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Abstract: This paper studies the idea of weighted sharing and proves two main theorems which generalize some results given by G. Brosch, Q. Zhang and other authors. [Copyright &y& Elsevier]

Abstract: The paper considers non-negative increasing functions on intervals with left endpoint closed at zero and investigates the duality between subadditivity and superadditivity via the inverse function and pseudo-inverses. [Copyright &y& Elsevier]

Abstract: In the present paper, motivated by Stević''s iteration method, we show the stability result of the following unified iterative scheme for a ϕ-strongly pseudocontractive selfmapping T. This stability result implies the stability of Stević''s iteration scheme naturally. [Copyright &y& Elsevier]

Abstract: In this paper we introduce a new concept, namely that of a quasi-orthomorphism, on a vector lattice, which generalizes the notion of an orthomorphism. We consider quasi-multipliers on ℓ-algebras and establish the relationship between quasi-orthomorphisms and quasi-multipliers. We prove that, for certain Banach algebras, the quasi-orthomorphisms form a Dedekind complete Banach f-algebra with a multiplicative identity. We conclude with a Kakutani type representation theorem for . [Copyright &y& Elsevier]

Abstract: In this paper, we establish some relationships between vector variational-like inequality and vector optimization problems under the assumptions of α-invex functions. We identify the vector critical points, the weakly efficient points and the solutions of the weak vector variational-like inequality problems, under pseudo-α-invexity assumptions. These conditions are more general than those of existing ones in the literature. In particular, this work extends the earlier work of Ruiz-Garzon et al. [G. Ruiz-Garzon, R. Osuna-Gomez, A. Rufian-Lizan, Relationships between vector variational-like inequality and optimization problems, European J. Oper. Res. 157 (2004) 113–119] to a wider class of functions, namely the pseudo-α-invex functions studied in a recent work of Noor [M.A. Noor, On generalized preinvex functions and monotonicities, J. Inequal. Pure Appl. Math. 5 (2004) 1–9]. [Copyright &y& Elsevier]

Abstract: The purpose of this paper is to study the existence and multiplicity of nonzero periodic solutions with saddle point character for the following nonautonomous second order systems: Some new existence and multiplicity theorems are obtained by using saddle point reduction method and a three-critical-point theorem proposed by Brezis and Nirenberg. [Copyright &y& Elsevier]

Abstract: In this paper, we extend the classes of generalized type I vector-valued functions introduced by Aghezzaf and Hachimi in [J. Global Optim. 18 (2000) 91–101] to generalized univex type I vector-valued functions and consider a multiple-objective optimization problem involving generalized type I univex functions. A number of Kuhn–Tucker type sufficient optimality conditions are obtained for a feasible solution to be an efficient solution. The Mond–Weir and general Mond–Weir type duality results are also presented. [Copyright &y& Elsevier]

Using the Jordan algebras methods, specially the properties of Peirce decomposition and the Frobenius transformation, we compute the coefficients of the zeta functional equation, in the case of Jordan algebras of type II. As particular cases of our result, we can cite the case of V=M(n,R) studied by Gelbart [Mem. Amer. Math. Soc. 108 (1971)] and Godement and Jacquet [Zeta functions of simple algebras, Lecture Notes in Math., vol. 260, Springer-Verlag, Berlin, 1972], and the case of V=Herm(3,Os) studied by Muro [Adv. Stud. Pure Math. 15 (1989) 429]. Let us also mention, that recently, Bopp and Rubenthaler have obtained a more general result on the zeta functional equation by using methods based on the algebraic properties of regular graded algebras which are in one-to-one correspondence with simple Jordan algebras [Local Zeta Functions Attached to the Minimal Spherical Series for a Class of Symmetric Spaces, IRMA, Strasbourg, 2003]. The method used in this paper is a direct application of specific properties of Jordan algebras of type II. [Copyright &y& Elsevier]

Abstract: In this paper we study a model of phase relaxation for the Stefan problem with the Cattaneo–Maxwell heat flux law. We prove an existence and uniqueness result for the resulting problem and we show that its solution converges to the solution of the Stefan problem as the two relaxation parameters go to zero, provided a relation between these parameters holds. [Copyright &y& Elsevier]

We establish in this paper some inequalities for vertex distances of two simplices, and give some applications thereof. [Copyright &y& Elsevier]

In this paper, in the setting of sequential spaces, we consider the value functions vS and vI defined by vS(x)=supy∈K(x)f(x,y) and vI(x)=infy∈K(x)f(x,y), and we introduce sufficient conditions on the value functions and on the data, weaker than upper semicontinuity, which guarantee the existence of maximum for such functions. Various examples illustrate the results and the connections with previous results. [Copyright &y& Elsevier]

In this paper, we study a 2D dissipative Klein–Gordon equation with periodic boundary condition. The existence and uniqueness of a time-periodic solution is proved by the Galerkin method and Leray–Schauder fixed point theorem. [Copyright &y& Elsevier]

The idea of almost convergence for double sequences was introduced by Moricz and Rhoades [Math. Proc. Cambridge Philos. Soc. 104 (1988) 283–294] and they also characterized the four dimensional strong regular matrices. In this paper we define and characterize the almost strongly regular matrices for double sequences and apply these matrices to establish a core theorem. [Copyright &y& Elsevier]

Consider the persistence and the global asymptotic stability of the following discrete model of pure-delay nonautonomous Lotka–Volterra type: Ni(p+1)=Ni(p)expci(p)−∑lower limit j=1, upper limit n ∑lower limit l=0, upper limit m aijl(p)Nj(p−kl),p=0,1,2,…, 1⩽i⩽n,Ni(p)=Ni,p⩾0, p⩽0, and Ni,0>0, 1⩽i⩽n, where each ci(p) and aijl(p) are bounded for p⩾0 and inflower limit p⩾0 ∑lower limit l=0, upper limit m aiil(p)>0, aijl(p)⩾0, i⩽j⩽n, 1⩽i⩽n, and kl⩾0, 1⩽l⩽m. In this paper, for the above discrete system of pure-delay type, by improving the former work [J. Math. Anal. Appl. 273 (2002) 492–511] which extended the averaged condition offered by S. Ahmad and A.C. Lazer [Nonlinear Anal. 40 (2000) 37–49], we offer conditions of persistence, and considering a Lyapunov-like discrete function to the above discrete system, we establish sufficient conditions of global asymptotic stability. [Copyright &y& Elsevier]

In this paper, we consider boundary value problems for nonlinear differential equations on the semi-axis (0,∞) and also on the whole axis (−∞,∞), under the assumption that the left-hand side being a second order linear differential expression belongs to the Weyl limit-circle case. The boundary value problems are considered in the Hilbert spaces L2(0,∞) and L2(−∞,∞), and include boundary conditions at infinity. The existence and uniqueness results for solutions of the considered boundary value problems are established. [Copyright &y& Elsevier]

This paper is concerned with the nonoscillatory problems of odd-dimensional systems of linear retarded functional differential equations. Based upon the corresponding characteristic equations, we get some criteria for nonoscillations by utilizing the matrix measures. [Copyright &y& Elsevier]

In this paper, we consider positive solutions of the logistic type p-Laplacian equation −Δpu=a(x)&z.sfnc;u&z.sfnc;p−2u−b(x)&z.sfnc;u&z.sfnc;q−1u, x∈RN (N⩾2). We show that under rather general conditions on a(x) and b(x) for large &z.sfnc;x&z.sfnc;, the behavior of the positive solutions for large &z.sfnc;x&z.sfnc; can be determined. This is then used to show that there is a unique positive solution. Our results improve the corresponding ones in J. London Math. Soc. (2) 64 (2001) 107–124 and J. Anal. Math., in press. [Copyright &y& Elsevier]

In this paper, a pair of nondifferentiable multiobjective programming problems is first formulated, where each of the objective functions contains a support function of a compact convex set in Rn. For a differentiable function h :Rn×Rn→R, we introduce the definitions of the higher-order F-convexity (F-pseudo-convexity, F-quasi-convexity) of function f :Rn→R with respect to h. When F and h are taken certain appropriate transformations, all known other generalized invexity, such as η-invexity, type I invexity and higher-order type I invexity, can be put into the category of the higher-order F-invex functions. Under these the higher-order F-convexity assumptions, we prove the higher-order weak, higher-order strong and higher-order converse duality theorems related to a properly efficient solution. [Copyright &y& Elsevier]

In this paper we characterize matrices that map every bounded sequence into one whose σ-core is a subset of the I-core of the original sequence. [Copyright &y& Elsevier]

In this paper, we construct an example of a cylindrical measure μ and a norm &z.dfnc;·&z.dfnc; such that ∥·∥ is μ-measurable by Dudley et al. and not μ-measurable by Gross and moreover is γ-measurable. [Copyright &y& Elsevier]

The existence of multiple positive solutions to superlinear periodic boundary value problems with repulsive singular forces is discussed in this paper. Our nonlinearity may be singular in its dependent variable and our analysis relies on a nonlinear alternative of Leray–Schauder type and on a fixed point theorem in cones. [Copyright &y& Elsevier]