Search

Abstract: In this paper, by means of a series of counterexamples, we study in a systematic way the relationships among (pseudo, quasi) α-preinvexity, (strict, strong, pseudo, quasi) α-invexity and (strict, strong, pseudo, quasi) αη-monotonicity. Results obtained in this paper can be viewed as a refinement and improvement of the results of Noor and Noor [M.A. Noor, K.I. Noor, Some characterizations of strongly preinvex functions, J. Math. Anal. Appl. 316 (2006) 697–706]. [Copyright &y& Elsevier]

Abstract: In this paper, characterizations of the existence of the directional derivative and second-order parabolic directional derivative of a locally Lipschitzian function are established. These characterizations involve the adjacent cone and second-order adjacent set of the graph of the function. [Copyright &y& Elsevier]

Abstract: Let and be analytic in the unit disk. The Hadamard product of f and g is defined by . This paper gives some characterizations of functions in spaces in terms of the Hadamard products. [Copyright &y& Elsevier]

Abstract: In this paper, we study the normality of a family of meromorphic functions and obtain some normality results for meromorphic functions, which improve and generalize the related results of Gu, Bergweiler and Lin. [Copyright &y& Elsevier]

Abstract: Some new generalizations of the Hilbert integral inequality by introducing real functions and . The results of this paper reduce to those of the corresponding inequalities proved by Gao [Mingzhe Gao, On Hilbert''s integral inequality, Math. Appl. 11 (3) (1998) 32–35]. Some applications are considered. [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]

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]

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]