摘要:

We study abstract convex functions with respect to the set of all abstract affine functions of the form x→ mini=l,…,n+l[li,x] - c. We describe large classes of abstract convex functions and give conditions guaranteeing subdifferentiability of these functions. Some applications to the study of problems of global optimization are discussed.

ISSN:0163-0563    

DOI:10.1080/01630569808816848

出版商:Marcel Dekker, Inc.    

年代:1998

数据来源: Taylor

摘要:

The paper gives characterizations of convexity, quasiconvexity, invexity and pseudoconvexity for a (radially) upper-semicontinuous function f in a topological vector space via appropriate properties of a bifunction which is majorized by the upper radial derivative of f and which stands for a generalized derivative of some sort.

ISSN:0163-0563    

DOI:10.1080/01630569808816849

出版商:Marcel Dekker, Inc.    

年代:1998

数据来源: Taylor

摘要:

We prove constructively existence and uniqueness of a conlinuous fixed-point for a class of decreasing and pointwise nzonotonically continuous (nonlinear) operators in spaces of (vector-valued) functions, without resorting to conzplete continuity. As an application, we rediscuss and improve recent results for a class of perturbed nonlinear integral equations.

ISSN:0163-0563    

DOI:10.1080/01630569808816850

出版商:Marcel Dekker, Inc.    

年代:1998

数据来源: Taylor

摘要:

We introduce and analyze a fully discrete numerical method for solving second order integrodifferential equations modelling dynamical systems whose evolution depends also on the past states. We show it is fourth order convergent. Then from the numerical approximate values for the unknown function, we reconstruct by means of deficient quartic splines a smooth solution of the problem. The reconstruction scheme is shown to be cubically convergent. Both methods when assuming analytic evaluation of the integrals are convergent with superquartic and supercubical rates respectively. For ordinary differential equations the scheme for the calculation of the solution at the grid knots gains one order of convergence. Numerical experiments confirm our theoretical findings.

ISSN:0163-0563    

DOI:10.1080/01630569808816851

出版商:Marcel Dekker, Inc.    

年代:1998

数据来源: Taylor

ISSN:0163-0563    

DOI:10.1080/01630569808816837

出版商:Marcel Dekker, Inc.    

年代:1998

数据来源: Taylor