## On-line version ISSN 0719-0646

### Cubo vol.13 no.1 Temuco  2011

#### http://dx.doi.org/10.4067/S0719-06462011000100008

CUBO A Mathematical Journal Vol.13, N° 01, (125-136). March 2011

CONTENTS

Multiple Objective Programming Involving Differentiable (Hp , r)-invex Functions

Xiaoling Liu, Dehui Yuan, Shengyun Yang, Guoming Lai y Chuanqing Xu

Department of Mathematics and Inform., Tech.,Hanshan Normal University, Chaozhou, Guangdong, 521041, China. email: ydhliu@gmail.com, ydhlxl@sohu.com

Department of Mathematics, Beijing Armed Forced Eng. Institute, Beijing 100072, China.

ABSTRACT

In this paper, we introduce new types of generalized convex functions which include locally (Hp, r)-pre-invex functions and (Hp, r)-invex functions. Relationship between these two new classes of functions are established. We also present the conditions for optimality in differentiable mathematical programming problems where the functions considered are (Hp, r)-invex functions introduced in this paper.

Keywords: Differentiable mathematical programming.

RESUMEN

Este trabajo, establece nuevos tipos de funciones convexas generalizadas que incluyen localmente funciones (Hp, r) de pre-invex y funciones (Hp, r)-invex. La relacin entre estas dos nuevas clases de funciones estn establecidas. Tambin se presentan las condiciones de optimalidad en diferenciables problemas de programacin matemtica, donde las funciones consideradas en este artculo son funciones (Hp, r)-invex.

Mathematics Subject Classification: 90B50.

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Received: September 2009. Revised: November 2009.