Generalizations of E-convex and B-vex functions

  • Syau Y
  • Jia L
  • Stanley Lee E
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Abstract

A class of functions called E-B-vex functions is defined as a generalization of E-convex and B-vex functions. Similarly, a class of E-B-preinvex functions, which are generalizations of E-convex and B-preinvex functions, is introduced. In addition, the concept of B-linear functions is also generalized to E-B-linear functions. Some properties of these proposed classes are studied. Furthermore, the equivalence between the class of E-B-vex functions and that of E-quasiconvex functions is proved. © 2009 Elsevier Ltd. All rights reserved.

Author-supplied keywords

  • B-vex functions
  • E-B-vex functions
  • E-convex functions
  • E-quasiconvex functions
  • Generalized convexity

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Authors

  • Yu Ru Syau

  • Lixing Jia

  • E. Stanley Lee

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