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B-vex functions

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A class of functions, called b-vex functions, is introduced by relaxing the definition of convexity of a function. Both the differentiable and nondifferentiable cases are presented. Members of this class satisfy most of the basic properties of convex functions. This class forms a subset of the sets of both semistrictly quasiconvex as well as quasiconvex functions, but are not necessarily included in the class of preinvex functions.

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The first author is thankful to the Natural Science and Engineering Research Council of Canada for financial support through Grant A-5319. The authors are also grateful to an anonymous referee for the constructive criticism of the first version of the paper, to Dr. Collen Knickerbocker of St. Lawrence University, and to Mrs. Meena K. Bector for their help in sharpening Examples 2.1 and 2.2, respectively.

Communicated by M. Avriel

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Bector, C.R., Singh, C. B-vex functions. J Optim Theory Appl 71, 237–253 (1991). https://doi.org/10.1007/BF00939919

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Key Words

  • Convexity
  • b-vexity
  • preinvexity
  • quasiconvexity
  • pseudoconvexity