Some Properties of Geodesic Strongly E-b-vex Functions

Main Article Content

Wedad Saleh

Abstract

Geodesic E-b-vex sets and geodesic E-b-vex functions on a Riemannian manifold are extended to the so called geodesic strongly E-b-vex sets and geodesic strongly E-b-vex functions. Some basic properties of geodesic strongly E-b-vex sets are also studied.

Article Details

References

  1. I. A. Abou-Tair and W. T. Sulaiman, Inequalities via convex functions, Int. J.Math. Sci. 22(1999), 543-546.
  2. C. R. Bector and C. Singh, B-vex functions, J. Optim. Theory Appl. 71(2) (1991), 237-253.
  3. V. Boltyanski, H. Martini and P.S. Soltan, Excursions Into Combinatorial Geometry, Springer, Berlin, 1997.
  4. L. Danzer, B. Gr ¨unbaum and V. Klee, Helly's theorem and its relatives. In: V. Klee (ed.) Convexity. Proc. Sympos. Pure Math., vol.7, pp.101-180. Amer. Math. Soc., Providence, 1963.
  5. A. Iqbal, S. Ali and I. Ahmad, On geodesic E-convex sets, geodesic E-convex functions and E-epigraphs, J. Optim. Theory Appl. 55(1)(2012), 239-251.
  6. M. A. Jim ´enez, G. R. Garz ´on and A. R. Lizana, Optimality conditions in vector optimization. Bentham Science Publishers, 2010.
  7. A. Kili ¸cman and W. Saleh, On geodesic strongly E-convex sets and geodesic strongly E-convex functions, J. Inequal. Appl. 2015 (2015), 297.
  8. A. Kili ¸cman and W. Saleh, On properties of geodesic semilocal E-preinvex functions, J. Inequal. Appl. 2018 (2018), 353.
  9. H.Martini and K.J. Swanepoel, Generalized Convexity notions and Combinatorial Geometry, Gongr. Numer. 164 (2003), 65-93.
  10. H. Martini and K.J. Swanepoel, The geometry of minkowski spaces- a survey, Part II. Expo. Math. 22 (2004), 14-93.
  11. F. Mirzapour, A. Mirzapour and M. Meghdadi, Generalization of some important theorems to E-midconvex functions, Appl. Math. Lett. 24(8) (2011),1384-1388.
  12. M. A. Noor, Fuzzy preinvex functions, Fuzzy Sets Syst. 64(1994), 95-104.
  13. M. A. Noor, K. I. Noor and M. U. Awan, Generalized convexity and integral inequalities, Appl. Math. Inf. Sci. 9(1)(2015), 233-243.
  14. T. Rapcsak, Smooth Nonlinear Optimizatio in Rn, Kluwer Academic, 1997.
  15. Y. R. Syau, Lixing Jia, and E. Stanley Lee, Generalizations of E-convex and B-vex functions, Comput. Math. Appl. 58(4) (2009), 711-716.
  16. C. Udrist, Convex Funcions and Optimization Methods on Riemannian Manifolds, Kluwer Academic, 1994.
  17. E. A. Youness, On E-convex sets, E-convex functions and E-convex programming, J. Optim.Theory Appl. 102 (1999), 439-450.
  18. E. A. Youness and Tarek Emam, Strongly E-convex sets and strongly E-convex functions, J. Interdisciplinary Math. 8(1)(2005), 107-117.
  19. G.Y. Wang, Some Properties of strongly E-B-vex functions, Sustainable Development-Special track within SCET 2012(2012), 247.