In this study, we introduce a new class of function called geodesic semi E-b-vex functions and generalized geodesic semi E-b-vex functions and discuss some of their properties.
Department of Mathematics, University Putra Malaysia, 43400 UPM, Serdang, Selangor, Malaysia,
Bibliografia
[1] Boltyanski V., Martini H., Soltan P.S., Excursions into combinatorial geometry, Springer, Berlin, 1997.
[2] Chen X., Some properties of semi-E-convex functions, Journal of Mathematical Analysis and Applications, 2002, 275, 251–262.
[3] Danzer L., Grünbaum B., Klee V., Helly’s theorem and its relatives. In: V. Klee (ed.) Convexity, Proc. Sympos. Pure Math., 1963, 7, 101–180.
[4] Duca D. I., Lupsa L., On the E-epigraph of an E-convex functions,Journal of Optimization Theory and Applications, 2006, 129, 341–348.
[5] Fulga C., Preda V., Nonlinear programming with E-preinvex and local E-preinvex functions, European Journal of Operational Research, 2009, 192(3), 737–743. [WoS]
[6] Iqbal A.,Ahmad I., Ali S., Some properties of geodesic semi-E-convex functions, Nonlinear Analysis: Theory, Method and Application,2011, 74(17), 6805–6813.
[7] Iqbal A., Ali S., Ahmad I., On geodesic E-convex sets, geodesic E-convex functions and E-epigraphs, J.Optim Theory Appl., 2012, 55(1), 239–251. [WoS]
[8] Jiménez M. A., Garzón G.R., Lizana A.R, Optimality conditions in vector optimization, Bentham Science Publishers, 2010.
[9] Kiliçman A., Saleh W., A note on starshaped sets in2-dimensional manifolds without conjugate points, Journal of Function Spaces, 2014, 2014(3), Article ID 675735. [WoS]
[10] Kiliçman A., Saleh W., On Geodesic Strongly E-convex Sets and Geodesic Strongly E-convex Functions, Journal of Inequalities and Applications, 2015, 2015(1), 1–10.
[11] Martini H., Swanepoel K.J., Generalized convexity notions and combinatorial geometry, Gongr. Numer., 2003, 164, 65–93.
[12] Martini H., Swanepoel K.J , The geometry of minkowski spaces- a survey, part ii, Expo. Math., 2004, 22,14–93.
[13] Mishra S.K., Mohapatra R.N. and Youness E.A.,Some properties of semi E–b-vex functions, Applied Mathematics and Computation, 2011,217(12), 5525–5530.