Affiliation:
1. Mathematics Department, COMSATS University Islamabad, Islamabad, Pakistan
Abstract
In this paper, we introduce and study some new classes of invex sets and
preinvex functions with respect to an arbitrary function k and the
bifunction ?(.,.); which are called the generalized preinvex functions.
These functions are nonconvex functions and include the preinvex function,
convex functions and k-convex as special cases. We study some properties of
generalized preinvex functions. It is shown that the minimum of generalized
preinvex functions on the generalized invex sets can be characterized by a
class of variational inequalities, which is called the directional
variational-like inequalities. Using the auxiliary technique, several new
inertial type methods for solving the directional variational-like
inequalities are proposed and analyzed . Convergence analysis of the
proposed methods is considered under suitable conditions. Some open problems
are also suggested for future research.
Publisher
National Library of Serbia
Reference40 articles.
1. A. Ben-Isreal and B. Mond, What is invexity? J. Austral. Math. Soc., Ser. B, 28(1)(1986),1-9.
2. G. Crestescu, M. Gaianu and M. U. Awan, Regularity properties and integral inequalities realted to (k, h1, h2)-convexity of functions, Analele Universit. Vest Timisoara, Ser. Math.-Informat. LIII(1)(2015),19-35.
3. G. Cristescu and L. Lupsa, Non-Connected Convexities and Applications, Kluwer Academic Publisher, Dordrechet, (2002)
4. G. Cristescu and M. G˘aianu, Shape properties of Noors’ convex sets, Proceed. of the Twelfth Symposium of Mathematics and its Applications, Timisoara, (2009),1-13,
5. R. Glowinski, J.L. Lions and R. Tremolieres, Numerical Analysis of Variational Inequalities, North-Holland, Amsterdam, 1981.
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