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Journal of Function Spaces
Volume 2017 (2017), Article ID 2148529, 9 pages
Research Article

On Harmonically -Preinvex Functions

1Department of Mathematics, Longyan University, Longyan, Fujian 364012, China
2Abdus Salam School of Mathematical Sciences, GC University, Lahore, Pakistan
3Department of Mathematics, Faculty of Arts and Sciences, Giresun University, 28200 Giresun, Turkey

Correspondence should be addressed to Shan-He Wu

Received 19 August 2016; Revised 17 December 2016; Accepted 4 January 2017; Published 31 January 2017

Academic Editor: Adrian Petrusel

Copyright © 2017 Shan-He Wu et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We define a new generalized class of harmonically preinvex functions named harmonically -preinvex functions, which includes harmonic -preinvex functions, harmonic -preinvex functions, harmonic -preinvex functions, and -convex functions as special cases. We also investigate the properties and characterizations of harmonically -preinvex functions. Finally, we establish some integral inequalities to show the applications of harmonically -preinvex functions.