eng Science and Education Publishing Turkish Journal of Analysis and Number Theory 2014-08-21 2 4 134 139 10.12691/tjant-2-4-6 TJANT2014246 article Refinements and Sharpening of some Huygens and Wilker Type Inequalities Wei-Dong Jiang 1 Qiu-Ming Luo 2 Feng Qi qifeng618@gmail.com, qifeng618@hotmail.com, qifeng618@qq.com 3 4 5 Department of Information Engineering, Weihai Vocational University, Weihai, Shandong, China Department of Mathematics, Chongqing Normal University, Chongqing City, China College of Mathematics, Inner Mongolia University for Nationalities, Tongliao City, Inner Mongolia Autonomous Region, China In the article, some Huygens and Wilker type inequalities involving trigonometric and hyperbolic functions are refined and sharpened. http://pubs.sciepub.com/tjant/2/4/6/tjant-2-4-6.pdf refinement sharpening Huygens inequality Wilker inequality trigonometric function hyperbolic function