JIPAM

Inequalities Involving a Logarithmically Convex Function and Their Applications to Special Functions  
 
  Authors: Edward Neuman,  
  Keywords: Logarithmically convex functions, inequalities, gamma function, Riemann's zeta function, complete elliptic integrals of the first kind.  
  Date Received: 29/10/05  
  Date Accepted: 09/11/05  
  Subject Codes:

Pri: 26D07, 26D20. Sec: 33B15, 11M06, 33

  
  Editors: Themistocles M. Rassias,  
 
  Abstract:

It has been shown that if $ f$ is a differentiable, logarithmically convex function on nonnegative semi-axis, then the function $ [f(x)]^a/f(ax)$, ($ a ge 1$) is decreasing on its domain. Applications to inequalities involving gamma function, Riemann's zeta function, and the complete elliptic integrals of the first kind are included. ;


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