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    STUDIA MATHEMATICA - Issue no. 3 / 2015  
         
  Article:   EXTENSION OF KARAMATA INEQUALITY FOR GENERALIZED INVERSE TRIGONOMETRIC FUNCTIONS.

Authors:  .
 
       
         
  Abstract:  

 Discussing Ramanujan’s Question 294, Karamata established the inequality 

which is the cornerstone of this paper. We generalize the above inequality transforming into terms of arctan and artanh. Moreover, we expand the established result to the class of generalized inverse p–trigonometric arctanp and to hyperbolic artanhp functions.

Mathematics Subject Classification (2010): 26D99, 39B62, 39B72.

Keywords: Karamata’s inequality, Ramanujan’s question 294, zero-balanced hypergeometric functions, generalized inverse trigonometric functions, rational upper bounds.

 
         
     
         
         
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