Mathematical means and its inequalities
An overview of convexities, concavities, Ky Fan Typeinequalities and Index set
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This book describes some genuinely exceptional criteria, with an appropriate literature review referring to the most recent advancements and popularity of mathematical means. The topics included are convexities and concavities among means, inequalities for the arguments lying on linear and curved path, mean inequalities for the arguments in index and conjugate index set, harmonic and heron mean inequalities for arguments in different intervals.For special combinations of means defined in functional form, concavity or convexity can be verified using Vandermonde's determinant condition. Since th...
This book describes some genuinely exceptional criteria, with an appropriate literature review referring to the most recent advancements and popularity of mathematical means. The topics included are convexities and concavities among means, inequalities for the arguments lying on linear and curved path, mean inequalities for the arguments in index and conjugate index set, harmonic and heron mean inequalities for arguments in different intervals.For special combinations of means defined in functional form, concavity or convexity can be verified using Vandermonde's determinant condition. Since the convexity and concavity plays a major role in analysing the nature of a function, contains good number of convexity and concavity results among Greek means, which is based on the determinant convexity conditions among different mean functions, the theorems are verified with suitable values. Also, the condition can be verified for more functions at a time and the conditions expressed in terms of Vander monde's determinant, maybe reduced to diagonal form or triangular form.
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