Systematic and Durable Analysis of the Rule based Cauchy’s Inequality in solving the n-order Differential Equations

Systematic and Durable Analysis of the Rule based Cauchy’s Inequality in solving the n-order Differential Equations

Sathwik Gangisetti1, Rayi Geeta Krishna1, Swarna Sai Sreekar1, Jnana Venkata Subhash Boyapati1, Kothamasu Praneeth Kumar1, Chandanam Akshaya2 ,Pavuluri Poojitha2
, 1School of Computer Science and Engineering, VIT-AP University, G-30, Inavolu, Beside AP Secretariat Amaravati, Andhra Pradesh 522237

, 2Department of Computer Science and Engineering, R.V.R. & J.C.College of Engineering, G-30, Chowdavaram, Andhra Pradesh 522019

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Abstract – This paper instigates the multivariate generalization of the widely used Cauchy inequality 1 + x ≤ ex where x can be any non-negative real number. The results of this study can be the solution for the Cauchy’s problem for particular Ordinary Differential Equation (ODE). This is also related to study of the complete monotone function and the divided differences theory. The proof is based on the empty product convention notion and the Beppo Levi theorem of Monotone convergence. This study is also extended to multivariate generalization of the simultaneous inequalities.

Key Words: ODEs, Inequalities, Population Dynamics, Simultaneous Inequalities, Divided differences.