Please use this identifier to cite or link to this item: http://prr.hec.gov.pk/jspui/handle/123456789/17304
Title: Generalization of Cycle Refinements of Jensen's Inequalities
Authors: Mehmood, Nasir
Keywords: Physical Sciences
Mathematics
Issue Date: 2021
Publisher: COMSATS University, Islamabad
Abstract: Generalizations of Cyclic Refinements of Jensen’s Inequalities In recent years, the concept of convex functions has been generalized extensively. Applications of convex functions are widely seen in many areas of modern analysis. Convex functions also have significant relation with the theory of inequalities and many useful inequalities are the result of the applications of convex functions. The Jensen's inequality has tremendous implications in many fields of modern analysis. It helps computing useful upper bounds for several entropic measures used in information theory. We consider discrete and continuous cyclic refinements of Jensen's inequality and extend them from convex to higher order convex function by using new Green functions introduced by us and employing different interpolating polynomials and identities. We formulate monotonicity of the linear functionals for n convex functions at a point. We calculate some new Grüss and Ostrowski type bounds. As an application of our obtained results we give new bounds for Shannon, Relative and Zipf-Mandelbrot entropies.
Gov't Doc #: 23505
URI: http://prr.hec.gov.pk/jspui/handle/123456789/17304
Appears in Collections:PhD Thesis of All Public / Private Sector Universities / DAIs.

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