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New improvements of Jensen’s type inequalities via 4-convex functions with applications

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Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas Aims and scope Submit manuscript

Abstract

In this article, we present some new improvements of Jensen’s type inequalities via 4-convex and Green functions. These improvements are demonstrated in discrete as well as in integral versions. The aforesaid results enable us to give some improvements of Jensen’s and the Jensen–Steffensen inequalities. Also, we present some improvements of the reverse Jensen’s and the Jensen–Steffensen inequalities. Then as consequences of the improved Jensen’s inequality, we deduce some new bounds for the power, geometric and quasi-arithmetic means, also obtain bounds for the Hermite–Hadamard gap and improvements of the Hölder inequality. Finally as applications of the improved Jensen’s inequality, we present some new bounds for various divergences and Zipf–Mandelbrot entropy.

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Acknowledgements

The authors would like to express their sincere thanks to the anonymous reviewer for their helpful comments and suggestions.

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Authors and Affiliations

  1. Department of Mathematics, University of Peshawar, Peshawar, 25000, Pakistan

    Muhammad Adil Khan & Shahid Khan

  2. Catholic University of Croatia, Ilica 242, 10000, Zagreb, Croatia

    Ɖilda Pečarić

  3. RUDN University, Miklukho-Maklaya str. 6, 117198, Moscow, Russia

    Josip Pečarić

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  1. Muhammad Adil Khan
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  2. Shahid Khan
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  3. Ɖilda Pečarić
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  4. Josip Pečarić
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Correspondence to Muhammad Adil Khan.

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The publication was supported by the Ministry of Education and Science of the Russian Federation (the Agreement number No. 02.a03.21.0008.).

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Adil Khan, M., Khan, S., Pečarić, Ɖ. et al. New improvements of Jensen’s type inequalities via 4-convex functions with applications. RACSAM 115, 43 (2021). https://doi.org/10.1007/s13398-020-00971-8

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