Inequalities for 3-convex functions and applications

Yıl 2022, , 1 - 12, 30.04.2022

Praphull Chhabra

https://doi.org/10.54187/jnrs.978216

Öz

In this article, we derived new information inequalities on Jain-Saraswat's functional coefficient of distance (2013) for 3-convex functions. Further, we evaluated some important relations among Relative Jensen Shannon coefficient of distance, Relative Arithmetic Geometric coefficient of distance, Triangular discrimination, Chi-square coefficient of distance and many more. Moreover, we explained the series version of this functional coefficient of distance by using the Taylor's series with both Lagrange's and Cauchy's form of remainders.

Anahtar Kelimeler

Contra harmonic mean coefficient, Taylor, 3-Convex functions, Jain-Saraswat, Chi-m coefficients

Kaynakça

• E. Issacsson, H. B. Keller, Analysis of numerical methods, Dover Publications Inc. Wiley, New York, 367-374, 1966.
• Y. Khurshid, M. Adil Khan, Y. M. Chu, Z. A. Khan, Hermite Hadamard Fejer inequalities for conformable fractional integrals via preinvex functions, Journal of Function Spaces, 2019, (2019) Article ID: 3146210, 1-9.
• X. M. Zhang, Y. M. Chu, X. H. Zhang, The Hermite Hadamard type inequality of GA-convex functions and its applications, Journal of Inequalities and Applications, 2010, (2010) Article ID: 507560, 1-11.
• U. S. Zaheer, M. Adil Khan, Y. M. Chu, Majorization of theorems for strongly convex functions, Journal of Inequalities and Applications, 2019, (2019) Article ID: 58, 1-13.
• M. Adil Khan, Y. M. Chu, T. U. Khan, J. Khan, Some new inequalities of Hermite-Hadamard type for s-convex functions with applications, Open Mathematics, 15(1), (2017) 1414-1430.
• S. Naz, M. N. Naeem, Y. M. Chu, Ostrowski-type inequalities for n-polynomial P-convex function for k-fractional Hilfer-Katugampola derivative, Journal of Inequalities and Applications, 2021, (2021) Article Number: 117, 1-23.
• M. Amer Latif, S. Hussain, Y. M. Chu, Generalized Hermite-Hadamard type inequalities for differentiable harmonically-convex and harmonically quasi-convex functions, Journal of Mathematical Inequalities, 15(2), (2021) 755-766.
• M. Aamir Ali, H. Budak, G. Murtaza, Y. M. Chu, Post-quantum Hermite-Hadamard type inequalities for interval-valued convex functions, Journal of Inequalities and Applications, 2021, (2021) Article Number: 84, 1-19.
• Y. M. Chu, S. Rashid, T. Abdeljawad, A. Khalid, H. Kalsoom, On new generalized unified bounds via generalized exponentially harmonically s-convex functions on fractal sets, Advances in Difference Equations, 2021, (2021) Article Number: 218, 1-33. https://doi.org/10.1186/s13662-021-03380-2
• H. Kara, H. Budak, M. A. Ali, M. Z. Sarikaya, Y. M. Chu, Weighted Hermite-Hadamard type inclusions for products of co-ordinated convex interval-valued functions, Advances in Difference Equations, 2021, (2021) Article Number:104, 1-16. https://doi.org/10.1186/s13662-021-03261-8
• H. Kalsoom, M. A. Latif, S. Rashid, D. Baleanu, Y. M. Chu, New (p,q)-estimates for different types of integral inequalities via (α,m)-convex mappings, Open Mathematics, 18(1), (2020) 1830-1854. https://doi.org/10.1515/math-2020-0114
• B. Feng, M. Ghafoor, Y. M. Chu, M. I. Qureshi, X. Feng, C. Yao, X. Qiao, Hermite-Hadamard and Jensen's type inequalities for modified (p,h)-convex functions, AIMS Mathematics, 5(6), (2020) 6959-6971.
• C. Y. Jung, M. Yussouf, Y. M. Chu, G. Farid, S. M. Kang, Generalized fractional Hadamard and Fejér-Hadamard inequalities for generalized harmonically convex functions, Journal of Mathematics, 2020, (2020) Article ID: 8245324, 1-13. https://doi.org/10.1155/2020/8245324
• K. C. Jain, R. N. Saraswat, Some bounds of information divergence measure in term of Relative arithmetic-geometric divergence measure, International Journal of Applied Mathematics and Statistics, 32(2), (2013) 48-58.
• P. Chhabra, New information inequalities on absolute value of the functions and its application, Journal of Applied Mathematics and Informatics, 35(03-04), (2017) 371-385.
• K. C. Jain, P. Chhabra, New information inequalities in terms of Relative Arithmetic-Geometric divergence and Renyi's entropy, Palestine Journal of Mathematics, 6(2) (2017) 314-319.
• K. C. Jain, P. Chhabra, New information inequalities and its special cases, Journal of Rajasthan Academy of Physical Sciences, 13(1), (2014) 39-50.
• R. Mikic, Ð. Pecaric, J. Pecaric, Inequalities of the Edmundson-Lah-Ribaric type for 3-convex functions with applications, Ukrainian Mathematical Journal, 73(1), (2021) 99-119.
• K. Pearson, On the Criterion that a given system of deviations from the probable in the case of correlated system of variables is such that it can be reasonable supposed to have arisen from random sampling, The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science Series 5, 50(302), (1900) 157-172.
• I. J. Taneja, Inequalities among logarithmic mean measures, Available online: http://arxiv.org/abs/1103.2580v1, 2011.
• D. Dacunha-Castelle, H. Heyer, B. Roynette, Ecoled-Ete de Probabilites de, Saint-Flour VII-1977, Berlin, Heidelberg, New York: Springer, 1978.
• R. Sibson, Information radius, Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete, (14), (1969) 149-160.
• I. J. Taneja, New developments in generalized information measures, Chapter in: Advances in Imaging and Electron Physics, Edition, P. W. Hawkes, 91, (1995) 37-135.
• S. S. Dragomir, V. Gluscevic, C. E. M. Pearce, Approximation for the Csiszar's f-divergence via midpoint inequalities, in Inequality Theory and Applications -Y. J. Cho, J. K. Kim, S. S. Dragomir (Eds.), Nova Science Publishers, Incorpartion., Huntington, New York, 1 (2001) 139-154.
• A. N. Kolmogorov, On the approximation of distributions of sums of independent summands by infinitely divisible distributions, Contributions to Statistics, Sankhya, 25, (1965) 159-174. https://doi.org/10.1016/B978-1-4832-3160-0.50016-6
• J. Burbea, C. R. Rao, On the convexity of some discriminating measures based on entropy functions, IEEE Transactions on Information Theory, IT-28, (1982) 489-495.
• E. Hellinger, Neue begrundung der theorie der quadratischen formen von unendlichen vielen veranderlichen, Journal für die reine und angewand te Mathematik, 136, (1909) 210-271.
• S. S. Dragomir, J. Sunde, C. Buse, New inequalities for Jeffreys divergence measure, Tamusi Oxford Journal of Mathematical Sciences, 16(2), (2000) 295-309.
• H. Jeffreys, An invariant form for the prior probability in estimation problem, Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences, 186(1007), (1946) 453-461.
• S. Kullback, R. A. Leibler, On information and sufficiency, The Annals of Mathematical Statistics, 22(1), (1951) 79-86.
• S. S. Dragomir, A General coefficient of distance measure for monotonic functions and applications in information theory, Science Direct Working Paper No S1574-0358(04)70438-4, 14 Pages Posted: 14 May 2018.