Title: On Giaccardi's Inequality and Associated Functional in the Plane
Author(s): Atiq Ur Rehman, M. Hassaan Akbar, G. Farid
Pages: 178-192
Cite as:
Atiq Ur Rehman, M. Hassaan Akbar, G. Farid, On Giaccardi's Inequality and Associated Functional in the Plane, Int. J. Anal. Appl., 16 (2) (2018), 178-192.

Abstract


In this paper the authors extend Giaccardi's inequality to coordinates in the plane. The authors consider the nonnegative associated functional due to Giaccardi's inequality in plane and discuss its properties for certain class of parametrized functions. Also the authors proved related mean value theorems.

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References


  1. S. Butt, J. Peˇ cari´ c and Atiq ur Rehman, Exponential Convexity of Petrovi´ c and Related Functional, J. Inequal. Appl. 2011 (2011), Art. ID 89. Google Scholar

  2. S. S Dragomir, On Hadamards Inequality for Convex Functions on the Co-ordinates in a Rectangle from the Plane, Taiwanese J Mat. 4 (2001), 775–788 Google Scholar

  3. G. Farid, M. Marwan, and A. U. Rehman, Fejer-Hadamard Inequality for Convex Functions on the Coordinates in a Rectangle from the Plane, Int. J. Analysis Appl. 10(1) (2016), 40–47. Google Scholar

  4. G. Farid, M. Marwan and A. U. Rehman, New Mean Value Theorems and Generalization of Hadamard Inequality via Coordinated m−Convex Functions, J. Inequal. Appl. 2015 (2015), Art. ID 283. Google Scholar

  5. D. S. Mitrinovic, J. Peˇ cari´ c and A.M Fink, Classical and New Inequalities in Analysis, Vol. 61, Springer Science & Business Media, 2013. Google Scholar

  6. M. A. Noor, F. Qi and M. U. Awan , Some Hermite-Hadamard Type Inequalities for Log-h-Convex Functions, Analysis, 33(4) (2013), 367–375. Google Scholar

  7. C.P. Niculescu, The Hermite-Hadamard Inequality for Log-convex Functions, Nonlinear Analysis, 75 (2012) 662–669. Google Scholar

  8. J. Peˇ cari´ c, F. Proschan, Y. L. Tong, Convex functions, partial orderings and statistical applications, Academic Press, New York, 1992. Google Scholar

  9. J. Peˇ cari´ c and Atiq Ur Rehman, On Logarithmic Convexity for Power Sums and Related Results, J. Inequal. Appl. 2008 (2008), Art. ID 389410. Google Scholar

  10. J. Peˇ cari´ c and Atiq Ur Rehman, On Logarithmic Convexity for Giaccardi’s Difference, Rad HAZU. 515 (2013), 01–10. Google Scholar

  11. A. U. Rehman, Muhammad Mudessir, Hafiza Tahira Fazal and Ghulam Farid, Petrovi´ c’s Inequality on Coordinates and Related Results, Cogent Math. 3(1) (2016), Art. ID 1227298. Google Scholar

  12. Xiaoming Zhang and Weidong Jiang, Some Properties of Log-convex Function and Applications for the Exponential Function, Comput. Math. Appl. 63(6) (2012), 1111–1116. Google Scholar


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