Rad HAZU, Matematičke znanosti, Vol. 18 (2014), 107-123.

ON POTENTIAL INEQUALITY FOR THE ABSOLUTE VALUE OF FUNCTIONS

Neven Elezović, Josip Pečarić and Marjan Praljak

Faculty of Textile Technology, University of Zagreb, Prilaz baruna Filipovića 28a 10000 Zagreb, Croatia
e-mail: pecaric@element.hr

Faculty of Food Technology and Biotechnology, University of Zagreb, Pierottijeva 6, 10000 Zagreb, Croatia
e-mail: mpraljak@pbf.hr

Abstract.   Potential inequality was introduced in [4] and later extended to the case of general convex and concave functions in [1]. The main goal of this paper is to derive the potential inequality for the case where the function at which the potential is evaluated is replaced by its absolute value. The results obtained, together with methods from [2], are used to construct new families of exponentially convex functions.

2010 Mathematics Subject Classification.   26D15.

Key words and phrases.   Potential inequality, exponential convexity.

References:

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4. M. Rao and H. Šikić, Potential inequality, Israel J. Math. 83 (1993), 97-127.
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5. J. L. Schiff, The Laplace transform. Theory and applications, Undergraduate Texts in Mathematics, Springer-Verlag, New York, 1999.
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