On Certain Properties of Trigonometrically *ρ*-Convex Functions

ABSTRACT

The aim of this paper is to prove that the average function of a trigonometrically*ρ*-convex function is trigonometrically *ρ*-convex. Furthermore, we show the existence of support curves implies the trigonometric *ρ*-convexity, and prove an extremum property of this function.

The aim of this paper is to prove that the average function of a trigonometrically

Cite this paper

M. Salem Ali, "On Certain Properties of Trigonometrically*ρ*-Convex Functions," *Advances in Pure Mathematics*, Vol. 2 No. 5, 2012, pp. 337-340. doi: 10.4236/apm.2012.25047.

M. Salem Ali, "On Certain Properties of Trigonometrically

References

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[1] B. Ya. Levin, “Lectures on Entire Functions,” American Mathematical Society, 1996.

[2] L. S. Maergoiz, “Asymptotic Characteristics of Entire Functions and Their Applications in Mathematics and Biophysics,” Kluwer Academic Publishers, New York, 2003.

[3] A. W. Roberts and D. E. Varberg, “Convex Functions,” Academic Press, New York, 1973.

[4] M. J. Miles, “An Extremum Property of Convex Func- tions,” American Mathematical Monthly, Vol. 76, 1969, pp. 921-922. doi:10.2307/2317948

[5] A. M. Bruckner and E. Ostrow, “Some Functions Classes Related to the Class of Convex Functions,” Pacific Journal of Mathematics, Vol. 12, 1962, pp. 1203-1215.

[6] E. F. Beckenbach, “Convex Functions,” Bulletin of the American Mathematical Society, Vol. 54, No. 5, 1948, pp. 439-460. doi:10.1090/S0002-9904-1948-08994-7

[7] J. W. Green, “Support, Convergence, and Differentiability Properties of Generalized Convex Functions,” Pro- ceedings of the American Mathematical Society, Vol. 4, No. 3, 1953, pp. 391-396. doi:10.1090/S0002-9939-1953-0056039-2

[8] M. M. Peixoto, “On the Existence of Derivatives of Gen- eralized Convex Functions,” Summa Brasilian Mathematics, Vol. 2, No. 3, 1948, pp. 35-42.

[9] M. M. Peixoto, “Generalized Convex Functions and Sec- ond Order Differential Inequlities,” Bulletin of the American Mathematical Society, Vol. 55, No. 6, 1949, pp. 563-572. doi:10.1090/S0002-9904-1949-09246-7

[10] F. F. Bonsall, “The Characterization of Generalized Convex Functions,” The Quarterly Journal of Mathematics Oxford Series, Vol. 1, 1950, pp. 100-111.doi:10.1093/qmath/1.1.100