ERRATUM TO “MORE RESULTS ON HERMITE-HDAMARD TYPE INEQUALITIES THROUGH (<i>α,m</i>)-PREINVEXITY”

Muhammad Amer Latif

doi:10.11948/2017090

2017 Volume 7 Issue 4

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Muhammad Amer Latif. ERRATUM TO “MORE RESULTS ON HERMITE-HDAMARD TYPE INEQUALITIES THROUGH (α,m)-PREINVEXITY”[J]. Journal of Applied Analysis & Computation, 2017, 7(4): 1478-1487. doi: 10.11948/2017090

Citation:

Muhammad Amer Latif. ERRATUM TO “MORE RESULTS ON HERMITE-HDAMARD TYPE INEQUALITIES THROUGH (α,m)-PREINVEXITY”[J]. Journal of Applied Analysis & Computation, 2017, 7(4): 1478-1487. doi: 10.11948/2017090

ERRATUM TO “MORE RESULTS ON HERMITE-HDAMARD TYPE INEQUALITIES THROUGH (α,m)-PREINVEXITY”

Muhammad Amer Latif

Department of Basic Sciences, Deanship of Preparatory Year University of Hail, Kingdom of Saudi Arabia

Abstract

Abstract

In this paper, we present some corrections to definitions of mpreinvex, (α,m)-preinvex functions and statements of the theorems of the results proved in[7].
- Hermite-Hadamard's inequality /
- invex set /
- preinvex function /
- mpreinvex function /
- (α,m)-preinvex function /
- Hölder's integral inequality /
- powermean inequality
MSC: 26D15;26D20;26D07

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References

[1]	A. Barani, A. G. Ghazanfari and S. S. Dragomir, Hermite-Hadamard inequality for functions whose derivatives absolute values are preinvex, Journal of Inequalities and Applications, 2012, 2012(1):247. Google Scholar
[2]	A. Ben-Israel and B. Mond, What is invexity?, J. Austral. Math. Soc., Ser. B, 1986, 28(1), 1-9. Google Scholar
[3]	M. K. Bakula, M. E. Özdemir and J. Pečarić, Hadamard type inequalities for m-convex and (α,m)-convex functions, J. Inequal. Pure Appl. Math. 2008, 9, no. 4, Art. 96, 12 pages. Google Scholar
[4]	S. S. Dragomir and R. P. Agarwal, Two inequalities for differentiable mappings and applications to special means of real numbers and trapezoidal formula, Appl. Math. Lett., 1998, 11(5), 91-95. Google Scholar
[5]	S. S. Dragomir, On some new inequalities of Hermite-Hadamard type for mconvex functions, Tamkang J. Math., 2002, 33, 45-55. Google Scholar
[6]	S. S. Dragomir and G. Toader, Some inequalities for m-convex functions, Studia Univ. Babeş-Bolyai Math., 1993, 38, 21-28. Google Scholar
[7]	S. Hussain and S. Qaisar, More Results on Hermite-Hadamard type inequality through (α,m)-preinvexity, Journal of Applied Analysis and Computation, 2016, 6(2), 293-305. Google Scholar
[8]	M. A. Hanson, On sufficiency of the Kuhn-Tucker conditions, J. Math. Anal. Appl., 1981, 80, 545-550. Google Scholar
[9]	M. A. Latif, On Hermite-Hadamard type integral inequalities for n-times differentiable preinvex functions with applications, Studia Univ. Babeş-Bolyai Math., 2013, 58(3), 325-343. Google Scholar
[10]	M. A. Latif and M. Shoaib, Hermite-Hadamard type integral inequalities for differentiable m-preinvex and (α,m)-preinvex functions, Journal of the Egyptian Mathematical Society, 2015, 23(2), 236-241. Google Scholar
[11]	S. R. Mohan and S. K. Neogy, On invex sets and preinvex functions, J. Math. Anal. Appl., 1995, 189, 901-908. Google Scholar
[12]	V. G. Mihesan, A generalization of the convexity, Seminar on Functional Equations, Approx. Convex, Cluj-Napoca, 1993. (Romania) Google Scholar
[13]	M. E. Özdemir, M. Avci and E. Set, On some inequalities of Hermite-Hadamard type via m-convexity, Appl. Math. Lett., 2010, 23(9), 1065-1070. Google Scholar
[14]	M. E. Özdemir, M. Avcı and H. Kavurmacı, Hermite-Hadamard-type inequalities via (α,m)-convexity, Comput. Math. Appl., 2011, 61, 2614-2620. Google Scholar
[15]	R. Pini, Invexity and generalized convexity, Optimization, 1991, 22, 513-525. Google Scholar
[16]	G. Toader, Some generalizations of the convexity, Proceedings of the Colloquium on Approximation and Optimization, Univ. Cluj-Napoca, Cluj-Napoca, 1985, 329-338. Google Scholar
[17]	T. Weir, and B. Mond, Preinvex functions in multiple bjective optimization, Journal of Mathematical Analysis and Applications. 136(1998) 29-38. Google Scholar
[18]	X. M. Yang and D. Li, On properties of preinvex functions, J. Math. Anal. Appl., 2001, 256, 229-241. Google Scholar
[19]	X. M. Yang, X. Q. Yang and K. L. Teo, Characterizations and applications of prequasiinvex functions, properties of preinvex functions, J. Optim. Theo. Appl., 2001, 110(3), 645-668. Google Scholar
[20]	X. M. Yang, X. Q. Yang, K. L. Teo, Generalized invexity and generalized invariant monotonocity, Journal of Optimization Theory and Applications, 2003, 117(3), 607-625. Google Scholar