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Some Inequalities Related to $\eta -$Strongly Convex Functions

Year 2018, Volume: 10, 207 - 214, 29.12.2018

Abstract

The aim of this paper, is to establish some new inequalities of Hermite-Hadamard type by using $\eta -$strongly convex function.  Moreover, we also consider their relevances for other related known results. The aim of this paper, is to establish some new inequalities of Hermite-Hadamard type by using  $\eta -$strongly convex function. Moreover, we also consider their relevances for other related known results.

References

  • Aleman, A., On some generalizations of convex sets and convex functions, Anal. Numer.Theor. Approx., 14(1985), 1–6.
  • Bector, C.R., Singh, C., B-Vex functions, J. Optim. Theory. Appl., 71(2)(1991), 237–253.
  • De, B., . . . netti, Sulla strati. . . cazioni convesse, Ann. Math. Pura. Appl., 30(1949), 173–183.
  • Dragomir, S.S., Inequalities of Hermite-Hadamard type for $\lambda$ -convex functions on linear spaces, Preprint RGMIA Res. Rep. Coll. 17(2014), Art. 13, pp.18. [Online http://rgmia.org/papers/v17/v17a13.pdf].
  • Fejer, L., Uberdie fourierreihen, II, Math. Naturwise. Anz Ungar. Akad. Wiss., 24(1906), 369–390.
  • Hanson, M.A., On sufficiency of the Kuhn-Tucker conditions, J. Math. Anal. Appl., 80(1981), 545–550.
  • Hyers, D.H., Ulam, S.M., Approximately convex functions, Proc. Amer. Math. Soc., 3(1952), 821–828.
  • Hsu, I., Kuller, R.G., Convexity of vector-valued functions, Proc. Amer. Math. Soc., 46(1974), 363–366.
  • Jensen, J.L.W.V., On konvexe funktioner og uligheder mellem middlvaerdier, Nyt. Tidsskr. Math. B., 16(1905), 49-69.
  • Luc, D.T., Theory of Vector Optimization, Springer-Verlag, Berlin, 1989.
  • Mangasarian, O.L., Pseudo-Convex functions, SIAM Journal on Control, 3(1965), 281–290.
  • Özdemir, M.E., Avci, M., Kavurmaci, H., Hermite-Hadamard-type inequalities via ( $\alpha $;m)-convexity, Comput. Math. Appl., 61(9)(2011), 2614–2620.
  • Peˇcari´c, J.E., Proschan, F., Tong, Y.L., Convex functions, Partial Orderings and Statistical Applications, Academic Press, Boston, 1992.
  • Polyak, B.T., Existence theorems and convergence of minimizing sequences in extremum problems with restrictions, Soviet Math. Dokl., 7(1966) 72–75.
  • Rajba, T., On strong delta-convexity and Hermite-Hadamard type inequalities for delta convex functions of higher order, Math. Inequal. Appl., 18(1)(2015), 267–293.
  • Robert, A.W., Varbeg, D.E., Convex Functions, Academic Press, 1973.
Year 2018, Volume: 10, 207 - 214, 29.12.2018

Abstract

References

  • Aleman, A., On some generalizations of convex sets and convex functions, Anal. Numer.Theor. Approx., 14(1985), 1–6.
  • Bector, C.R., Singh, C., B-Vex functions, J. Optim. Theory. Appl., 71(2)(1991), 237–253.
  • De, B., . . . netti, Sulla strati. . . cazioni convesse, Ann. Math. Pura. Appl., 30(1949), 173–183.
  • Dragomir, S.S., Inequalities of Hermite-Hadamard type for $\lambda$ -convex functions on linear spaces, Preprint RGMIA Res. Rep. Coll. 17(2014), Art. 13, pp.18. [Online http://rgmia.org/papers/v17/v17a13.pdf].
  • Fejer, L., Uberdie fourierreihen, II, Math. Naturwise. Anz Ungar. Akad. Wiss., 24(1906), 369–390.
  • Hanson, M.A., On sufficiency of the Kuhn-Tucker conditions, J. Math. Anal. Appl., 80(1981), 545–550.
  • Hyers, D.H., Ulam, S.M., Approximately convex functions, Proc. Amer. Math. Soc., 3(1952), 821–828.
  • Hsu, I., Kuller, R.G., Convexity of vector-valued functions, Proc. Amer. Math. Soc., 46(1974), 363–366.
  • Jensen, J.L.W.V., On konvexe funktioner og uligheder mellem middlvaerdier, Nyt. Tidsskr. Math. B., 16(1905), 49-69.
  • Luc, D.T., Theory of Vector Optimization, Springer-Verlag, Berlin, 1989.
  • Mangasarian, O.L., Pseudo-Convex functions, SIAM Journal on Control, 3(1965), 281–290.
  • Özdemir, M.E., Avci, M., Kavurmaci, H., Hermite-Hadamard-type inequalities via ( $\alpha $;m)-convexity, Comput. Math. Appl., 61(9)(2011), 2614–2620.
  • Peˇcari´c, J.E., Proschan, F., Tong, Y.L., Convex functions, Partial Orderings and Statistical Applications, Academic Press, Boston, 1992.
  • Polyak, B.T., Existence theorems and convergence of minimizing sequences in extremum problems with restrictions, Soviet Math. Dokl., 7(1966) 72–75.
  • Rajba, T., On strong delta-convexity and Hermite-Hadamard type inequalities for delta convex functions of higher order, Math. Inequal. Appl., 18(1)(2015), 267–293.
  • Robert, A.W., Varbeg, D.E., Convex Functions, Academic Press, 1973.
There are 16 citations in total.

Details

Primary Language English
Subjects Engineering
Journal Section Articles
Authors

Seda Kılınç

Abdullah Akkurt

Hüseyin Yıldırım

Publication Date December 29, 2018
Published in Issue Year 2018 Volume: 10

Cite

APA Kılınç, S., Akkurt, A., & Yıldırım, H. (2018). Some Inequalities Related to $\eta -$Strongly Convex Functions. Turkish Journal of Mathematics and Computer Science, 10, 207-214.
AMA Kılınç S, Akkurt A, Yıldırım H. Some Inequalities Related to $\eta -$Strongly Convex Functions. TJMCS. December 2018;10:207-214.
Chicago Kılınç, Seda, Abdullah Akkurt, and Hüseyin Yıldırım. “Some Inequalities Related to $\eta -$Strongly Convex Functions”. Turkish Journal of Mathematics and Computer Science 10, December (December 2018): 207-14.
EndNote Kılınç S, Akkurt A, Yıldırım H (December 1, 2018) Some Inequalities Related to $\eta -$Strongly Convex Functions. Turkish Journal of Mathematics and Computer Science 10 207–214.
IEEE S. Kılınç, A. Akkurt, and H. Yıldırım, “Some Inequalities Related to $\eta -$Strongly Convex Functions”, TJMCS, vol. 10, pp. 207–214, 2018.
ISNAD Kılınç, Seda et al. “Some Inequalities Related to $\eta -$Strongly Convex Functions”. Turkish Journal of Mathematics and Computer Science 10 (December 2018), 207-214.
JAMA Kılınç S, Akkurt A, Yıldırım H. Some Inequalities Related to $\eta -$Strongly Convex Functions. TJMCS. 2018;10:207–214.
MLA Kılınç, Seda et al. “Some Inequalities Related to $\eta -$Strongly Convex Functions”. Turkish Journal of Mathematics and Computer Science, vol. 10, 2018, pp. 207-14.
Vancouver Kılınç S, Akkurt A, Yıldırım H. Some Inequalities Related to $\eta -$Strongly Convex Functions. TJMCS. 2018;10:207-14.