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

Year 2018, Volume 10, Issue , 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, Issue , 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.

Details

Primary Language English
Subjects Engineering
Journal Section Articles
Authors

Seda KILINÇ (Primary Author)
Türkiye


Abdullah AKKURT
0000-0001-5644-1276


Hüseyin YILDIRIM
0000-0001-8855-9260
Türkiye

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

Cite

Bibtex @conference paper { tjmcs452143, journal = {Turkish Journal of Mathematics and Computer Science}, issn = {}, eissn = {2148-1830}, address = {}, publisher = {Matematikçiler Derneği}, year = {2018}, volume = {10}, pages = {207 - 214}, doi = {}, title = {Some Inequalities Related to \$\\eta -\$Strongly Convex Functions}, key = {cite}, author = {Kılınç, Seda and Akkurt, Abdullah and Yıldırım, Hüseyin} }
APA Kılınç, S. , Akkurt, A. & Yıldırım, H. (2018). Some Inequalities Related to $\eta -$Strongly Convex Functions . Turkish Journal of Mathematics and Computer Science , Volume 10 (Special Issue: Proceedings of ICMME 2018) , 207-214 . Retrieved from https://dergipark.org.tr/en/pub/tjmcs/issue/42027/452143
MLA Kılınç, S. , Akkurt, A. , Yıldırım, H. "Some Inequalities Related to $\eta -$Strongly Convex Functions" . Turkish Journal of Mathematics and Computer Science 10 (2018 ): 207-214 <https://dergipark.org.tr/en/pub/tjmcs/issue/42027/452143>
Chicago Kılınç, S. , Akkurt, A. , Yıldırım, H. "Some Inequalities Related to $\eta -$Strongly Convex Functions". Turkish Journal of Mathematics and Computer Science 10 (2018 ): 207-214
RIS TY - JOUR T1 - Some Inequalities Related to $\eta -$Strongly Convex Functions AU - Seda Kılınç , Abdullah Akkurt , Hüseyin Yıldırım Y1 - 2018 PY - 2018 N1 - DO - T2 - Turkish Journal of Mathematics and Computer Science JF - Journal JO - JOR SP - 207 EP - 214 VL - 10 IS - SN - -2148-1830 M3 - UR - Y2 - 2018 ER -
EndNote %0 Turkish Journal of Mathematics and Computer Science Some Inequalities Related to $\eta -$Strongly Convex Functions %A Seda Kılınç , Abdullah Akkurt , Hüseyin Yıldırım %T Some Inequalities Related to $\eta -$Strongly Convex Functions %D 2018 %J Turkish Journal of Mathematics and Computer Science %P -2148-1830 %V 10 %N %R %U
ISNAD Kılınç, Seda , Akkurt, Abdullah , Yıldırım, Hüseyin . "Some Inequalities Related to $\eta -$Strongly Convex Functions". Turkish Journal of Mathematics and Computer Science 10 / (December 2018): 207-214 .
AMA Kılınç S. , Akkurt A. , Yıldırım H. Some Inequalities Related to $\eta -$Strongly Convex Functions. TJMCS. 2018; 10: 207-214.
Vancouver Kılınç S. , Akkurt A. , Yıldırım H. Some Inequalities Related to $\eta -$Strongly Convex Functions. Turkish Journal of Mathematics and Computer Science. 2018; 10: 207-214.
IEEE S. Kılınç , A. Akkurt and H. Yıldırım , "Some Inequalities Related to $\eta -$Strongly Convex Functions", Turkish Journal of Mathematics and Computer Science, vol. 10, pp. 207-214, Dec. 2018