Araştırma Makalesi
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ON INTEGRAL INEQUALITIES FOR INVEX FUNCTIONS SATISFYING LIPSCHITZIAN REQUIREMENT

Yıl 2020, Cilt: 3 Sayı: 1, 1 - 10, 31.01.2020
https://doi.org/10.33773/jum.679836

Öz

Some new type of integral inequalities for functions from the Lipschitz class are obtained. These results involve some different types of integral
averages for Lipschitzian functions. Special cases which are naturally included in the main results of the paper are also discussed.

Kaynakça

  • Hadamard J. Etude sur les proprietes des fonctions entieres et en particulier dune fonction consideree par Riemann, J. Math. Pures Appl., 171-215, 58 (1893).
  • İşcan, İ. Hermite-Hadamard type inequalities for harmonically convex functions, Hacettepe Journal of Mathematics and Statistics, Volume 43 (6), 935-942, (2014).
  • Kilbas, A.A. Srivastava, H.M. and Trujillo, J., Theory and applications of fractional differential equations, Elsevier, Amsterdam (2006).
  • Roberts, A.W. and Varberg, D.E. Convex Functions. Academic Press, 300pp, New York (1973).
  • Dragomir, S.S. Cho, Y.J. and Kim, S.S., Inequalities of Hadamard's type for Lipschitzian mappings and their applications, Journal of Mathematical Analysis and Applications, vol. 245, no. 2, pp. 489-501, (2000).
  • Hwang, S.R. Hsu, K.C. and Tseng, K.L., Hadamard-type inequalities for Lipschitzian functions in one and two variables with applications, Journal of Mathematical Analysis and Applications, vol. 405, no. 2, 546-554, (2013).
  • İşcan, İ. New general integral inequalities for Lipschitzianfunctions via Hadamard fractional integrals, International Journal of Analysis, volume 2014, Article ID 353924, 8 pages, (2014).
  • İşcan, İ., Hadamard-type and Bullen-type inequalities for Lipschitzian functions via fractional integrals, Mathematical Sciences and Applications E-Notes, 4 (1), 77-87, (2016).
  • Hadamard J. " Etude sur les proprietes des fonctions entieres et en particulier dune fonction consideree par Riemann" , J. Math. Pures Appl., 58 , 171-215, (1893).
  • Hanson, M.A., On sufficiency of the Kuhn-Tucker conditions, J. Math. Anal. Appl. 80, 545-550, (1981).
  • İşcan, İ., Kadakal, M.,Aydın A., 'Some New integral inequalities for Lipschitzian functions' IJOCTA vol.8, no. 2, pp. 259-265, (2018).
  • Kilinc, S., Akkurt, A., and Yıldırım, H., Integral Inequalities for Hypergeometric Operators via Fractional Integral, Journal of Inequalities & Special Functions 8 (5), (2017).
  • Noor, M.A., Awan, M.U. and Noor, K.I., On some inequalities for relative semi-convex functions, Journal of Inequalities and Applications, 2013.
  • Noor, M.A., Noor, K.I. and Awan, M.U., Hermite-Hadamard inequalities for relative semiconvex functions and applications, Filomat, in press.
  • Mohan, S.R., Neogy, S.K., On Invex Sets and Preinvex Functions, Journal of Mathematical Analysis and Applications, 1995.
  • Noor, M.A., Awan, M.U., Some Integral inequalities for two senses of convexities via fractional integrals, TJMM 5(2013), no.2, 129-136.
Yıl 2020, Cilt: 3 Sayı: 1, 1 - 10, 31.01.2020
https://doi.org/10.33773/jum.679836

Öz

Kaynakça

  • Hadamard J. Etude sur les proprietes des fonctions entieres et en particulier dune fonction consideree par Riemann, J. Math. Pures Appl., 171-215, 58 (1893).
  • İşcan, İ. Hermite-Hadamard type inequalities for harmonically convex functions, Hacettepe Journal of Mathematics and Statistics, Volume 43 (6), 935-942, (2014).
  • Kilbas, A.A. Srivastava, H.M. and Trujillo, J., Theory and applications of fractional differential equations, Elsevier, Amsterdam (2006).
  • Roberts, A.W. and Varberg, D.E. Convex Functions. Academic Press, 300pp, New York (1973).
  • Dragomir, S.S. Cho, Y.J. and Kim, S.S., Inequalities of Hadamard's type for Lipschitzian mappings and their applications, Journal of Mathematical Analysis and Applications, vol. 245, no. 2, pp. 489-501, (2000).
  • Hwang, S.R. Hsu, K.C. and Tseng, K.L., Hadamard-type inequalities for Lipschitzian functions in one and two variables with applications, Journal of Mathematical Analysis and Applications, vol. 405, no. 2, 546-554, (2013).
  • İşcan, İ. New general integral inequalities for Lipschitzianfunctions via Hadamard fractional integrals, International Journal of Analysis, volume 2014, Article ID 353924, 8 pages, (2014).
  • İşcan, İ., Hadamard-type and Bullen-type inequalities for Lipschitzian functions via fractional integrals, Mathematical Sciences and Applications E-Notes, 4 (1), 77-87, (2016).
  • Hadamard J. " Etude sur les proprietes des fonctions entieres et en particulier dune fonction consideree par Riemann" , J. Math. Pures Appl., 58 , 171-215, (1893).
  • Hanson, M.A., On sufficiency of the Kuhn-Tucker conditions, J. Math. Anal. Appl. 80, 545-550, (1981).
  • İşcan, İ., Kadakal, M.,Aydın A., 'Some New integral inequalities for Lipschitzian functions' IJOCTA vol.8, no. 2, pp. 259-265, (2018).
  • Kilinc, S., Akkurt, A., and Yıldırım, H., Integral Inequalities for Hypergeometric Operators via Fractional Integral, Journal of Inequalities & Special Functions 8 (5), (2017).
  • Noor, M.A., Awan, M.U. and Noor, K.I., On some inequalities for relative semi-convex functions, Journal of Inequalities and Applications, 2013.
  • Noor, M.A., Noor, K.I. and Awan, M.U., Hermite-Hadamard inequalities for relative semiconvex functions and applications, Filomat, in press.
  • Mohan, S.R., Neogy, S.K., On Invex Sets and Preinvex Functions, Journal of Mathematical Analysis and Applications, 1995.
  • Noor, M.A., Awan, M.U., Some Integral inequalities for two senses of convexities via fractional integrals, TJMM 5(2013), no.2, 129-136.
Toplam 16 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Matematik
Bölüm Araştırma Makalesi
Yazarlar

Seda Kılınç

Abdullah Akkurt 0000-0001-5644-1276

Hüseyin Yildirim

Yayımlanma Tarihi 31 Ocak 2020
Gönderilme Tarihi 24 Ocak 2020
Kabul Tarihi 27 Şubat 2020
Yayımlandığı Sayı Yıl 2020 Cilt: 3 Sayı: 1

Kaynak Göster

APA Kılınç, S., Akkurt, A., & Yildirim, H. (2020). ON INTEGRAL INEQUALITIES FOR INVEX FUNCTIONS SATISFYING LIPSCHITZIAN REQUIREMENT. Journal of Universal Mathematics, 3(1), 1-10. https://doi.org/10.33773/jum.679836
AMA Kılınç S, Akkurt A, Yildirim H. ON INTEGRAL INEQUALITIES FOR INVEX FUNCTIONS SATISFYING LIPSCHITZIAN REQUIREMENT. JUM. Ocak 2020;3(1):1-10. doi:10.33773/jum.679836
Chicago Kılınç, Seda, Abdullah Akkurt, ve Hüseyin Yildirim. “ON INTEGRAL INEQUALITIES FOR INVEX FUNCTIONS SATISFYING LIPSCHITZIAN REQUIREMENT”. Journal of Universal Mathematics 3, sy. 1 (Ocak 2020): 1-10. https://doi.org/10.33773/jum.679836.
EndNote Kılınç S, Akkurt A, Yildirim H (01 Ocak 2020) ON INTEGRAL INEQUALITIES FOR INVEX FUNCTIONS SATISFYING LIPSCHITZIAN REQUIREMENT. Journal of Universal Mathematics 3 1 1–10.
IEEE S. Kılınç, A. Akkurt, ve H. Yildirim, “ON INTEGRAL INEQUALITIES FOR INVEX FUNCTIONS SATISFYING LIPSCHITZIAN REQUIREMENT”, JUM, c. 3, sy. 1, ss. 1–10, 2020, doi: 10.33773/jum.679836.
ISNAD Kılınç, Seda vd. “ON INTEGRAL INEQUALITIES FOR INVEX FUNCTIONS SATISFYING LIPSCHITZIAN REQUIREMENT”. Journal of Universal Mathematics 3/1 (Ocak 2020), 1-10. https://doi.org/10.33773/jum.679836.
JAMA Kılınç S, Akkurt A, Yildirim H. ON INTEGRAL INEQUALITIES FOR INVEX FUNCTIONS SATISFYING LIPSCHITZIAN REQUIREMENT. JUM. 2020;3:1–10.
MLA Kılınç, Seda vd. “ON INTEGRAL INEQUALITIES FOR INVEX FUNCTIONS SATISFYING LIPSCHITZIAN REQUIREMENT”. Journal of Universal Mathematics, c. 3, sy. 1, 2020, ss. 1-10, doi:10.33773/jum.679836.
Vancouver Kılınç S, Akkurt A, Yildirim H. ON INTEGRAL INEQUALITIES FOR INVEX FUNCTIONS SATISFYING LIPSCHITZIAN REQUIREMENT. JUM. 2020;3(1):1-10.