Research Article
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Year 2020, Volume 3, Issue 1, 1 - 10, 31.01.2020
https://doi.org/10.33773/jum.679836

Abstract

References

  • 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.

ON INTEGRAL INEQUALITIES FOR INVEX FUNCTIONS SATISFYING LIPSCHITZIAN REQUIREMENT

Year 2020, Volume 3, Issue 1, 1 - 10, 31.01.2020
https://doi.org/10.33773/jum.679836

Abstract

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.

References

  • 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.

Details

Primary Language English
Subjects Mathematics
Journal Section Research Article
Authors

Seda KILINÇ
KAHRAMANMARAŞ SÜTÇÜ İMAM ÜNİVERSİTESİ
Türkiye


Abdullah AKKURT
KAHRAMANMARAŞ SÜTÇÜ İMAM ÜNİVERSİTESİ
0000-0001-5644-1276
Türkiye


Hüseyin YİLDİRİM
KAHRAMANMARAŞ SÜTÇÜ İMAM ÜNİVERSİTESİ
0000-0001-8855-9260
Türkiye

Publication Date January 31, 2020
Application Date January 24, 2020
Acceptance Date February 27, 2020
Published in Issue Year 2020, Volume 3, Issue 1

Cite

Bibtex @research article { jum679836, journal = {Journal of Universal Mathematics}, issn = {2618-5660}, eissn = {2618-5660}, address = {editorinchief@junimath.com}, publisher = {Gökhan ÇUVALCIOĞLU}, year = {2020}, volume = {3}, pages = {1 - 10}, doi = {10.33773/jum.679836}, title = {ON INTEGRAL INEQUALITIES FOR INVEX FUNCTIONS SATISFYING LIPSCHITZIAN REQUIREMENT}, key = {cite}, author = {Kılınç, Seda and Akkurt, Abdullah and Yildirim, Hüseyin} }
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 . DOI: 10.33773/jum.679836
MLA Kılınç, S. , Akkurt, A. , Yildirim, H. "ON INTEGRAL INEQUALITIES FOR INVEX FUNCTIONS SATISFYING LIPSCHITZIAN REQUIREMENT" . Journal of Universal Mathematics 3 (2020 ): 1-10 <https://dergipark.org.tr/en/pub/jum/issue/52380/679836>
Chicago Kılınç, S. , Akkurt, A. , Yildirim, H. "ON INTEGRAL INEQUALITIES FOR INVEX FUNCTIONS SATISFYING LIPSCHITZIAN REQUIREMENT". Journal of Universal Mathematics 3 (2020 ): 1-10
RIS TY - JOUR T1 - ON INTEGRAL INEQUALITIES FOR INVEX FUNCTIONS SATISFYING LIPSCHITZIAN REQUIREMENT AU - Seda Kılınç , Abdullah Akkurt , Hüseyin Yildirim Y1 - 2020 PY - 2020 N1 - doi: 10.33773/jum.679836 DO - 10.33773/jum.679836 T2 - Journal of Universal Mathematics JF - Journal JO - JOR SP - 1 EP - 10 VL - 3 IS - 1 SN - 2618-5660-2618-5660 M3 - doi: 10.33773/jum.679836 UR - https://doi.org/10.33773/jum.679836 Y2 - 2020 ER -
EndNote %0 Journal of Universal Mathematics ON INTEGRAL INEQUALITIES FOR INVEX FUNCTIONS SATISFYING LIPSCHITZIAN REQUIREMENT %A Seda Kılınç , Abdullah Akkurt , Hüseyin Yildirim %T ON INTEGRAL INEQUALITIES FOR INVEX FUNCTIONS SATISFYING LIPSCHITZIAN REQUIREMENT %D 2020 %J Journal of Universal Mathematics %P 2618-5660-2618-5660 %V 3 %N 1 %R doi: 10.33773/jum.679836 %U 10.33773/jum.679836
ISNAD Kılınç, Seda , Akkurt, Abdullah , Yildirim, Hüseyin . "ON INTEGRAL INEQUALITIES FOR INVEX FUNCTIONS SATISFYING LIPSCHITZIAN REQUIREMENT". Journal of Universal Mathematics 3 / 1 (January 2020): 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. 2020; 3(1): 1-10.
Vancouver Kılınç S. , Akkurt A. , Yildirim H. ON INTEGRAL INEQUALITIES FOR INVEX FUNCTIONS SATISFYING LIPSCHITZIAN REQUIREMENT. Journal of Universal Mathematics. 2020; 3(1): 1-10.
IEEE S. Kılınç , A. Akkurt and H. Yildirim , "ON INTEGRAL INEQUALITIES FOR INVEX FUNCTIONS SATISFYING LIPSCHITZIAN REQUIREMENT", Journal of Universal Mathematics, vol. 3, no. 1, pp. 1-10, Jan. 2020, doi:10.33773/jum.679836