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Some general integral inequalities for Lipschitzian functions via conformable fractional integral

Yıl 2020, Cilt: 69 Sayı: 1, 952 - 968, 30.06.2020

Sercan Turhan İmdat İşcan Selim Numan

https://doi.org/10.31801/cfsuasmas.473090
Cited By: 1

Öz

In this paper, the author establishes some Hadamard-type and Bullen-type inequalities for Lipschitzian functions via Riemann Liouville fractional integral.

Anahtar Kelimeler

Lipschitzian functions Hadamard inequality Bullen inequality conformable fractional integral

Kaynakça

  • Ostrowski, A. Uber die Absolutabweichung einer dierentienbaren Funktionen von ihren Integralmittelwert. Comment. Math. Helv., 10 (1938), 226-227.
  • Dahmani, Z., On Minkowski and Hermite-Hadamard integral inequalities via fractional via fractional integration. Ann. Funct. Anal., 1 (1) (2010), 51-58.
  • Dragomir, S.S., Agarwal R.P., Cerone, P., On Simpson's inequality and applications, J. of Inequal. Appl., 5 (2000), 533-579.
  • Dragomir, S.S., Cho, Y.J., Kim, S.S., Inequalities of Hadamard's Type for Lipschitzian Mappings and Their Applications, J. Math. Anal. Appl., 245 (2000), 489-501.
  • Dragomir, S.S., Pearce, C.E.M. , Selected Topics on Hermite-Hadamard Inequalities and Applications, RGMIA Monographs, Victoria University, 2000.
  • Dragomir, S.S., Rassias, Th. M., Ostrowski type inequalities and applications in numerical integration, Kluwer Academic Publishers, Dorcdrecht, Boston, London, 2002.
  • Hadamard, J.S., Etude sur les propiètés des fonctions entieres et en particulier d'une fontion considerer per Riemann, J. Math. Pure and Appl., 58 (1893), 171-215.
  • Hwang, S.-R., Hsu, K.-C. and Tseng, K.-L., Hadamard-type inequalities for Lipschitzian functions in one and two variables with applications, J. Math. Anal. Appl., 405 (2013), 546--554.
  • İşcan, İ., New general integral inequalities for Lipschitzian functions via Hadamard fractional integrals. Int. J. Anal., 2014 (2014), Article ID 353924, 8 pages.
  • İşcan,İ. , Hadamard-type and Bullen-type inequalities for Lipschitzian functions via fractional integrals, Mathematical Sciences and Applications E-Notes, 4 (1) (2016), 77-87.
  • Sarıkaya, M.Z.,Aktan N. , On the generalization of some integral inequalities and their applications, Mathematical and Computer Modelling, 54 (2011), 2175-2182.
  • Set, E. , Akdemir, A.O. , Mumcu, I., The Hermite-Hadamard's inequality and its extentions for conformable fractioanal integrals of any order α>0. Available online at: https://www.researchgate.net/publication/303382221.
  • Samko, S.G., Kilbas, A.A., Marichev, O.I., Fractional Integrals and Derivatives Theory and Application, Gordan and Breach Science, New York, 1993.
  • Sarıkaya, M.Z., Ogunmez, H., On new inequalities via Riemann-Liouville fractional integration. Abstr. Appl. Anal. 2012 (2012), Article ID 428983, 10 pages.
  • Sarıkaya, M.Z., Set, E., Yaldız, H., Başak, N., Hermite-Hadamard's inequalities for fractional integrals and related fractional inequalities. Math. Comput. Modelling, 57 (2013), 2403-2407.
  • Tseng, K.-L., Hwang, S.-R., Dragomir, S.S., Fejér-type inequalities (1). J. Inequal. Appl., 2010 (2010), Article ID 531976, 7 pages.
  • Tseng, K.-L., Hwang, S.-R., Hsu, K.-C., Hadamard-type and Bullen-type inequalities for Lipschitzian functions and their applications, Comput. Math. Appl., 64 (4) (2012), 651-660.
  • Yang, G.-S., Tseng, K.-L., Inequalities of Hadamard's Type for Lipschitzian Mappings, J. Math. Anal. Appl., 260 (1) (2001), 230--238.
  • Zhu, C., Fečkan, M., Wang, J., Fractional integral inequalities for differentiable convex mappings and applications to special means and a midpoint formula, J. Appl. Math. Stat. Inform. 8 (2) (2012), 21-28.

Yıl 2020, Cilt: 69 Sayı: 1, 952 - 968, 30.06.2020

Sercan Turhan İmdat İşcan Selim Numan

https://doi.org/10.31801/cfsuasmas.473090
Cited By: 1

Öz

Kaynakça

  • Ostrowski, A. Uber die Absolutabweichung einer dierentienbaren Funktionen von ihren Integralmittelwert. Comment. Math. Helv., 10 (1938), 226-227.
  • Dahmani, Z., On Minkowski and Hermite-Hadamard integral inequalities via fractional via fractional integration. Ann. Funct. Anal., 1 (1) (2010), 51-58.
  • Dragomir, S.S., Agarwal R.P., Cerone, P., On Simpson's inequality and applications, J. of Inequal. Appl., 5 (2000), 533-579.
  • Dragomir, S.S., Cho, Y.J., Kim, S.S., Inequalities of Hadamard's Type for Lipschitzian Mappings and Their Applications, J. Math. Anal. Appl., 245 (2000), 489-501.
  • Dragomir, S.S., Pearce, C.E.M. , Selected Topics on Hermite-Hadamard Inequalities and Applications, RGMIA Monographs, Victoria University, 2000.
  • Dragomir, S.S., Rassias, Th. M., Ostrowski type inequalities and applications in numerical integration, Kluwer Academic Publishers, Dorcdrecht, Boston, London, 2002.
  • Hadamard, J.S., Etude sur les propiètés des fonctions entieres et en particulier d'une fontion considerer per Riemann, J. Math. Pure and Appl., 58 (1893), 171-215.
  • Hwang, S.-R., Hsu, K.-C. and Tseng, K.-L., Hadamard-type inequalities for Lipschitzian functions in one and two variables with applications, J. Math. Anal. Appl., 405 (2013), 546--554.
  • İşcan, İ., New general integral inequalities for Lipschitzian functions via Hadamard fractional integrals. Int. J. Anal., 2014 (2014), Article ID 353924, 8 pages.
  • İşcan,İ. , Hadamard-type and Bullen-type inequalities for Lipschitzian functions via fractional integrals, Mathematical Sciences and Applications E-Notes, 4 (1) (2016), 77-87.
  • Sarıkaya, M.Z.,Aktan N. , On the generalization of some integral inequalities and their applications, Mathematical and Computer Modelling, 54 (2011), 2175-2182.
  • Set, E. , Akdemir, A.O. , Mumcu, I., The Hermite-Hadamard's inequality and its extentions for conformable fractioanal integrals of any order α>0. Available online at: https://www.researchgate.net/publication/303382221.
  • Samko, S.G., Kilbas, A.A., Marichev, O.I., Fractional Integrals and Derivatives Theory and Application, Gordan and Breach Science, New York, 1993.
  • Sarıkaya, M.Z., Ogunmez, H., On new inequalities via Riemann-Liouville fractional integration. Abstr. Appl. Anal. 2012 (2012), Article ID 428983, 10 pages.
  • Sarıkaya, M.Z., Set, E., Yaldız, H., Başak, N., Hermite-Hadamard's inequalities for fractional integrals and related fractional inequalities. Math. Comput. Modelling, 57 (2013), 2403-2407.
  • Tseng, K.-L., Hwang, S.-R., Dragomir, S.S., Fejér-type inequalities (1). J. Inequal. Appl., 2010 (2010), Article ID 531976, 7 pages.
  • Tseng, K.-L., Hwang, S.-R., Hsu, K.-C., Hadamard-type and Bullen-type inequalities for Lipschitzian functions and their applications, Comput. Math. Appl., 64 (4) (2012), 651-660.
  • Yang, G.-S., Tseng, K.-L., Inequalities of Hadamard's Type for Lipschitzian Mappings, J. Math. Anal. Appl., 260 (1) (2001), 230--238.
  • Zhu, C., Fečkan, M., Wang, J., Fractional integral inequalities for differentiable convex mappings and applications to special means and a midpoint formula, J. Appl. Math. Stat. Inform. 8 (2) (2012), 21-28.
Toplam 19 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Matematik
Bölüm Research Article
Yazarlar

Sercan Turhan 0000-0002-4392-2182

İmdat İşcan 0000-0001-6749-0591

Selim Numan Bu kişi benim 0000-0002-5483-6861

Yayımlanma Tarihi 30 Haziran 2020
Gönderilme Tarihi 22 Ekim 2018
Kabul Tarihi 2 Mayıs 2020
Yayımlandığı Sayı Yıl 2020 Cilt: 69 Sayı: 1

Kaynak Göster

APA Turhan, S., İşcan, İ., & Numan, S. (2020). Some general integral inequalities for Lipschitzian functions via conformable fractional integral. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, 69(1), 952-968. https://doi.org/10.31801/cfsuasmas.473090
AMA Turhan S, İşcan İ, Numan S. Some general integral inequalities for Lipschitzian functions via conformable fractional integral. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. Haziran 2020;69(1):952-968. doi:10.31801/cfsuasmas.473090
Chicago Turhan, Sercan, İmdat İşcan, ve Selim Numan. “Some General Integral Inequalities for Lipschitzian Functions via Conformable Fractional Integral”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 69, sy. 1 (Haziran 2020): 952-68. https://doi.org/10.31801/cfsuasmas.473090.
EndNote Turhan S, İşcan İ, Numan S (01 Haziran 2020) Some general integral inequalities for Lipschitzian functions via conformable fractional integral. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 69 1 952–968.
IEEE S. Turhan, İ. İşcan, ve S. Numan, “Some general integral inequalities for Lipschitzian functions via conformable fractional integral”, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., c. 69, sy. 1, ss. 952–968, 2020, doi: 10.31801/cfsuasmas.473090.
ISNAD Turhan, Sercan vd. “Some General Integral Inequalities for Lipschitzian Functions via Conformable Fractional Integral”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 69/1 (Haziran 2020), 952-968. https://doi.org/10.31801/cfsuasmas.473090.
JAMA Turhan S, İşcan İ, Numan S. Some general integral inequalities for Lipschitzian functions via conformable fractional integral. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2020;69:952–968.
MLA Turhan, Sercan vd. “Some General Integral Inequalities for Lipschitzian Functions via Conformable Fractional Integral”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, c. 69, sy. 1, 2020, ss. 952-68, doi:10.31801/cfsuasmas.473090.
Vancouver Turhan S, İşcan İ, Numan S. Some general integral inequalities for Lipschitzian functions via conformable fractional integral. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2020;69(1):952-68.

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