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Year 2016, , 77 - 87, 15.04.2016
https://doi.org/10.36753/mathenot.421413

Abstract

References

  • [1] Dahmani, Z., On Minkowski and Hermite-Hadamard integral inequalities via fractional via fractional integration. Ann. Funct. Anal. 1 (2010), no. 1, 51-58.
  • [2] Dragomir, S.S., Cho, Y.J. and Kim, S.S., Inequalities of Hadamard’s Type for Lipschitzian Mappings and Their Applications. J. Math. Anal. Appl. 245 (2000), 489-501.
  • [3] 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.
  • [4]İşcan, İ., New general integral inequalities for Lipschitzian functions via Hadamard fractional integrals. Int. J. Anal. 2014 (2014), Article ID 353924, 8 pages.
  • [5] Samko, S.G., Kilbas, A.A. and Marichev, O.I., Fractional Integrals and Derivatives Theory and Application. Gordan and Breach Science, New York, 1993.
  • [6] Sarıkaya, M.Z. and Ogunmez, H., On new inequalities via Riemann-Liouville fractional integration. Abstr. Appl. Anal. 2012 (2012), Article ID 428983, 10 pages.
  • [7] Sarıkaya, M.Z., Set, E., Yaldız, H. and Başak, N., Hermite-Hadamard’s inequalities for fractional integrals and related fractional inequalities. Math. Comput. Modelling 57 (2013), 2403-2407.
  • [8] Tseng, K.-L., Hwang, S.-R. and Dragomir, S.S., Fejér-type inequalities (1). J. Inequal. Appl. 2010 (2010), Article ID 531976, 7 pages.
  • [9] Tseng, K.-L., Hwang, S.-R. and Hsu, K.-C., Hadamard-type and Bullen-type inequalities for Lipschitzian functions and their applications. Comput. Math. Appl. 64 (2012), no. 4, 651-660.
  • [10] Yang, G.-S. and Tseng, K.-L., Inequalities of Hadamard’s Type for Lipschitzian Mappings. J. Math. Anal. Appl. 260 (2001), no. 1, 230-238.
  • [11] Zhu, C., Feckan, M. and Wang, J., Fractional integral inequalities for differentiable convex mappings and applications to special means and a midpoint formula. J. Appl. Math. Stat. Inform. 8 (2012), no. 2, 21-28.

Hadamard-type and Bullen-type inequalities for Lipschitzian functions via fractional integrals

Year 2016, , 77 - 87, 15.04.2016
https://doi.org/10.36753/mathenot.421413

Abstract

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

References

  • [1] Dahmani, Z., On Minkowski and Hermite-Hadamard integral inequalities via fractional via fractional integration. Ann. Funct. Anal. 1 (2010), no. 1, 51-58.
  • [2] Dragomir, S.S., Cho, Y.J. and Kim, S.S., Inequalities of Hadamard’s Type for Lipschitzian Mappings and Their Applications. J. Math. Anal. Appl. 245 (2000), 489-501.
  • [3] 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.
  • [4]İşcan, İ., New general integral inequalities for Lipschitzian functions via Hadamard fractional integrals. Int. J. Anal. 2014 (2014), Article ID 353924, 8 pages.
  • [5] Samko, S.G., Kilbas, A.A. and Marichev, O.I., Fractional Integrals and Derivatives Theory and Application. Gordan and Breach Science, New York, 1993.
  • [6] Sarıkaya, M.Z. and Ogunmez, H., On new inequalities via Riemann-Liouville fractional integration. Abstr. Appl. Anal. 2012 (2012), Article ID 428983, 10 pages.
  • [7] Sarıkaya, M.Z., Set, E., Yaldız, H. and Başak, N., Hermite-Hadamard’s inequalities for fractional integrals and related fractional inequalities. Math. Comput. Modelling 57 (2013), 2403-2407.
  • [8] Tseng, K.-L., Hwang, S.-R. and Dragomir, S.S., Fejér-type inequalities (1). J. Inequal. Appl. 2010 (2010), Article ID 531976, 7 pages.
  • [9] Tseng, K.-L., Hwang, S.-R. and Hsu, K.-C., Hadamard-type and Bullen-type inequalities for Lipschitzian functions and their applications. Comput. Math. Appl. 64 (2012), no. 4, 651-660.
  • [10] Yang, G.-S. and Tseng, K.-L., Inequalities of Hadamard’s Type for Lipschitzian Mappings. J. Math. Anal. Appl. 260 (2001), no. 1, 230-238.
  • [11] Zhu, C., Feckan, M. and Wang, J., Fractional integral inequalities for differentiable convex mappings and applications to special means and a midpoint formula. J. Appl. Math. Stat. Inform. 8 (2012), no. 2, 21-28.
There are 11 citations in total.

Details

Primary Language English
Journal Section Articles
Authors

İmdat İşcan

Publication Date April 15, 2016
Submission Date March 4, 2015
Published in Issue Year 2016

Cite

APA İşcan, İ. (2016). Hadamard-type and Bullen-type inequalities for Lipschitzian functions via fractional integrals. Mathematical Sciences and Applications E-Notes, 4(1), 77-87. https://doi.org/10.36753/mathenot.421413
AMA İşcan İ. Hadamard-type and Bullen-type inequalities for Lipschitzian functions via fractional integrals. Math. Sci. Appl. E-Notes. April 2016;4(1):77-87. doi:10.36753/mathenot.421413
Chicago İşcan, İmdat. “Hadamard-Type and Bullen-Type Inequalities for Lipschitzian Functions via Fractional Integrals”. Mathematical Sciences and Applications E-Notes 4, no. 1 (April 2016): 77-87. https://doi.org/10.36753/mathenot.421413.
EndNote İşcan İ (April 1, 2016) Hadamard-type and Bullen-type inequalities for Lipschitzian functions via fractional integrals. Mathematical Sciences and Applications E-Notes 4 1 77–87.
IEEE İ. İşcan, “Hadamard-type and Bullen-type inequalities for Lipschitzian functions via fractional integrals”, Math. Sci. Appl. E-Notes, vol. 4, no. 1, pp. 77–87, 2016, doi: 10.36753/mathenot.421413.
ISNAD İşcan, İmdat. “Hadamard-Type and Bullen-Type Inequalities for Lipschitzian Functions via Fractional Integrals”. Mathematical Sciences and Applications E-Notes 4/1 (April 2016), 77-87. https://doi.org/10.36753/mathenot.421413.
JAMA İşcan İ. Hadamard-type and Bullen-type inequalities for Lipschitzian functions via fractional integrals. Math. Sci. Appl. E-Notes. 2016;4:77–87.
MLA İşcan, İmdat. “Hadamard-Type and Bullen-Type Inequalities for Lipschitzian Functions via Fractional Integrals”. Mathematical Sciences and Applications E-Notes, vol. 4, no. 1, 2016, pp. 77-87, doi:10.36753/mathenot.421413.
Vancouver İşcan İ. Hadamard-type and Bullen-type inequalities for Lipschitzian functions via fractional integrals. Math. Sci. Appl. E-Notes. 2016;4(1):77-8.

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