Skip to main content
SpringerLink
Log in

Hermite–Hadamard Type Inequalities For Functions Whose Derivatives Are Strongly \(\eta \)-Convex Via Fractional Integrals

  • Conference paper
  • First Online:
Optimization, Variational Analysis and Applications (IFSOVAA 2020)

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 355))

Abstract

In this chapter, we establish some Hermite–Hadamard and Féjer type inequalities for strongly \(\eta \)-convex functions. We derive fractional integral inequalities for strongly \(\eta \)-convex functions. Further, some applications of these results to special means of real numbers are also discussed. Moreover, our results include several new and known results in particular cases.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 149.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 199.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 199.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Awan, M.U., Noor, M.A., Noor, K.I., Safdar, F.: On strongly generalized convex functions. Filomat. 31(18), 5783–5790 (2017)

    Article  MathSciNet  Google Scholar 

  2. Delavar, M.R., Sen, M.D.L.: Some Hermite–Hadamard–Féjer type integral inequalities for differentiable \(\eta \)-convex functions with applications. J. Math. 2017 (2017)

    Google Scholar 

  3. Dragomir, S.S., Pearce, C.E.M.: Selected topics on Hermite-Hadamard inequalities and applications. Victoria University, Australia (2000)

    Google Scholar 

  4. Gordji, M.E., Delavar, M.R., Dragomir, S.S.: Some inequalities related to \(\eta \)-convex functions. RGMIA 18 (2015)

    Google Scholar 

  5. Gordji, M.E., Delavar, M.R., Sen, M.D.L.: On \(\varphi \)-convex functions. J. Math. Inequal. 10(1), 173–183 (2016)

    Article  MathSciNet  Google Scholar 

  6. Işcan, I.: Hermite-Hadamard Féjer type inequalities for convex functions via fractional integrals. Stud. Univ. Babes-Bolyai Math. 60(3), 355–366 (2015)

    MathSciNet  MATH  Google Scholar 

  7. Jiang, W.D., Niu, D.W., Hua, Y., Qi, F.: Generalizations of Hermite-Hadamard inequality to n-time differentiable functions which are s-convex in the second sense. Analysis (Munich) 32(3), 209–220 (2012)

    MathSciNet  MATH  Google Scholar 

  8. Karamardian, S.: The nonlinear complementarity problem with applications. Part 2. J. Optim. Theory Appl. 4(3), 167–181 (1969)

    Google Scholar 

  9. Kwun, Y.C., Saleem, M.S., Ghafoor, M., Nazeer, W., Kang, S.M.: Hermite-Hadamard type inequalities for functions whose derivatives are \(\eta -\)convex via fractional integrals. J. Inequal. Appl. 2019(1), 1–16 (2019)

    Article  MathSciNet  Google Scholar 

  10. Merentes, N., Nikodem, K.: Remarks on strongly convex functions. Aequ. Math. 80, 193–199 (2010)

    Article  MathSciNet  Google Scholar 

  11. Mishra, S.K., Sharma, N.: On strongly generalized convex functions of higher order. Math. Inequal. Appl. 22(1), 111–121 (2019)

    Article  MathSciNet  Google Scholar 

  12. Nikodem, K., Páles, Z.: Characterizations of inner product spaces by strongly convex functions. Banach J. Math. Anal. 5(1), 83–87 (2011)

    Article  MathSciNet  Google Scholar 

  13. Pachpatte, B.G.: On some inequalities for convex functions. RGMIA Res. Rep. Coll. 6(1), 1–9 (2003)

    MathSciNet  Google Scholar 

  14. Park, J.: Inequalities of Hermite-Hadamard-Féjer type for convex functions via fractional integrals. Int. J. Math. Anal. 8(59), 2927–2937 (2014)

    Article  Google Scholar 

  15. Sharma, N., Mishra, S.K., Hamdi, A.: Weighted version of Hermite-Hadamard type inequalities for strongly GA-convex functions. Int. J. Adv. Appl. Sci. 7(3), 113–118 (2020)

    Article  Google Scholar 

  16. Xi, B.Y., Qi, F.: Some integral inequalities of Hermite–Hadamard type for convex functions with applications to means. J. Funct. Spaces Appl. Artical ID 980438 (2012)

    Google Scholar 

  17. Yang, Y., Saleem, M.S., Ghafoor, M., Qureshi, M.I.: Fractional integral inequalities of Hermite–Hadamard type for differentiable generalized h-convex functions. 2020, 13 (2020)

    Google Scholar 

Download references

Acknowledgements

The authors are grateful to the referees for valuable comments and suggestions that helped us improve this chapter.

Author information

Authors and Affiliations

  1. Department of Mathematics, Institute of Science, Banaras Hindu University, Varanasi, 221005, India

    Nidhi Sharma, Jaya Bisht & S. K. Mishra

Authors
  1. Nidhi Sharma
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Jaya Bisht
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. S. K. Mishra
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to S. K. Mishra .

Editor information

Editors and Affiliations

  1. Institute of Science, Banaras Hindu University, Varanasi, Uttar Pradesh, India

    Vivek Laha

  2. Institut de Mathématiques de Toulouse, Paul Sabatier University, Toulouse, France

    Pierre Maréchal

  3. Institute of Science, Banaras Hindu University, Varanasi, Uttar Pradesh, India

    S. K. Mishra

Rights and permissions

Reprints and permissions

Copyright information

© 2021 The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd.

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Sharma, N., Bisht, J., Mishra, S.K. (2021). Hermite–Hadamard Type Inequalities For Functions Whose Derivatives Are Strongly \(\eta \)-Convex Via Fractional Integrals. In: Laha, V., Maréchal, P., Mishra, S.K. (eds) Optimization, Variational Analysis and Applications. IFSOVAA 2020. Springer Proceedings in Mathematics & Statistics, vol 355. Springer, Singapore. https://doi.org/10.1007/978-981-16-1819-2_5

Download citation

Publish with us

Policies and ethics

Search

Navigation