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New Variants of Hermite-Hadamard Type Inequalities via Generalized Fractional Operator for Differentiable Functions

Year 2022, Volume: 7 Issue: 3, 185 - 201, 30.12.2022

Jamshed Nasir Professor Dr. Mustafa Ali Dokuyucu Ahmet Ocak Akdemir

Abstract

The main motivation of this study is to present new Hermite-Hadamard (HH) type inequalities via a certain fractional operators. We establish two new identities and give new estimations of HH- type inequalities for differentiable and convex mapping via Katugampola-fractional operators. Here, we gave new Lemmas having identities for differentiable functions and construct related inequalities. Main findings of this study would provide elegant connections and general variants of well known results established recently. These results can be extended to different kinds of convex functions as well as pre-invex functions.

Keywords

Convex functions Hermite-Hadamard inequalities Katugampola-fractional integrals

References

  • A. Kilbas, H.M. Srivastava and J.J. Trujillo,Theory and applications of fractional differential equations, Elsevier B.V., Amsterdam, Netherlands, (2006). K. S. Miller and B. Ross, An introduction to fractional calculus and fractional differential equations, A Wiley-Interscience Publication, John Wiley and Sons, Inc., New York, (1993). H. Chen, U.N. Katugampola, Hermite-Hadamard and Hermite-Hadamar-Fejer type inequalityies for generalized fractional integrals , J.Math. Anal. Appl. , 26(2013), 742-753.

Year 2022, Volume: 7 Issue: 3, 185 - 201, 30.12.2022

Jamshed Nasir Professor Dr. Mustafa Ali Dokuyucu Ahmet Ocak Akdemir

Abstract

Keywords

Convex functions Hermite-Hadamard inequalities Katugampola-fractional integrals

References

  • A. Kilbas, H.M. Srivastava and J.J. Trujillo,Theory and applications of fractional differential equations, Elsevier B.V., Amsterdam, Netherlands, (2006). K. S. Miller and B. Ross, An introduction to fractional calculus and fractional differential equations, A Wiley-Interscience Publication, John Wiley and Sons, Inc., New York, (1993). H. Chen, U.N. Katugampola, Hermite-Hadamard and Hermite-Hadamar-Fejer type inequalityies for generalized fractional integrals , J.Math. Anal. Appl. , 26(2013), 742-753.
There are 1 citations in total.

Details

Primary Language English
Journal Section Volume VII Issue III
Authors

Jamshed Nasir 0000-0002-7141-4089

Professor Dr. 0000-0001-7192-8269

Mustafa Ali Dokuyucu 0000-0001-9331-8592

Ahmet Ocak Akdemir 0000-0003-2466-0508

Publication Date December 30, 2022
Published in Issue Year 2022 Volume: 7 Issue: 3

Cite

APA Nasir, J., Dr., P., Dokuyucu, M. A., Akdemir, A. O. (2022). New Variants of Hermite-Hadamard Type Inequalities via Generalized Fractional Operator for Differentiable Functions. Turkish Journal of Science, 7(3), 185-201.
AMA Nasir J, Dr. P, Dokuyucu MA, Akdemir AO. New Variants of Hermite-Hadamard Type Inequalities via Generalized Fractional Operator for Differentiable Functions. TJOS. December 2022;7(3):185-201.
Chicago Nasir, Jamshed, Professor Dr., Mustafa Ali Dokuyucu, and Ahmet Ocak Akdemir. “New Variants of Hermite-Hadamard Type Inequalities via Generalized Fractional Operator for Differentiable Functions”. Turkish Journal of Science 7, no. 3 (December 2022): 185-201.
EndNote Nasir J, Dr. P, Dokuyucu MA, Akdemir AO (December 1, 2022) New Variants of Hermite-Hadamard Type Inequalities via Generalized Fractional Operator for Differentiable Functions. Turkish Journal of Science 7 3 185–201.
IEEE J. Nasir, P. Dr., M. A. Dokuyucu, and A. O. Akdemir, “New Variants of Hermite-Hadamard Type Inequalities via Generalized Fractional Operator for Differentiable Functions”, TJOS, vol. 7, no. 3, pp. 185–201, 2022.
ISNAD Nasir, Jamshed et al. “New Variants of Hermite-Hadamard Type Inequalities via Generalized Fractional Operator for Differentiable Functions”. Turkish Journal of Science 7/3 (December 2022), 185-201.
JAMA Nasir J, Dr. P, Dokuyucu MA, Akdemir AO. New Variants of Hermite-Hadamard Type Inequalities via Generalized Fractional Operator for Differentiable Functions. TJOS. 2022;7:185–201.
MLA Nasir, Jamshed et al. “New Variants of Hermite-Hadamard Type Inequalities via Generalized Fractional Operator for Differentiable Functions”. Turkish Journal of Science, vol. 7, no. 3, 2022, pp. 185-01.
Vancouver Nasir J, Dr. P, Dokuyucu MA, Akdemir AO. New Variants of Hermite-Hadamard Type Inequalities via Generalized Fractional Operator for Differentiable Functions. TJOS. 2022;7(3):185-201.
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