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Fractal Fract
Volume 10
Issue 5
10.3390/fractalfract10050341
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This is an early access version, the complete PDF, HTML, and XML versions will be available soon.
Article

Computational Analysis of Newton-Type Inequalities for Differentiable Strongly Convex Functions via RL-Integrals

by
Ghulam Abbas
1,
Saima Riaz
1,
Tamador Alihia
2,*,
Khuram Ali Khan
3,
Saba Yasmin
1 and
Ramy M. Hafez
4
1
Department of Mathematics, Government Graduate College Bhalwal, Bhalwal 40410, Pakistan
2
Department of Mathematics, College of Science, Qassim University, Buraydah 51452, Saudi Arabia
3
Department of Mathematics, University of Sargodha, Sargodha 40100, Pakistan
4
Department of Mathematics and Statistics, College of Science, Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh 11432, Saudi Arabia
*
Author to whom correspondence should be addressed.
Fractal Fract. 2026, 10(5), 341; https://doi.org/10.3390/fractalfract10050341
Submission received: 6 April 2026 / Revised: 6 May 2026 / Accepted: 12 May 2026 / Published: 18 May 2026
Versions Notes

Abstract

In this paper, new generalizations of Newton-type inequalities for the class of strongly convex functions by utilizing Riemann–Liouville fractional integrals are established. New estimates are obtained for functions that are strongly convex. The established inequalities are further improved. Examples, along with graphs, are provided to demonstrate the validity of the newly established inequalities and comparisons with existing results. It is expected that the results of this paper will open up new avenues of research and may be generalized to other types of fractional operators and generalized convex functions.
Keywords: convex functions; Riemann–Liouville fractional integrals; Simpson inequality; mathematical operators; strongly convex function convex functions; Riemann–Liouville fractional integrals; Simpson inequality; mathematical operators; strongly convex function

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MDPI and ACS Style

Abbas, G.; Riaz, S.; Alihia, T.; Khan, K.A.; Yasmin, S.; Hafez, R.M. Computational Analysis of Newton-Type Inequalities for Differentiable Strongly Convex Functions via RL-Integrals. Fractal Fract. 2026, 10, 341. https://doi.org/10.3390/fractalfract10050341

AMA Style

Abbas G, Riaz S, Alihia T, Khan KA, Yasmin S, Hafez RM. Computational Analysis of Newton-Type Inequalities for Differentiable Strongly Convex Functions via RL-Integrals. Fractal and Fractional. 2026; 10(5):341. https://doi.org/10.3390/fractalfract10050341

Chicago/Turabian Style

Abbas, Ghulam, Saima Riaz, Tamador Alihia, Khuram Ali Khan, Saba Yasmin, and Ramy M. Hafez. 2026. "Computational Analysis of Newton-Type Inequalities for Differentiable Strongly Convex Functions via RL-Integrals" Fractal and Fractional 10, no. 5: 341. https://doi.org/10.3390/fractalfract10050341

APA Style

Abbas, G., Riaz, S., Alihia, T., Khan, K. A., Yasmin, S., & Hafez, R. M. (2026). Computational Analysis of Newton-Type Inequalities for Differentiable Strongly Convex Functions via RL-Integrals. Fractal and Fractional, 10(5), 341. https://doi.org/10.3390/fractalfract10050341

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