Best Researcher Award

Saima Riaz is a Pakistani mathematician, lecturer, and emerging researcher specializing in convex analysis, fractional calculus, mathematical inequalities, and integral inequalities. She is affiliated with the Department of Mathematics at the University of Sargodha and has contributed to the advancement of generalized convexity theory and fractional integral inequalities through analytical and computational approaches. Her research work focuses on modified hyperbolic p-convex functions, Newton-type inequalities, Hermite–Hadamard inequalities, and Riemann–Liouville fractional integrals.[1]

Abstract

Saima Riaz has established an emerging academic profile in the field of mathematical inequalities and fractional calculus through research centered on convex functions and generalized integral inequalities. Her work investigates modified classes of hyperbolic p-convex functions and their applications in deriving generalized forms of Hermite–Hadamard, Simpson, and Newton-type inequalities. Through analytical derivations and computational validation using Mathematica and LaTeX documentation systems, her contributions have expanded the theoretical understanding of fractional integral operators and convex analysis.[2]

Keywords

Fractional Calculus, Convex Analysis, Integral Inequalities, Hyperbolic p-Convex Functions, Newton-Type Inequalities, Hermite–Hadamard Inequalities, Riemann–Liouville Fractional Integrals, Mathematical Analysis, Functional Analysis, Generalized Convexity

Introduction

The study of convexity and fractional integral operators has become an important area in modern mathematical analysis due to its applications in optimization theory, applied mathematics, engineering analysis, and numerical approximation. Researchers in this domain continue to extend classical inequalities by introducing generalized convex structures and fractional integral frameworks. Saima Riaz has contributed to this evolving area by exploring modified p-convex and hyperbolic convex functions and applying these concepts to derive generalized forms of integral inequalities.[3]

Her research combines theoretical derivations with symbolic computational methods and graphical validation techniques. Through collaborative and independent investigations, she has participated in developing generalized inequality models that improve approximation methods and broaden the applications of fractional calculus within mathematical sciences.[4]

Research Profile

Saima Riaz completed her Bachelor of Science in Mathematics at the University of Sargodha with a CGPA of 3.98/4.00 and was awarded a Gold Medal for academic excellence. She subsequently pursued an M.Phil. in Mathematics at the same institution, achieving a perfect CGPA of 4.00/4.00. Her M.Phil. thesis focused on the “Modified Class of Hyperbolic p-convex Function with Application to Integral Inequalities.”[5]

In addition to her academic training, she has served as a Mathematics Lecturer at Superior College Bhalwal, Government Graduate College Bhalwal, and the University of Sargodha. Her teaching profile includes advanced calculus, real analysis, functional analysis, and fractional calculus. She has also supervised undergraduate thesis projects related to Newton-type inequalities and generalized convex functions.[4]

• Specialization in convex analysis and generalized integral inequalities.
• Research focus on fractional calculus and modified convex structures.
• Application of Mathematica for symbolic computation and visualization.
• Preparation of professional mathematical manuscripts using LaTeX.
• Participation in national and international mathematical conferences.

Research Contributions

Saima Riaz has contributed to the theoretical development of mathematical inequalities involving generalized convexity and fractional integral operators. Her work particularly focuses on deriving generalized Newton-type, Simpson-type, and Hermite–Hadamard inequalities for differentiable convex and hyperbolic p-convex functions.[2]

Her research contributions include extending classical inequalities using Katugampola fractional integrals and general (k,p)-Riemann–Liouville fractional integrals. These studies provide refined approximation methods and generalized bounds useful in advanced mathematical analysis and applied fractional calculus.[3]

• Development of modified hyperbolic p-convex function classes.
• Extension of Newton-type inequalities under generalized convexity assumptions.
• Analytical investigation of fractional integral inequalities.
• Computational validation using Mathematica-generated visualizations.
• Research collaboration on advanced convex analysis and fractional operators.

Publications

• Wang, X., Khan, K. A., Riaz, S., Nosheen, A., & Hamed, Y. S. (2025). Modified class of hyperbolic p-convex function with application to integral inequalities. Ain Shams Engineering Journal, 16(8), 2090-4479.
• Latif, M., Riaz, S., Khan, K. A., Nosheen, A., & Kahungu, K. M. (2026). Better Approximation of Integral form of mid-point formula using p-convex function via Katugampola Fractional Integrals. Journal of Function Spaces. Accepted.
• Riaz, S., Khan, K. A., & Nosheen, A. (2026). Numerical and Graphical Comparisons of Newton-Type Inequalities Via General (k,p)-Riemann-Liouville Fractional Integrals. Afrika Mathematika. Under Review.
• Khan, K. A., & Riaz, S. (2026). Newton-Type Inequalities for Differentiable Convex Functions Via Raina Fractional Integrals. Under Review.
• Riaz, S., & Khan, K. A. (2026). Novel Simpson-Type Inequalities for Modified Sinh p-Convex Functions on Fractal Domains with Applications. Under Review.
• Riaz, S., & Khan, K. A. (2026). Novel Simpson-Type Inequalities on Fractal Domains via Modified (s,p)-Convexity with Applications. Under Review.

Research Impact

The research contributions of Saima Riaz demonstrate a developing impact in the field of mathematical inequalities and fractional calculus. Her published and ongoing studies contribute to the broader mathematical understanding of generalized convex structures and their applications in approximation theory and advanced analysis.[5]

Her academic engagement extends beyond publications to include conference participation, undergraduate mentorship, and collaborative mathematical research activities. The combination of theoretical rigor and computational verification has strengthened the reliability and applicability of her research findings.[2]

Award Suitability

Saima Riaz is considered a suitable candidate for recognition within the category of emerging research excellence in mathematics due to her sustained contributions to convex analysis and fractional integral inequalities. Her academic achievements, including a Gold Medal in Mathematics and multiple peer-reviewed publications, demonstrate scholarly consistency and research potential.[1]

Her research combines originality, analytical depth, and computational validation while addressing modern developments in generalized inequalities and fractional operators. Furthermore, her active participation in international conferences and commitment to mathematical education reflect both academic and professional engagement within the broader mathematical community.[4]

Conclusion

Saima Riaz represents an emerging generation of mathematical researchers contributing to the advancement of convex analysis and fractional calculus through rigorous theoretical investigation and computational methodologies. Her growing publication record, teaching contributions, and active participation in mathematical research forums collectively demonstrate her dedication to scholarly development and academic excellence.[5]

External Links

• Scopus Profile
  
• ORCID Profile

References

1. University of Sargodha. (2026). Academic and research profile of Saima Riaz.
   https://su.edu.pk/
   
2. Wang, X., Khan, K. A., Riaz, S., Nosheen, A., & Hamed, Y. S. (2025). Modified class of hyperbolic p-convex function with application to integral inequalities. Ain Shams Engineering Journal. https://www.sciencedirect.com/science/article/pii/S2090447925001868
3. Elsevier. (2025). Research developments in fractional calculus and convex inequalities.
   https://www.elsevier.com/
   
4. Journal of Function Spaces. (2026). Accepted articles in generalized convex analysis and fractional operators.
   https://www.hindawi.com/journals/jfs/
   
5. University of Sargodha. (2025). M.Phil. thesis archive in mathematics and applied analysis.
   https://su.edu.pk/