Browsing by Author "Dr. Sadia Khalid"

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    Convexity, Its Variations, and Related Integral Inequalities
    (Library Information Services, COMSATS University Islamabad, Lahore Campus, 2025) Saima Akhtar; CIIT/Sp24-rmt-022/LHR; Dr. Sadia Khalid; LHR TP 10082
    This study explores the concept of convexity, its various generalized forms, and their relationships with integral inequalities in mathematical analysis. The research focuses on investigating different classes of convex functions and extending classical convexity concepts through advanced analytical approaches. Several integral inequalities associated with these variations are derived and analyzed under different conditions. The obtained results contribute to the theoretical development of convex analysis and provide broader applications in optimization theory, numerical analysis, economics, and applied mathematics. The study highlights the importance of generalized convexity in establishing new mathematical inequalities and solving complex analytical problems.
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    Fink’s Identity and Related Inequalities
    (Library Information Services COMSATS University Lahore.Campus, 2023-03-12) SP22-RMT-010; Muhammad Waheed Anwar; Dr. Sadia Khalid; LHR TP 8717
    In this thesis, we present some refinements of the majorization theorems by using Fink's identity. Further, we use Green's function of order two together with Fink's identity and present a refinement of the majorization-type inequality. In addition, we give some results related to the Lidstone polynomial for 2n and (2n+2)-convex functions. Finally, we present some identities and inequalities related to the Lidstone polynomial and the Green functions.
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    Hermite-Hadamard and Bullen’s Type Inequalities and Related Results
    (2024-03-18) Faisal Abbas; SP23-RMT-008/; Dr. Sadia Khalid; LHR TP 9571
    New findings pertaining to Bullen’s type and Bullen-Mercer’s type inequalities are exam ined in this thesis. It refines a number of previous findings and offers generalizations of the Bullen-Mercer’s type inequalities. Applications of these inequalities are also included in the study, along with graphical representations that show the results. Our goal in doing this study is to advance our knowledge and comprehension of these inequalities in mathematical analysis.
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    Hermite–Hadamard Type Integral Inequalities via Different Convexities And Applications
    (Library Information Services COMSATS University Lahore Campus, 2024-03-17) Muhammad Jahanzaib; Fa22-rmt-031; Dr. Sadia Khalid; LHR TP 9374
    Hermite–Hadamard TypeIntegral Inequalities via Different Convexities AndApplications
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    Hermite-Hadamard, Midpoint, Trapezoidal, and Simpson Type Inequalities and Related Results
    (Library Information Services, COMSATS University Islamabad, Lahore Campus, 2025) Muhammad Bilal Aslam; FA23-RMT-027; Dr. Sadia Khalid; LHR TP 9773
    This thesis explores integral inequalities of the Hermite-Hadamard, Trapezoidal, Midpoint, and Simpson types inequalities for s-convex, Quasi-convex and P-convex functions. We present the refinements of Trapezoidal type inequalities and derive better upper bounds for the Midpoint and Simpson's type inequalities. Finally, some applications and graphical representations are also presented.
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    Integral Inequalities for Different Types of Convexity with Applications
    (Library Information Services COMSATS University Lahore Campus, 2024-03-17) Ayman Masood; FA22-RMT-005; Dr. Sadia Khalid; LHR TP 9379
    We present new inequalities for various types of convex functions and give few refinements and upper bounds of some integral inequalities that hold for functions whose derivatives of absolute values are geometrically geometrically convex and geometrically arithmetically convex. We also present the applications of our research work.
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    Refinements for Discrete and Continuous Forms of Hölder’s Inequality and Related Results
    (Library Information Services, COMSATS University Islamabad, Lahore Campus, 2021) Haider Bilal; CIIT/SP19-RMT-031/LHR; Dr. Sadia Khalid; LHR TP 7616
    We present refinements for discrete and continuous forms of H¨older inequality. Further, we improve some inequalities associated to the H¨older’s inequality. We prove that the derived inequalities are better than the previous results. Finally, we give some interesting applications.