M.Phil / MS
Permanent URI for this collectionhttps://repository.cuilahore.edu.pk/handle/123456789/52
This collection archives the complete set of theses produced by students of the COMSATS University Islamabad, Lahore Campus.
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Item Results For Generalized Steffensen' S Inequality(Library Information Services, COMSATS University Islamabad, Lahore Campus, 2019) Adil Naseer; FA17-RMT-003; Dr. Saad Ihsan Butt; LHR TP 5642This thesis present a study of some of the most notable and primal integral inequalities developed for n- convex functions. Thus, allowing us to assemble new developments in this research area under a specified frame. We construct new bounds of Gr¨uss and Ostrwoski type inequality associated to generalized Steffensen’s inequality by using ˇ Cebyˇsev functional. Finally, we construct new linear functionals for 2n-convex func tions and investigate their properties.Item Generalized Hermite--Jensen--Mercer-Type Inequalities in Fractal Sense(Library Information Services, COMSATS University Islamabad, Lahore Campus, 2021) Saba Yousaf; CIIT/FA19-RMT-007/LHR; Dr. Saad Ihsan Butt; LHR TP 7445The most notable inequality pertaining convex functions is Jensen’s inequality which has tremendous applications in several fields. Mercer introduced an important variant of Jensen’s inequality called as Jensen-Mercer’s inequality. Fractal sets are useful tools for describing the accuracy of inequalities in convex functions. We establish a generalized Jensen–Mercer inequality and generalized Hermite-Hadamard–Mercer inequalities for a generalized con- vex function on a real linear fractal set Rς ( 0 < ς ≤ 1). Further, we also demonstrate some generalized Jensen–Mercer type inequalities by employing local fractional calculus. We establish two new lemmas involving local fractional integrals. By using these lemmas, we obtain several results related to generalized Hermite–Hadamard–Mercer type integral in- equalities for local differentiable generalized convex functions on real linear fractal space. Lastly, some applications related to Jensen–Mercer inequality, ς -type special means, and probability density functions are given. The present approach is efficient, reliable, and may motivate further research in this area.Item New Generalized Fractional Variants of Integral Inequalities(Library Information Services, COMSATS University Islamabad, Lahore Campus, 2022) Iram Javed; FA20-RMT-041; LHR TP 7942; Dr. Saad Ihsan ButtThe graphical elegance of fractal theory takes into account the development’s achievability and exceptionalism. Due to its fascinating existence in the mathematical fields of sci- ences, there is a clear association between fractal sets and convexity. In this proposal, we will present generalized convexity and related integral inequalities on a fractal set Rv ( 0 < v 1). In the context of the Beta function, this research presents a new class of gener- alized Hermite-Hadamard type inequalities. This research contributes significant results of novel versions of fractal H¨ older’s and Young’s inequalities. We derive some general con- clusions that capture novel results under investigation. One more remarkable contribution of the study is that two novel auxiliary results along with Trapezoidal and Midpoint type inequalities are provided. Hence, these new results will lead us to generalization of prior results.Item Face Labeling of Graph Embedded on the Surface of Klein Bottle(Library Information Services, COMSATS University Islamabad, Lahore Campus, 2016) Sharafat Ali; SP15-RMT-004; LHR TP 7004; Dr. Saad Ihsan ButtWe deal with the problem of labeling the Klein Grid’s Km n vertices, edges and faces with mn squares by the consecutive positive integers from 1 up to jV(Km n )j + jE(Km n )j + jF(Km n )j in such a way that if we add up all the labels of a 4-sided face that becomes the weight of that face. With common difference d these weight of the faces form an arithmetic progression. We will find out the existence of such type of labelings for several differences of d.Item New Generalized Ostrowski, Simpson and Boole’s Type Inequalities(Library Information Services COMSATS University Islamabad Lahore Campus, 2025) Muhammad Mehtab (FA23-RMT-028); Dr. Saad Ihsan Butt; LHR TP 9774In this proposal firstly, we introduce a parametric identity for generalized differentiable functions using a generalized fractal-fractional integral operators. Based on this identity, we establish several variants of parameterized inequalities for functions whose local fractional derivatives in absolute value satisfy generalized convexity conditions. Furthermore, we demonstrate that our main results reduce to well-known Ostrowski and Simpson type inequalities by selecting suitable parameters. These inequalities contribute to finding tight bounds for various integrals over fractal spaces. By comparing the classical H¨older and Power mean inequalities with their new generalized versions, we show that the improved forms yield sharper and more refined upper bounds. In particular, we illustrate that the generalizations of H¨older and Power mean inequalities provide better results when applied to fractal integrals, with their tighter bounds supported by graphical representations. Finally, a series of applications are discussed, including generalized special means, generalized probability density functions and generalized quadrature formulas, which highlight the practical significance of the proposed results in fractal analysis.Item New Perspectives of Solution of Heat Equation Using Neural Networks and Jensen’s Inequality(Library Information Services COMSATS University Islamabad Lahore Campus, 2025) Rafay Ahmed (FA23-RMT-031); Dr. Saad Ihsan Butt; LHR TP 9777In this study, we used Physics-Informed Neural Networks (PINNs) to solve the 1D, 2D, and 3D heat equation. To enhance training stability and accuracy, we replaced Jensen’s inequality as the loss function with more traditional methods such as Mean Square Error (MSE). We aimed to demonstrate that it is possible for PINNs to efficiently solve the heat equation with minimal data. In order to implement the model, we used a number of libraries, such as TensorFlow and Keras for creating the neural networks and NumPy, SciPy, and Matplotlib for managing the data and displaying the outcomes.Item Fractional Hermite-Hadamard Type Inequalities in Information Theory via Interval Calculus(Library Information Services COMSATS University Islamabad Lahore Campus, 2025) Raheem Khan (FA23-RMT-032); Dr. Saad Ihsan Butt; LHR TP 9778This thesis applies interval-valued analysis to information theory by using interval calculus to obtain fractional versions of information inequalities for convex functions. A novel center radius (cr)-order relation is introduced. The P-superquadratic variants of Hermite- Hadamard, Jensen’s, Jensen-Mercer inequalities along with their fractional extensions are further investigated and represented in interval-valued form. By proposing modifications to HH ¡-divergence inequalities for convex functions, information inequalities are also linked to contemporary studies. These efforts provide interval-valued estimates for a range of divergence metrics including Kullback-Leibler, Hellinger and c2.