Browsing by Author "Dr.Saad Ihsan Butt"

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General Results for Fractional Integral Inequalities Via New Class of Convex Function.
(Library Information Services COMSATS University Islamabad Lahore Campus, 2021) Shahid Shaokat; FA19-RMT-047; LHR TP 7378; Dr.Saad Ihsan Butt
In this work, we will present some new results allied with fractional integrals for twice-differentiable functions using new class of convex function and we will give some new applications along with some new definitions. For the development of these new integrals inequalities, we will use Holder integral inequality, Power Mean integral inequality, Holder- Iscan integral inequality and improved Power Mean integral inequality by using Riemann-Liouville fractional integral operator for new class of convex function. We will give some new inequalities for midpoint and trapezoid formula for new class of convex function. Hence, these new results will lead us to the generalization of prior results.
Generalized Convexity and Related Integral Inequalities on Fractal Sets
(Library Information Services, COMSATS University Islamabad, Lahore Campus, 2021) Arslan Razzaq; CIIT/SP20-RMT-034/LHR; Dr.Saad Ihsan Butt; LHR TP 7637
In this proposal we will present the generalized convexity and related integral inequali- ties on fractal sets Rϖ ( 0 < ϖ ≤ 1). Thus, these developments allow us to develop new bounds for integral inequalities. We will give generalized Hermite-Hadmard (H-H) type inequalities in fractal sense. In this research work we will present some new results by em- ploying local fractional calculus for twice differentiable functions and we will give some new applications along with some new deﬁnitions. For the development of these new in- tegral inequalities, we will use generalized H¨older-integral inequalities and Power mean integral inequalities by using local fractional calculus. We will give some new inequalities for midpoint and trapezoid formula for new class of local fractal calculus. Hence, these new results will lead us to generalization of prior results.
Strong Estimations of Information Inequalities
(Library Information Services COMSATS University Lahore Campus, 2024-03-17) Tehreem Fatima; FA22-RMT-013; Dr.Saad Ihsan Butt; LHR TP 9346
We explore a specific subclass of convex functions that exhibit enhanced and superior char acteristics, known as strong convex functions. By focusing on strong convexity, we revisit classical inequalities like Jensen’s and Hermite-Hadamard (HH) type inequalities. This ap proach leads to more robust estimates and refinements of well-known divergence measures such as Kullback-Liebler (KL), χ 2 - and Jeffreys divergence, among others. Moreover, we extend our investigations to improving Riemann-Liouville HH ϒ-divergence inequal ities specifically designed for strongly convex functions. These improvements serve as a foundation to bridge fractional information inequalities with recent significant research outcomes, providing valuable insights and connections within the field of mathematical analysis and information theory. We explore various novel bounds for Csiszar and related divergences and for Zipf-Mandelbrot entropy by means of Jensen-Mercer’s inequality via strongly convex function.