Department of Mathematics

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Author: search.filters.author.Dr. Saad Ihsan ButtSubject: search.filters.subject.MATHEMATICS

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    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 5642
    This 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.
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    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 7445
    The 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.
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    Generalizations of Cyclic Refinements of Jensen’s Inequalities
    (Library Information Services COMSATS University Islamabad Lahore Campus, 2020) Nasir Mehmood; FA14-PMATH-005; LHR TP 7451; Dr. Saad Ihsan Butt
    In recent years, the concept of convex functions has been generalized extensively. Applications of convex functions are widely seen in many areas of modern analysis. Convex functions also have significant relation with the theory of inequalities and many useful inequalities are the result of the applications of convex functions. The Jensen's inequality has tremendous implications in many fields of modern analysis. It helps computing useful upper bounds for several entropic measures used in information theory. We consider discrete and continuous cyclic refinements of Jensen's inequality and extend them from convex to higher order convex function by using new Green functions introduced by us and employing different interpolating polynomials and identities. We formulate monotonicity of the linear functionals for nconvex functions at a point. We calculate some new Grüss and Ostrowski type bounds. As an application of our obtained results we give new bounds for Shannon, Relative and Zipf-Mandelbrot entropies.
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    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 Butt
    We 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.
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    Fractional Integral Inequalities via Multiplicative Caputo-Fabrizio Integral operator
    (Library Information Services, COMSATS University Islamabad, Lahore Campus, 2025) Muhammad Qais Ali (FA20-BSM-055) : Raheel Abbas (FA20-BSM-052); Dr. Saad Ihsan Butt; LHR TP 9919
    Fractional integral operator generalize the classical concept of integration to non-integer or ders.In our work, first we establish the Hermite-Hadamard’s inequality via Multiplicative Caputo-Frabrizio operator then using this inequality we establish Mid-point, Trapezoidal equalities. After that we establish our main lemma by using this lemma we establish dif ferent result like, Power mean inequality, Holder inequality and absolute value inequality. BYusing these inequalities we obtain new error estimates.