Papers by Muhammad Amer Latif
Journal of Inequalities and Applications, Dec 1, 2013
In this paper, we present weighted integral inequalities of Hermite-Hadamard type for differentia... more In this paper, we present weighted integral inequalities of Hermite-Hadamard type for differentiable preinvex and prequasiinvex functions. Our results, on the one hand, give a weighted generalization of recent results for preinvex functions and, on the other hand, extend several results connected with the Hermite-Hadamard type integral inequalities. Applications of the obtained results are provided as well.
Journal of Mathematical Inequalities, 2022
In this paper, new weighted Hermite-Hadamard type inequalities for differentiable strongly convex... more In this paper, new weighted Hermite-Hadamard type inequalities for differentiable strongly convex and strongly quasi-convex mappings are proved. These results strengthen many results proved in earlier works for these classes of functions. Applications of some of our results to statistics are provided.
International Journal of Analysis and Applications, 2019
The purpose of this paper is to establish weighted version of Ostrowski type integral inequalitie... more The purpose of this paper is to establish weighted version of Ostrowski type integral inequalities. The inequalities are obtained by using a newly developed special type of five steps weighted kernel. The introduction of this new Kernel gives some new error bounds for various quadrature rules. Applications for Cumulative Distributive Functions are considered.
Le Matematiche, May 14, 2012
Miskolc Mathematical Notes, 2019
A weighted version of Ostrowski type integral inequalities is established. We use a newly develop... more A weighted version of Ostrowski type integral inequalities is established. We use a newly developed special type of three steps kernel. Our findings give some new error bounds for various quadrature rules. We apply our results to cumulative distributive functions.
Journal of Mathematical Inequalities, 2021
Some new Hermite-Hadamard type inequalities for differentiable harmonically-convex and harmonical... more Some new Hermite-Hadamard type inequalities for differentiable harmonically-convex and harmonically quasi-convex functions have been discussed, generalizing some existing results in literature. For validity of the results some numerically examples are given.
Georgian Mathematical Journal, 2016
In this paper, we establish a new integral identity for-times di erentiable functions defined on ... more In this paper, we establish a new integral identity for-times di erentiable functions defined on an invex subset of ℝ. Hermite-Hadamard type integral inequalities for-times di erentiable preinvex functions are then established by using this identity and Hölder's inequality.
In this paper we point out some inequalities of Hermite-Hadamard type for double integrals of fun... more In this paper we point out some inequalities of Hermite-Hadamard type for double integrals of functions whose partial derivatives in absolute value are preinvex on the coordinates on rectangle from the plane. Our established results generalize some recent results for functions whose partial derivatives in absolute value are convex on the coordinates on the rectangle from the plane.
The Punjab University journal of mathematics, Nov 30, 2022
In this study, we define some mappings connected to the Hermite-Hadamard type inequalities constr... more In this study, we define some mappings connected to the Hermite-Hadamard type inequalities constructed for harmonically convex mappings. We investigate some properties of these mappings and provide some refinement inequalities for the Hermite-Hadamard type inequalities that have already been established for harmonic convex functions.
Miskolc Mathematical Notes, 2022
In this paper, some new weighted Simpson's type integral inequalities are presented for the class... more In this paper, some new weighted Simpson's type integral inequalities are presented for the class of harmonically-preinvex functions by using power-mean integral inequality and Hölder's integral inequality.
Mathematics
In this study, the Hermite–Hadamard–Fejér inequalities for GA-h-convex are proved, and the result... more In this study, the Hermite–Hadamard–Fejér inequalities for GA-h-convex are proved, and the results for particular classes of functions are highlighted. In addition, several generalizations of the Hermite–Hadamard inequalities are presented. Some features of functions H and F that are naturally linked to the Hermite–Hadamard–Fejér-type inequalities for GA-h-convex have also been discussed. Finally, we obtain applications of the results related to the p-logarithmic mean and the mean of order p.
Filomat
In this paper, some new estimates on Fej?r sort inequalities via Riemann Liouville fractional int... more In this paper, some new estimates on Fej?r sort inequalities via Riemann Liouville fractional integral for the products of two harmonically-convex functions are obtained.
Punjab University Journal of Mathematics
In this study, we define some mappings connected to the Hermite-Hadamard type inequalities constr... more In this study, we define some mappings connected to the Hermite-Hadamard type inequalities constructed for harmonically convex mappings. We investigate some properties of these mappings and provide some refinement inequalities for the Hermite-Hadamard type inequalities that have already been established for harmonic convex functions.
Filomat
In this paper, the integral identity for differentiable functions with the wide range of applicat... more In this paper, the integral identity for differentiable functions with the wide range of applications is investigated. As an effect of this result, the paper provides some new Hermite-Hadamard type inequalities for differentiable functions that are in absolute value h-preinvex. Several special cases are also discussed. At the end, some applications for special means are given as well.
AIMS Mathematics
In this paper, using positive symmetric functions, we offer two new important identities of fract... more In this paper, using positive symmetric functions, we offer two new important identities of fractional integral form for convex and harmonically convex functions. We then prove new variants of the Hermite-Hadamard-Fejér type inequalities for convex as well as harmonically convex functions via fractional integrals involving an exponential kernel. Moreover, we also present improved versions of midpoint type Hermite-Hadamard inequality. Graphical representations are given to validate the accuracy of the main results. Finally, applications associated with matrices, q-digamma functions and modifed Bessel functions are also discussed.
Fractal and Fractional
The objective of this manuscript is to establish a link between the concept of inequalities and C... more The objective of this manuscript is to establish a link between the concept of inequalities and Center-Radius order functions, which are intriguing due to their properties and widespread use. We introduce the notion of the CR (Center-Radius)-order interval-valued preinvex function with the help of a total order relation between two intervals. Furthermore, we discuss some properties of this new class of preinvexity and show that the new concept unifies several known concepts in the literature and also gives rise to some new definitions. By applying these new definitions, we have amassed many classical and novel special cases that serve as applications of the key findings of the manuscript. The computations of cr-order intervals depend upon the following concept B=⟨Bc,Br⟩=⟨B¯+B̲2,B¯−B̲2⟩. Then, for the first time, inequalities such as Hermite–Hadamard, Pachpatte, and Fejér type are established for CR-order in association with the concept of interval-valued preinvexity. Some numerical ...
Punjab University Journal of Mathematics
In this study, some midpoint type Hermite-Hadamard fractional integral inequalities and related r... more In this study, some midpoint type Hermite-Hadamard fractional integral inequalities and related results for a class of convex functions with respect to an increasing function incorporating a positive-weighted symmetric function generalizing some classical results are discussed.
The authors have proved an identity with parameter for differentiable function with respect to an... more The authors have proved an identity with parameter for differentiable function with respect to another function via generalized integral operator. By applying the established identity, the generalized trapezium, Ostrowski and Simpson type integral inequalities have been discovered. Various special cases have been identified. Some applications of presented results to special means and new error estimates for the trapezium and midpoint quadrature formula have been analyzed. The ideas and techniques of this paper may stimulate further research in the field of integral inequalities.
A thesis submitted to the Faculty of Science, University of the Witwatersrand, Johannesburg, Sout... more A thesis submitted to the Faculty of Science, University of the Witwatersrand, Johannesburg, South Africa, in fulfilment of the requirements for the degree of Doctor of Philosophy. Johannesburg, 17 October 2016.
The Journal of Analysis, 2021
The authors have tried to prove a fractional integral identity generalizing already some existing... more The authors have tried to prove a fractional integral identity generalizing already some existing identities. Based on, some Ostrowski-type fractional integral inequalities for r-times differentiable functions have been discussed, generalizing some existing results in the literature. As a consequence, some new Ostrowski-type, Hermite–Hadamard type and mid point type inequalities have been derived.
Uploads
Papers by Muhammad Amer Latif