scholarly journals On Weighted Simpson’s 38 Rule

Symmetry ◽  
2021 ◽  
Vol 13 (10) ◽  
pp. 1933
Author(s):  
Mohsen Rostamian Delavar ◽  
Artion Kashuri ◽  
Manuel De La De La Sen
Keyword(s):  
Quadrature Formula ◽  
Convex Functions ◽  
Type Inequality ◽  
Random Variables ◽  
Numerical Approximations ◽  
Weighted Version ◽  
Definite Integrals ◽  
Special Means ◽  
Error Estimations ◽  
Moments Of Random Variables

Numerical approximations of definite integrals and related error estimations can be made using Simpson’s rules (inequalities). There are two well-known rules: Simpson’s 13 rule or Simpson’s quadrature formula and Simpson’s 38 rule or Simpson’s second formula. The aim of the present paper is to extend several inequalities that hold for Simpson’s 13 rule to Simpson’s 38 rule. More precisely, we prove a weighted version of Simpson’s second type inequality and some Simpson’s second type inequalities for Lipschitzian, bounded variations, convex functions and the functions that belong to Lq. Some applications of the second type Simpson’s inequalities relate to approximations of special means and Simpson’s 38 formula, and moments of random variables are made.

scholarly journals On Some New Weighted Inequalities for Differentiable Exponentially Convex and Exponentially Quasi-Convex Functions with Applications

Mathematics ◽  
2019 ◽  
Vol 7 (8) ◽  
pp. 727 ◽  
Author(s):  
Dongming Nie ◽  
Saima Rashid ◽  
Ahmet Ocak Akdemir ◽  
Dumitru Baleanu ◽  
Jia-Bao Liu
Keyword(s):  
Numerical Analysis ◽  
Integral Inequality ◽  
Convex Functions ◽  
Random Variables ◽  
Higher Moments ◽  
Weighted Inequalities ◽  
Convex Mapping ◽  
Error Estimations ◽  
Moments Of Random Variables

In this article, we aim to establish several inequalities for differentiable exponentially convex and exponentially quasi-convex mapping, which are connected with the famous Hermite–Hadamard (HH) integral inequality. Moreover, we have provided applications of our findings to error estimations in numerical analysis and higher moments of random variables.

scholarly journals Hermite-Hadamard type inequalities via new exponential type convexity and their applications

Filomat ◽  
2021 ◽  
Vol 35 (6) ◽  
pp. 1803-1822
Author(s):  
Saad Butt ◽  
Artion Kashuri ◽  
Jamshed Nasir
Keyword(s):  
Convex Function ◽  
Error Estimates ◽  
Exponential Type ◽  
Convex Functions ◽  
Type Inequality ◽  
Absolute Value ◽  
First Derivative ◽  
Special Means ◽  
Algebraic Properties

In this paper, authors study the concept of (s,m)-exponential type convex functions and their algebraic properties. New generalizations of Hermite-Hadamard type inequality for the (s,m)-exponential type convex function ? and for the products of two (s,m)-exponential type convex functions ? and ? are proved. Some refinements of the (H-H) inequality for functions whose first derivative in absolute value at certain power are (s,m)-exponential type convex are obtain. Finally, many new bounds for special means and new error estimates for the trapezoidal and midpoint formula are provided as well.

scholarly journals Hermite–Hadamard-type inequalities via n-polynomial exponential-type convexity and their applications

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Saad Ihsan Butt ◽  
Artion Kashuri ◽  
Muhammad Tariq ◽  
Jamshed Nasir ◽  
Adnan Aslam ◽  
...  
Keyword(s):  
Convex Function ◽  
Error Estimates ◽  
Exponential Type ◽  
Convex Functions ◽  
Type Inequality ◽  
Hadamard Inequality ◽  
Absolute Value ◽  
Special Means ◽  
Algebraic Properties

Abstract In this paper, we give and study the concept of n-polynomial $(s,m)$ ( s , m ) -exponential-type convex functions and some of their algebraic properties. We prove new generalization of Hermite–Hadamard-type inequality for the n-polynomial $(s,m)$ ( s , m ) -exponential-type convex function ψ. We also obtain some refinements of the Hermite–Hadamard inequality for functions whose first derivatives in absolute value at certain power are n-polynomial $(s,m)$ ( s , m ) -exponential-type convex. Some applications to special means and new error estimates for the trapezoid formula are given.

scholarly journals Trapezium-Type Inequalities for k -Fractional Integral via New Exponential-Type Convexity and Their Applications

2020 ◽  
Vol 2020 ◽  
pp. 1-12
Author(s):  
Artion Kashuri ◽  
Sajid Iqbal ◽  
Saad Ihsan Butt ◽  
Jamshed Nasir ◽  
Kottakkaran Sooppy Nisar ◽  
...  
Keyword(s):  
Applied Sciences ◽  
Convex Function ◽  
Error Estimates ◽  
Exponential Type ◽  
Convex Functions ◽  
Fractional Integral ◽  
Type Inequality ◽  
Trapezium Type ◽  
Special Means ◽  
Algebraic Properties

In this paper, the authors investigated the concept of s , m -exponential-type convex functions and their algebraic properties. New generalizations of Hermite–Hadamard-type inequality for the s , m -exponential-type convex function ψ and for the products of two s , m -exponential-type convex functions ψ and ϕ are proved. Many refinements of the (H–H) inequality via s , m -exponential-type convex are obtained. Finally, several new bounds for special means and new error estimates for the trapezoidal and midpoint formula are provided as well. The ideas and techniques of this paper may stimulate further research in different areas of pure and applied sciences.

scholarly journals Generalization of Some Inequalities for Differentiable Co-ordinated Convex Functions With Applications

2016 ◽  
Vol 2 (1) ◽  
pp. 12-32 ◽  
Author(s):  
M. A. Latif ◽  
S. S. Dragomir ◽  
E. Momoniat
Keyword(s):  
Quadrature Formula ◽  
Convex Functions ◽  
Random Variables ◽  
Integral Inequalities ◽  
Weighted Integral ◽  
Weighted Quadrature

Abstract In this paper, a new weighted identity for functions defined on a rectangle from the plane is established. By using the obtained identity and analysis, some new weighted integral inequalities for the classes of co-ordinated convex, co-ordinated wright-convex and co-ordinated quasi-convex functions on the rectangle from the plane are established which provide weighted generalization of some recent results proved for co-ordinated convex functions. Some applications of our results to random variables and 2D weighted quadrature formula are given as well.

scholarly journals Some new generalized $ \kappa $–fractional Hermite–Hadamard–Mercer type integral inequalities and their applications

2021 ◽  
Vol 7 (2) ◽  
pp. 3203-3220
Author(s):  
Miguel Vivas-Cortez ◽  
◽  
Muhammad Uzair Awan ◽  
Muhammad Zakria Javed ◽  
Artion Kashuri ◽  
...  
Keyword(s):  
Quadrature Formula ◽  
Integral Inequalities ◽  
Fractional Integrals ◽  
Real Numbers ◽  
Positive Real ◽  
Special Means ◽  
Special Cases ◽  
Type Integral ◽  
Error Estimations ◽  
Integral Identities

<abstract><p>In this paper, we have established some new Hermite–Hadamard–Mercer type of inequalities by using $ {\kappa} $–Riemann–Liouville fractional integrals. Moreover, we have derived two new integral identities as auxiliary results. From the applied identities as auxiliary results, we have obtained some new variants of Hermite–Hadamard–Mercer type via $ {\kappa} $–Riemann–Liouville fractional integrals. Several special cases are deduced in detail and some know results are recaptured as well. In order to illustrate the efficiency of our main results, some applications regarding special means of positive real numbers and error estimations for the trapezoidal quadrature formula are provided as well.</p></abstract>

scholarly journals Some new inequalities of Hermite-Hadamard type for GA-convex functions

2018 ◽  
Vol 72 (1) ◽  
pp. 55 ◽  
Author(s):  
Sever S. Dragomir
Keyword(s):  
Convex Functions ◽  
Weighted Version ◽  
Special Means ◽  
New Inequalities

Some new inequalities of Hermite-Hadamard type for GA-convex functions defined on positive intervals are given. Refinements and weighted version of known inequalities are provided. Some applications for special means are also obtained.

scholarly journals New fractional identities, associated novel fractional inequalities with applications to means and error estimations for quadrature formulas

2022 ◽  
Vol 2022 (1) ◽  
Author(s):  
Muhammad Uzair Awan ◽  
Artion Kashuri ◽  
Kottakkaran Sooppy Nisar ◽  
Muhammad Zakria Javed ◽  
Sabah Iftikhar ◽  
...  
Keyword(s):  
Convex Functions ◽  
Fractional Integral ◽  
Integral Inequalities ◽  
Quadrature Formulas ◽  
Real Numbers ◽  
Positive Real ◽  
Special Means ◽  
Error Estimations ◽  
Harmonic Convex ◽  
Integral Identities

AbstractIn this paper, the authors derive some new generalizations of fractional trapezium-like inequalities using the class of harmonic convex functions. Moreover, three new fractional integral identities are given, and on using them as auxiliary results some interesting integral inequalities are found. Finally, in order to show the efficiency of our main results, some applications to special means for different positive real numbers and error estimations for quadrature formulas are obtained.

scholarly journals Some weighted Simpson type inequalities for differentiable s–convex functions and their applications

2021 ◽  
Vol 1 (1) ◽  
pp. 75-94 ◽  
Author(s):  
Artion Kashuri ◽  
Badreddine Meftah ◽  
Pshtiwan Othman Mohammed
Keyword(s):  
Quadrature Formula ◽  
Convex Functions ◽  
Special Means ◽  
Special Cases

In this study, by using a new identity we establish some new Simpson type inequalities for differentiables–convex functions in the second sense. Various special cases have been studied in details. Also, in order to illustrate the efficient of our main results, some applications to special means and weighted Simpson quadrature formula are given. The obtained results generalize and refine certain known results. At the end, a brief conclusion is given as well.

Hermite-Hadamard and simpson-like type inequalities for differentiable p-quasi-convex functions

Filomat ◽  
2017 ◽  
Vol 31 (19) ◽  
pp. 5945-5953 ◽  
Author(s):  
İmdat İsçan ◽  
Sercan Turhan ◽  
Selahattin Maden
Keyword(s):  
Convex Functions ◽  
Real Numbers ◽  
Absolute Value ◽  
Special Means ◽  
Quasi Convexity

In this paper, we give a new concept which is a generalization of the concepts quasi-convexity and harmonically quasi-convexity and establish a new identity. A consequence of the identity is that we obtain some new general inequalities containing all of the Hermite-Hadamard and Simpson-like type for functions whose derivatives in absolute value at certain power are p-quasi-convex. Some applications to special means of real numbers are also given.

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