scholarly journals Estimates of trapezium-type inequalities for $ h $-convex functions with applications to quadrature formulae

2021 ◽  
Vol 6 (7) ◽  
pp. 7625-7648
Author(s):  
Muhammad Samraiz ◽  
◽  
Fakhra Nawaz ◽  
Bahaaeldin Abdalla ◽  
Thabet Abdeljawad ◽  
...  
Keyword(s):  
Convex Functions ◽  
Trapezium Type ◽  
Quadrature Formulae

scholarly journals Quantum Trapezium-Type Inequalities Using Generalized ϕ-Convex Functions

Axioms ◽  
2020 ◽  
Vol 9 (1) ◽  
pp. 12 ◽  
Author(s):  
Miguel J. Vivas-Cortez ◽  
Artion Kashuri ◽  
Rozana Liko ◽  
Jorge E. Hernández
Keyword(s):  
Hypergeometric Function ◽  
Convex Functions ◽  
Special Functions ◽  
Integral Inequalities ◽  
Quantum Calculation ◽  
Generalized Convex Functions ◽  
Hadamard Inequality ◽  
Trapezium Type ◽  
Quantum Integral

In this work, a study is conducted on the Hermite–Hadamard inequality using a class of generalized convex functions that involves a generalized and parametrized class of special functions within the framework of quantum calculation. Similar results can be obtained from the results found for functions such as the hypergeometric function and the classical Mittag–Leffler function. The method used to obtain the results is classic in the study of quantum integral inequalities.

scholarly journals Trapezium-Type Inequalities for an Extension of Riemann–Liouville Fractional Integrals Using Raina’s Special Function and Generalized Coordinate Convex Functions

Axioms ◽  
2020 ◽  
Vol 9 (4) ◽  
pp. 117
Author(s):  
Miguel Vivas-Cortez ◽  
Artion Kashuri ◽  
Rozana Liko ◽  
Jorge Eliecer Hernández Hernández
Keyword(s):  
Convex Functions ◽  
Special Function ◽  
Fractional Integrals ◽  
Generalized Convex Functions ◽  
Hadamard Inequality ◽  
Trapezium Type ◽  
Several Variables ◽  
Special Cases ◽  
Interesting Identity ◽  
Generalized Coordinate

In this paper, the authors analyse and study some recent publications about integral inequalities related to generalized convex functions of several variables and the use of extended fractional integrals. In particular, they establish a new Hermite–Hadamard inequality for generalized coordinate ϕ-convex functions via an extension of the Riemann–Liouville fractional integral. Furthermore, an interesting identity for functions with two variables is obtained, and with the use of it, some new extensions of trapezium-type inequalities using Raina’s special function via generalized coordinate ϕ-convex functions are developed. Various special cases have been studied. At the end, a brief conclusion is given as well.

scholarly journals Trapezium-Type Inequalities for Raina’s Fractional Integrals Operator Using Generalized Convex Functions

Symmetry ◽  
2020 ◽  
Vol 12 (6) ◽  
pp. 1034 ◽  
Author(s):  
Miguel Vivas-Cortez ◽  
Artion Kashuri ◽  
Jorge E. Hernández Hernández
Keyword(s):  
Convex Functions ◽  
Fractional Integral ◽  
Special Functions ◽  
Fractional Integrals ◽  
Generalized Convex Functions ◽  
Hadamard Inequality ◽  
Trapezium Type ◽  
Special Cases ◽  
The Right ◽  
The Relationship

The authors have reviewed a wide production of scientific articles dealing with the evolution of the concept of convexity and its various applications, and based on this they have detected the relationship that can be established between trapezoidal inequalities, generalized convex functions, and special functions, in particular with the so-called Raina function, which generalizes other better known ones such as the hypergeometric function and the Mittag–Leffler function. The authors approach this situation by studying the Hermite–Hadamard inequality, establishing a useful identity using Raina’s fractional integral operator in the setting of ϕ -convex functions, obtaining some integral inequalities connected with the right-hand side of Hermite–Hadamard-type inequalities for Raina’s fractional integrals. Various special cases have been identified.

scholarly journals New Quantum Estimates of Trapezium-Type Inequalities for Generalized ϕ-Convex Functions

Mathematics ◽  
2019 ◽  
Vol 7 (11) ◽  
pp. 1047 ◽  
Author(s):  
Miguel J. Vivas-Cortez ◽  
Rozana Liko ◽  
Artion Kashuri ◽  
Jorge E. Hernández Hernández
Keyword(s):  
Convex Function ◽  
Convex Functions ◽  
Type Inequality ◽  
Trapezium Type ◽  
New Class ◽  
Differentiable Functions ◽  
Special Cases

In this paper, a quantum trapezium-type inequality using a new class of function, the so-called generalized ϕ -convex function, is presented. A new quantum trapezium-type inequality for the product of two generalized ϕ -convex functions is provided. The authors also prove an identity for twice q - differentiable functions using Raina’s function. Utilizing the identity established, certain quantum estimated inequalities for the above class are developed. Various special cases have been studied. A brief conclusion is also given.

scholarly journals Hermite–Hadamard–Fejér-Type Inequalities and Weighted Three-Point Quadrature Formulae

Mathematics ◽  
2021 ◽  
Vol 9 (15) ◽  
pp. 1720
Author(s):  
Mihaela Ribičić Penava
Keyword(s):  
Quadrature Formula ◽  
Convex Functions ◽  
Integral Formula ◽  
Higher Order ◽  
Quadrature Formulae ◽  
Special Cases

The goal of this paper is to derive Hermite–Hadamard–Fejér-type inequalities for higher-order convex functions and a general three-point integral formula involving harmonic sequences of polynomials and w-harmonic sequences of functions. In special cases, Hermite–Hadamard–Fejér-type estimates are derived for various classical quadrature formulae such as the Gauss–Legendre three-point quadrature formula and the Gauss–Chebyshev three-point quadrature formula of the first and of the second kind.

scholarly journals New trapezium type inequalities of coordinated distance-disturbed convex type functions of higher orders via extended Katugampola fractional integrals

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Artion Kashuri ◽  
Sajid Iqbal ◽  
Rozana Liko ◽  
Muhammad Samraiz ◽  
Thabet Abdeljawad
Keyword(s):  
Convex Functions ◽  
Fractional Integrals ◽  
Trapezium Type ◽  
Special Cases ◽  
Sigma 1

AbstractIn this paper we establish some new results on trapezium type inequalities of coordinated distance-disturbed $(\ell _{1},h_{1})$ ( ℓ 1 , h 1 ) –$(\ell _{2},h_{2})$ ( ℓ 2 , h 2 ) -convex functions of higher orders $(\sigma _{1},\sigma _{2})$ ( σ 1 , σ 2 ) by using the Katugampola $(k_{1},k_{2})$ ( k 1 , k 2 ) -fractional integrals. As special cases of our general results, we recapture some earlier proved results.

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.

Fejér type inequalities for higher order convex functions and quadrature formulae

2021 ◽  
Author(s):  
J. Barić ◽  
Lj. Kvesić ◽  
J. Pečarić ◽  
M. Ribičić Penava
Keyword(s):  
Convex Functions ◽  
Higher Order ◽  
Quadrature Formulae
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