scholarly journals Some new inequalities for convex functions via generalized integral operators and their applications

Mathematica ◽  
2021 ◽  
Vol 63 (86) (2) ◽  
pp. 268-283
Author(s):  
Artion Kashuri ◽  
◽  
Themistocles M. Rassias ◽  
Keyword(s):  
Integral Equation ◽  
Integral Operator ◽  
Error Estimates ◽  
Integral Inequality ◽  
Convex Functions ◽  
Integral Operators ◽  
Absolute Value ◽  
Special Means ◽  
Type Integral ◽  
New Inequalities

The authors discover an identity for a generalized integral operator via differentiable function. By using this integral equation, we derive some new bounds on Hermite–Hadamard type integral inequality for differentiable mappings that are in absolute value at certain powers convex. Our results include several new and known results as particular cases. At the end, some applications of presented results for special means and error estimates for the mixed trapezium and midpoint formula have been analyzed. The ideas and techniques of this paper may stimulate further research in the field of integral inequalities.

scholarly journals On Strongly Convex Functions via Caputo–Fabrizio-Type Fractional Integral and Some Applications

2021 ◽  
Vol 2021 ◽  
pp. 1-10
Author(s):  
Qi Li ◽  
Muhammad Shoaib Saleem ◽  
Peiyu Yan ◽  
Muhammad Sajid Zahoor ◽  
Muhammad Imran
Keyword(s):  
Integral Operator ◽  
Fractional Calculus ◽  
Convex Functions ◽  
Fractional Integral ◽  
Optimization Problems ◽  
Fractional Integral Operator ◽  
Strongly Convex Functions ◽  
Strongly Convex ◽  
Special Means ◽  
New Inequalities

The theory of convex functions plays an important role in the study of optimization problems. The fractional calculus has been found the best to model physical and engineering processes. The aim of this paper is to study some properties of strongly convex functions via the Caputo–Fabrizio fractional integral operator. In this paper, we present Hermite–Hadamard-type inequalities for strongly convex functions via the Caputo–Fabrizio fractional integral operator. Some new inequalities of strongly convex functions involving the Caputo–Fabrizio fractional integral operator are also presented. Moreover, we present some applications of the proposed inequalities to special means.

scholarly journals Fejér type integral inequalities related with geometrically-arithmetically convex functions with applications

2019 ◽  
Vol 23 (1) ◽  
pp. 51-64
Author(s):  
S. S. Dragomir ◽  
M. A. Latif ◽  
E. Momoniat
Keyword(s):  
Differentiable Function ◽  
Integral Inequality ◽  
Convex Functions ◽  
Symmetric Function ◽  
Integral Inequalities ◽  
Real Numbers ◽  
Positive Real ◽  
Left Part ◽  
Special Means ◽  
Type Integral

A new identity involving a geometrically symmetric function and a differentiable function is established. Some new Fejér type integral inequalities, connected with the left part of Hermite–Hadamard type inequalities for geometrically-arithmetically convex functions, are presented by using the Hölder integral inequality and the notion of geometrically-arithmetically convexity. Applications of our results to special means of positive real numbers are given.

scholarly journals Some Fejér type integral inequalities for geometrically-arithmetically-convex functions with applications

Filomat ◽  
2018 ◽  
Vol 32 (6) ◽  
pp. 2193-2206 ◽  
Author(s):  
Muhammad Latif ◽  
Sever Dragomir ◽  
Ebrahim Momoniat
Keyword(s):  
Integral Inequality ◽  
Convex Functions ◽  
Symmetric Functions ◽  
Integral Inequalities ◽  
Real Numbers ◽  
Positive Real ◽  
Special Means ◽  
Type Integral

In this paper, the notion of geometrically symmetric functions is introduced. A new identity involving geometrically symmetric functions is established, and by using the obtained identity, the H?lder integral inequality and the notion of geometrically-arithmetically convexity, some new Fej?r type integral inequalities are presented. Applications of our results to special means of positive real numbers are given as well.

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 Different type parameterized inequalities via generalized integral operators with applications

2021 ◽  
Vol 66 (3) ◽  
pp. 423-440
Author(s):  
Artion Kashuri ◽  
Rozana Liko
Keyword(s):  
Integral Operator ◽  
Integral Operators ◽  
Integral Inequalities ◽  
Fractional Integrals ◽  
Recent Past ◽  
Special Means ◽  
Special Cases ◽  
Type Integral ◽  
Erentiable Function ◽  
Almost All

"The authors have proved an identity for a generalized integral operator via di erentiable function with parameters. By applying the established identity, the generalized trapezium, midpoint and Simpson type integral inequalities have been discovered. It is pointed out that the results of this research provide integral inequalities for almost all fractional integrals discovered in recent past decades. Various special cases have been identi ed. 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 eld of integral inequalities."

scholarly journals Some Integral Inequalities of Hermite-Hadamard Type for Convex Functions with Applications to Means

2012 ◽  
Vol 2012 ◽  
pp. 1-14 ◽  
Author(s):  
Bo-Yan Xi ◽  
Feng Qi
Keyword(s):  
Integral Inequality ◽  
Convex Functions ◽  
Integral Inequalities ◽  
Special Means ◽  
New Inequalities

The authors establish some new inequalities for differentiable convex functions, which are similar to the celebrated Hermite-Hadamard's integral inequality for convex functions, and apply these inequalities to construct inequalities for special means of two positive numbers.

scholarly journals Hermite-Hadamard Type Inequalities for convex functions via generalized fractional integral operators

2016 ◽  
Vol 5 (1) ◽  
pp. 55-62
Author(s):  
Erhan Set ◽  
Abdurrahman Gözpinar
Keyword(s):  
Convex Functions ◽  
Integral Identity ◽  
Fractional Integral ◽  
Integral Operators ◽  
Fractional Integral Operators ◽  
Absolute Value ◽  
Type Integral ◽  
Generalized Fractional Integral ◽  
Fractional Type ◽  
Generalized Fractional Integral Operators

AbstractIn this present work, the authors establish a new integral identity involving generalized fractional integral operators and by using this fractional-type integral identity, obtain some new Hermite-Hadamard type inequalities for functions whose first derivatives in absolute value are convex. Relevant connections of the results presented here with those earlier ones are also pointed out.

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 Some New Inequalities on Generalization of Hermite-Hadamard and Bullen Type Inequalities, Applications to Trapezoidal and Midpoint Formula

2021 ◽  
Vol 45 (4) ◽  
pp. 647-657
Author(s):  
İMDAT İŞCAN ◽  
◽  
TEKİN TOPLU ◽  
FATİH YETGİN ◽  
◽  
...  
Keyword(s):  
Error Estimates ◽  
Real Numbers ◽  
Absolute Value ◽  
General Identity ◽  
Differentiable Functions ◽  
Special Means ◽  
New Inequalities

In this paper, we give a new general identity for differentiable functions. A consequence of the identity is that we obtain some new general inequalities containing all of the Hermite-Hadamard and Bullen type for functions whose derivatives in absolute value at certain power are convex. Some applications to special means of real numbers are also given. Finally, some error estimates for the trapezoidal and midpoint formula are addressed.

scholarly journals Derivation of Bounds of an Integral Operator via Exponentially Convex Functions

2020 ◽  
Vol 2020 ◽  
pp. 1-9
Author(s):  
Hong Ye ◽  
Ghulam Farid ◽  
Babar Khan Bangash ◽  
Lulu Cai
Keyword(s):  
Integral Operator ◽  
Lower Bounds ◽  
Differentiable Function ◽  
Convex Functions ◽  
Integral Operators ◽  
Compact Form ◽  
Upper And Lower Bounds ◽  
Hadamard Inequality ◽  
Absolute Value ◽  
Exponentially Convex Functions

In this paper, bounds of fractional and conformable integral operators are established in a compact form. By using exponentially convex functions, certain bounds of these operators are derived and further used to prove their boundedness and continuity. A modulus inequality is established for a differentiable function whose derivative in absolute value is exponentially convex. Upper and lower bounds of these operators are obtained in the form of a Hadamard inequality. Some particular cases of main results are also studied.

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