scholarly journals New integral inequalities using exponential type convex functions with applications

2021 ◽  
Vol 6 (7) ◽  
pp. 7684-7703
Author(s):  
Jian Wang ◽  
◽  
Saad Ihsan But ◽  
Artion Kashuri ◽  
Muhammad Tariq ◽  
...  
Keyword(s):  
Exponential Type ◽  
Convex Functions ◽  
Integral Inequalities

scholarly journals Novel Analysis of Hermite–Hadamard Type Integral Inequalities via Generalized Exponential Type m-Convex Functions

Mathematics ◽  
2021 ◽  
Vol 10 (1) ◽  
pp. 31
Author(s):  
Muhammad Tariq ◽  
Hijaz Ahmad ◽  
Clemente Cesarano ◽  
Hanaa Abu-Zinadah ◽  
Ahmed E. Abouelregal ◽  
...  
Keyword(s):  
Exponential Type ◽  
Convex Functions ◽  
Integral Inequalities ◽  
The Novel ◽  
New Family ◽  
Algebraic Properties ◽  
Type Integral ◽  
Mathematical Sciences ◽  
Integral Identities ◽  
Intense Research

The theory of convexity has a rich and paramount history and has been the interest of intense research for longer than a century in mathematics. It has not just fascinating and profound outcomes in different branches of engineering and mathematical sciences, it also has plenty of uses because of its geometrical interpretation and definition. It also provides numerical quadrature rules and tools for researchers to tackle and solve a wide class of related and unrelated problems. The main focus of this paper is to introduce and explore the concept of a new family of convex functions namely generalized exponential type m-convex functions. Further, to upgrade its numerical significance, we present some of its algebraic properties. Using the newly introduced definition, we investigate the novel version of Hermite–Hadamard type integral inequality. Furthermore, we establish some integral identities, and employing these identities, we present several new Hermite–Hadamard H–H type integral inequalities for generalized exponential type m-convex functions. These new results yield some generalizations of the prior results in the literature.

scholarly journals Some Integral Inequalities Involving Exponential Type Convex Functions and Applications

2021 ◽  
Vol 2 (3) ◽  
pp. 62-76
Author(s):  
Muhammad Tariq Muhammad Tariq ◽  
Hijaz Ahmad ◽  
Soubhagya Kumar Sahoo ◽  
Jamshed Nasir
Keyword(s):  
Convex Function ◽  
Exponential Type ◽  
Convex Functions ◽  
Integral Inequalities ◽  
The Novel ◽  
New Family ◽  
Type Integral

In this present case, we focus and explore the idea of a new family of convex function namely exponentialtype m–convex functions. To support this newly introduced idea, we elaborate some of its nice algebraicproperties. Employing this, we investigate the novel version of Hermite–Hadamard type integral inequality.Furthermore, to enhance the paper, we present several new refinements of Hermite–Hadamard (H−H) inequality.Further, in the manner of this newly introduced idea, we investigate some applications of specialmeans. These new results yield us some generalizations of the prior results in the literature. We believe, themethodology investigated in this paper will further inspire intrigued researchers.

scholarly journals Hermite–Hadamard Type Inequalities via Generalized Harmonic Exponential Convexity and Applications

2021 ◽  
Vol 2021 ◽  
pp. 1-12
Author(s):  
Saad Ihsan Butt ◽  
Muhammad Tariq ◽  
Adnan Aslam ◽  
Hijaz Ahmad ◽  
Taher A. Nofal
Keyword(s):  
Exponential Type ◽  
Convex Functions ◽  
Integral Inequalities ◽  
Exponential Convexity ◽  
Algebraic Properties

In this work, we introduce the idea and concept of m –polynomial p –harmonic exponential type convex functions. In addition, we elaborate the newly introduced idea by examples and some interesting algebraic properties. As a result, several new integral inequalities are established. Finally, we investigate some applications for means. The amazing techniques and wonderful ideas of this work may excite and motivate for further activities and research in the different areas of science.

Some new generalizations for GA-convex functions

Filomat ◽  
2017 ◽  
Vol 31 (4) ◽  
pp. 1009-1016 ◽  
Author(s):  
Ahmet Akdemir ◽  
Özdemir Emin ◽  
Ardıç Avcı ◽  
Abdullatif Yalçın
Keyword(s):  
Convex Functions ◽  
Integral Identity ◽  
Integral Inequalities ◽  
General Integral ◽  
Second Derivatives ◽  
Derivatives Of

In this paper, firstly we prove an integral identity that one can derive several new equalities for special selections of n from this identity: Secondly, we established more general integral inequalities for functions whose second derivatives of absolute values are GA-convex functions based on this equality.

scholarly journals A new generalization of some quantum integral inequalities for quantum differentiable convex functions

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Yi-Xia Li ◽  
Muhammad Aamir Ali ◽  
Hüseyin Budak ◽  
Mujahid Abbas ◽  
Yu-Ming Chu
Keyword(s):  
Integral Inequality ◽  
Convex Functions ◽  
Integral Identity ◽  
Integral Inequalities ◽  
Quantum Integral ◽  
Special Cases

AbstractIn this paper, we offer a new quantum integral identity, the result is then used to obtain some new estimates of Hermite–Hadamard inequalities for quantum integrals. The results presented in this paper are generalizations of the comparable results in the literature on Hermite–Hadamard inequalities. Several inequalities, such as the midpoint-like integral inequality, the Simpson-like integral inequality, the averaged midpoint–trapezoid-like integral inequality, and the trapezoid-like integral inequality, are obtained as special cases of our main results.

scholarly journals Some Hermite–Hadamard type integral inequalities for convex functions defined on convex bodies in ℝn\mathbb{R}^{n}

2020 ◽  
Vol 26 (1) ◽  
pp. 67-77 ◽  
Author(s):  
Silvestru Sever Dragomir
Keyword(s):  
Euclidean Space ◽  
Convex Functions ◽  
Convex Bodies ◽  
Integral Inequalities ◽  
Divergence Theorem ◽  
Several Variables ◽  
Type Integral ◽  
Bounded Convex

AbstractIn this paper, by the use of the divergence theorem, we establish some integral inequalities of Hermite–Hadamard type for convex functions of several variables defined on closed and bounded convex bodies in the Euclidean space {\mathbb{R}^{n}} for any {n\geq 2}.

scholarly journals New Modifications of Integral Inequalities via ℘-Convexity Pertaining to Fractional Calculus and Their Applications

Mathematics ◽  
2021 ◽  
Vol 9 (15) ◽  
pp. 1753
Author(s):  
Saima Rashid ◽  
Aasma Khalid ◽  
Omar Bazighifan ◽  
Georgia Irina Oros
Keyword(s):  
Integral Operator ◽  
Convex Functions ◽  
Hypergeometric Functions ◽  
Fractional Integral ◽  
Type Inequality ◽  
Fractional Integral Operator ◽  
Integral Inequalities ◽  
Convex Mappings ◽  
Special Cases ◽  
Harmonically Convex Functions

Integral inequalities for ℘-convex functions are established by using a generalised fractional integral operator based on Raina’s function. Hermite–Hadamard type inequality is presented for ℘-convex functions via generalised fractional integral operator. A novel parameterized auxiliary identity involving generalised fractional integral is proposed for differentiable mappings. By using auxiliary identity, we derive several Ostrowski type inequalities for functions whose absolute values are ℘-convex mappings. It is presented that the obtained outcomes exhibit classical convex and harmonically convex functions which have been verified using Riemann–Liouville fractional integral. Several generalisations and special cases are carried out to verify the robustness and efficiency of the suggested scheme in matrices and Fox–Wright generalised hypergeometric functions.

scholarly journals New fractional inequalities of Hermite–Hadamard type involving the incomplete gamma functions

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Pshtiwan Othman Mohammed ◽  
Thabet Abdeljawad ◽  
Dumitru Baleanu ◽  
Artion Kashuri ◽  
Faraidun Hamasalh ◽  
...  
Keyword(s):  
Convex Functions ◽  
Special Functions ◽  
Integral Inequalities ◽  
Fractional Operators ◽  
Gamma Functions ◽  
Incomplete Gamma Functions ◽  
Type Integral

AbstractA specific type of convex functions is discussed. By examining this, we investigate new Hermite–Hadamard type integral inequalities for the Riemann–Liouville fractional operators involving the generalized incomplete gamma functions. Finally, we expose some examples of special functions to support the usefulness and effectiveness of our results.

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