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 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 Hermite-Hadamard Type Inequalities Associated with Coordinated((s,m),QC)-Convex Functions

2017 ◽  
Vol 2017 ◽  
pp. 1-8
Author(s):  
Yu-Mei Bai ◽  
Shan-He Wu ◽  
Ying Wu
Keyword(s):  
Convex Function ◽  
Convex Functions ◽  
Integral Inequalities ◽  
Type Integral ◽  
Definition Of

In this paper, we introduce the definition of coordinated((s,m),QC)-convex function and establish some Hermite-Hadamard type integral inequalities for coordinated((s,m),QC)-convex functions.

scholarly journals Novel Refinements via n –Polynomial Harmonically s –Type Convex Functions and Application in Special Functions

2021 ◽  
Vol 2021 ◽  
pp. 1-17
Author(s):  
Saad Ihsan Butt ◽  
Saima Rashid ◽  
Muhammad Tariq ◽  
Miao-Kun Wang
Keyword(s):  
Convex Function ◽  
Hypergeometric Function ◽  
Convex Functions ◽  
Special Functions ◽  
Integral Inequalities ◽  
Real Numbers ◽  
Algebraic Properties ◽  
Type Integral ◽  
Harmonically Convex Functions ◽  
Formula Type

In this work, we introduce the idea of n –polynomial harmonically s –type convex function. We elaborate the new introduced idea by examples and some interesting algebraic properties. As a result, new Hermite–Hadamard, some refinements of Hermite–Hadamard and Ostrowski type integral inequalities are established, which are the generalized variants of the previously known results for harmonically convex functions. Finally, we illustrate the applicability of this new investigation in special functions (hypergeometric function and special mean of real numbers).

scholarly journals A note on some Ostrowski type inequalities via Generalized Exponentially Convexity

2021 ◽  
Vol 2 (2) ◽  
pp. 1-15
Author(s):  
Muhammad Tariq ◽  
Jamshed Nasir Jamshed Nasir ◽  
Soubhagya Kumar Sahoo ◽  
Ayaz Ali Mallah
Keyword(s):  
Convex Function ◽  
Exponential Type ◽  
Convex Functions ◽  
The Novel ◽  
Algebraic Properties

In this paper, we define and investigate generalized exponential type convex functions namely exponentially $s$--convex function. In the support of this newly introduced idea, we attain the algebraic properties of this function, and furthermore, in the frame of simple calculus, we explore and attain the novel kind of Ostrowski type inequalities.

scholarly journals Some Ostrowski Type Integral Inequalities using Hypergeometric Functions

2021 ◽  
Vol 2 (1) ◽  
pp. 24-41
Author(s):  
Muhammad Tariq ◽  
Soubhagya Kumar Sahoo ◽  
Jamshed Nasir ◽  
Sher Khan Awan
Keyword(s):  
Convex Function ◽  
Hypergeometric Functions ◽  
Integral Inequalities ◽  
The Novel ◽  
Absolute Value ◽  
Algebraic Properties ◽  
Type Integral

The main objective of this paper is basically to acquire some new extensions of Ostrowski type inequalities for the function whose first derivatives' absolute value are $s$--type $p$--convex. We initially presented a new auxiliary definition namely $s$--type $p$--convex function. Some beautiful algebraic properties and examples related to the newly introduced definition are discussed. We additionally investigated some beautiful cases that can be derived from the novel refinements of the paper. These new results yield us some generalizations of the prior results. We trust that the techniques introduced in this paper will further motivate intrigued researchers.

scholarly journals Ostrowski-type inequalities for n-polynomial $\mathscr{P}$-convex function for k-fractional Hilfer–Katugampola derivative

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Samaira Naz ◽  
Muhammad Nawaz Naeem ◽  
Yu-Ming Chu
Keyword(s):  
Fractional Calculus ◽  
Convex Function ◽  
Convex Functions ◽  
Special Functions ◽  
Integral Inequalities ◽  
Power Mean ◽  
New Class ◽  
Special Means ◽  
New Directions ◽  
Type Integral

AbstractIn this article, we develop a novel framework to study a new class of convex functions known as n-polynomial $\mathscr{P} $ P -convex functions. The purpose of this article is to establish a new generalization of Ostrowski-type integral inequalities by using a generalized k-fractional Hilfer–Katugampola derivative. We employ this technique by using the Hölder and power-mean integral inequalities. We present analogs of the Ostrowski-type integrals inequalities connected with the n-polynomial $\mathscr{P}$ P -convex function. Some new exceptional cases from the main results are obtained, and some known results are recaptured. In the end, an application to special means is given as well. The article seeks to create an exciting combination of a convex function and special functions in fractional calculus. It is supposed that this investigation will provide new directions in fractional calculus.

scholarly journals Some fractional Hermite–Hadamard-type integral inequalities with s-$(\alpha,m)$-convex functions and their applications

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
R. N. Liu ◽  
Run Xu
Keyword(s):  
Convex Function ◽  
Convex Functions ◽  
Second Order ◽  
Integral Inequalities ◽  
Fractional Integrals ◽  
Special Means ◽  
Type Integral

AbstractUnder the new concept of s-$(\alpha,m)$ ( α , m ) -convex functions, we obtain some new Hermite–Hadamard inequalities with an s-$(\alpha,m)$ ( α , m ) -convex function. We use these inequalities to estimate Riemann–Liouville fractional integrals with second-order differentiable convex functions to enrich the Hermite–Hadamard-type inequalities. We give some applications to special means.

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 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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