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 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 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 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 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.

Exponential trigonometric convex functions and Hermite-Hadamard type inequalities

2021 ◽  
Vol 71 (1) ◽  
pp. 43-56
Author(s):  
Mahir Kadakal ◽  
İmdat İşcan ◽  
Praveen Agarwal ◽  
Mohamed Jleli
Keyword(s):  
Convex Function ◽  
Convex Functions ◽  
Integral Inequalities ◽  
Power Mean ◽  
Hadamard Inequality ◽  
Absolute Value ◽  
First Derivative ◽  
Algebraic Properties ◽  
Class Of Functions

Abstract In this manuscript, we introduce and study the concept of exponential trigonometric convex functions and their some algebraic properties. We obtain Hermite-Hadamard type inequalities for the newly introduced class of functions. We also obtain some refinements of the Hermite-Hadamard inequality for functions whose first derivative in absolute value, raised to a certain power which is greater than one, respectively at least one, is exponential trigonometric convex function. It has been shown that the result obtained with Hölder-İşcan and improved power-mean integral inequalities give better approximations than that obtained with Hölder and improved power-mean integral inequalities.

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 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 Some Ostrowski type inequalities via $ n $-polynomial exponentially $ s $-convex functions and their applications

2021 ◽  
Vol 6 (12) ◽  
pp. 13272-13290
Author(s):  
Muhammad Tariq ◽  
◽  
Soubhagya Kumar Sahoo ◽  
Jamshed Nasir ◽  
Hassen Aydi ◽  
...  
Keyword(s):  
Convex Function ◽  
Convex Functions ◽  
Real Numbers ◽  
Convex Mapping ◽  
Positive Real ◽  
Special Means ◽  
Special Cases ◽  
Algebraic Properties

<abstract><p>This paper deals with introducing and investigating a new convex mapping namely, $ n $-polynomial exponentially $ s $-convex. Here, we present some algebraic properties and some logical examples to validate the theory of newly introduced convexity. Some novel adaptations of the well-known Hermite-Hadamard and Ostrowski type inequalities for this convex function have been established. Additionally, some special cases of the newly established results are derived as well. Finally, as applications some new limits for special means of positive real numbers are given. These new outcomes yield a few generalizations of the earlier outcomes already published in the literature.</p></abstract>

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.

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