scholarly journals Some Inclusion Relationships of Certain Subclasses of -Valent Functions Associated with a Family of Integral Operators

2013 ◽  
Vol 2013 ◽  
pp. 1-8
Author(s):  
M. K. Aouf ◽  
R. M. El-Ashwah ◽  
Ahmed M. Abd-Eltawab
Keyword(s):  
Integral Operator ◽  
Convex Functions ◽  
Integral Operators

By making use of the new integral operator , we introduce and investigate several new subclasses of -valent starlike, -valent convex, -valent close-to-convex, and -valent quasi-convex functions. In particular, we establish some inclusion relationships associated with the aforementioned integral operators. Some of the results established in this paper would provide extensions of those given in earlier works.

scholarly journals Some Inequalities of Generalized p-Convex Functions concerning Raina’s Fractional Integral Operators

2021 ◽  
Vol 2021 ◽  
pp. 1-9
Author(s):  
Changyue Chen ◽  
Muhammad Shoaib Sallem ◽  
Muhammad Sajid Zahoor
Keyword(s):  
Integral Operator ◽  
Convex Function ◽  
Convex Functions ◽  
Fractional Integral ◽  
Applied Mathematics ◽  
Optimization Theory ◽  
Integral Operators ◽  
Fractional Integral Operator ◽  
Fractional Integral Operators

Convex functions play an important role in pure and applied mathematics specially in optimization theory. In this paper, we will deal with well-known class of convex functions named as generalized p-convex functions. We develop Hermite–Hadamard-type inequalities for this class of convex function via Raina’s fractional integral operator.

scholarly journals Some new generalizations of Ostrowski type inequalities for s-convex functions via fractional integral operators

Filomat ◽  
2018 ◽  
Vol 32 (16) ◽  
pp. 5595-5609
Author(s):  
Erhan Set
Keyword(s):  
Integral Operator ◽  
Convex Functions ◽  
Fractional Integral ◽  
Present Note ◽  
Integral Operators ◽  
Fractional Integral Operator ◽  
Integral Inequalities ◽  
Fractional Integral Operators ◽  
Special Cases ◽  
Class Of Functions

Remarkably a lot of Ostrowski type inequalities involving various fractional integral operators have been investigated by many authors. Recently, Raina [34] introduced a new generalization of the Riemann-Liouville fractional integral operator involving a class of functions defined formally by F? ?,?(x)=??,k=0 ?(k)/?(?k + ?)xk. Using this fractional integral operator, in the present note, we establish some new fractional integral inequalities of Ostrowski type whose special cases are shown to yield corresponding inequalities associated with Riemann-Liouville fractional integral operators.

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 Bounds of a Unified Integral Operator via Exponentially s,m-Convexity and Their Consequences

2020 ◽  
Vol 2020 ◽  
pp. 1-10
Author(s):  
Yi Hu ◽  
Ghulam Farid ◽  
Zijiang ◽  
Kahkashan Mahreen
Keyword(s):  
Integral Operator ◽  
Convex Functions ◽  
Integral Operators

Various known fractional and conformable integral operators can be obtained from a unified integral operator. The aim of this paper is to find bounds of this unified integral operator via exponentially s,m-convex functions. The resulting bounds provide compact formulas for the bounds of associated fractional and conformable integral operators. Several Hadamard-type inequalities have been produced from a compact version for unified integral operators for exponentially s,m-convex functions.

scholarly journals Inequalities for a Unified Integral Operator via α,m-Convex Functions

2020 ◽  
Vol 2020 ◽  
pp. 1-9
Author(s):  
Baizhu Ni ◽  
Ghulam Farid ◽  
Kahkashan Mahreen
Keyword(s):  
Integral Operator ◽  
Convex Functions ◽  
Integral Operators ◽  
Compact Form

Recently, a unified integral operator has been introduced by Farid, 2020, which produces several kinds of known fractional and conformable integral operators defined in recent decades (Kwun, 2019, Remarks 6 and 7). The aim of this paper is to establish bounds of this unified integral operator by means of α,m-convex functions. The resulting inequalities provide the bounds of all associated fractional and conformable integral operators in a compact form. Also, the results of this paper hold for different kinds of convex functions connected with α,m-convex functions.

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.

scholarly journals On Generalized Strongly Convex Functions and Unified Integral Operators

2021 ◽  
Vol 2021 ◽  
pp. 1-16
Author(s):  
Timing Yu ◽  
Ghulam Farid ◽  
Kahkashan Mahreen ◽  
Chahn Yong Jung ◽  
Soo Hak Shim
Keyword(s):  
Integral Operator ◽  
Convex Function ◽  
Convex Functions ◽  
Fractional Integral ◽  
Integral Operators ◽  
Integral Inequalities ◽  
Operator Inequalities ◽  
Strongly Convex Functions ◽  
Strongly Convex ◽  
Left And Right

In this paper, we define a strongly exponentially α , h − m -convex function that generates several kinds of strongly convex and convex functions. The left and right unified integral operators of these functions satisfy some integral inequalities which are directly related to many unified and fractional integral inequalities. From the results of this paper, one can obtain various fractional integral operator inequalities that already exist in the literature.

scholarly journals Inequalities for a Unified Integral Operator for Strongly α , m -Convex Function and Related Results in Fractional Calculus

2021 ◽  
Vol 2021 ◽  
pp. 1-8
Author(s):  
Chahn Yong Jung ◽  
Ghulam Farid ◽  
Kahkashan Mahreen ◽  
Soo Hak Shim
Keyword(s):  
Integral Operator ◽  
Fractional Calculus ◽  
Convex Function ◽  
Convex Functions ◽  
Fractional Integral ◽  
Integral Operators ◽  
Integral Inequalities ◽  
Special Cases ◽  
Definition Of

In this paper, we study integral inequalities which will provide refinements of bounds of unified integral operators established for convex and α , m -convex functions. A new definition of function, namely, strongly α , m -convex function is applied in different forms and an extended Mittag-Leffler function is utilized to get the required results. Moreover, the obtained results in special cases give refinements of fractional integral inequalities published in this decade.

SOME INCLUSION RELATIONSHIPS ASSOCIATED WITH A CERTAIN CLASS OF INTEGRAL OPERATORS

2010 ◽  
Vol 03 (04) ◽  
pp. 667-684 ◽  
Author(s):  
H. M. Srivastava ◽  
M. K. Aouf ◽  
R. M. El-Ashwah
Keyword(s):  
Analytic Function ◽  
Integral Operator ◽  
Convex Functions ◽  
Integral Operators ◽  
Function Classes

In this paper, we introduce and study some new subclasses of p-valently starlike, p-valently convex, p-valently close-to-convex and p-valently quasi-convex functions which are defined by means of a certain class of integral operators. Several inclusion relationships for these p-valently analytic function classes are established and an integral operator associated with the functions in these subclasses is discussed.

scholarly journals On generalization of Fejér type inequalities via fractional integral operators

Filomat ◽  
2018 ◽  
Vol 32 (16) ◽  
pp. 5537-5547 ◽  
Author(s):  
Erhan Set ◽  
Ahmet Akdemir ◽  
Barış Çelik
Keyword(s):  
Integral Operator ◽  
Convex Functions ◽  
Fractional Integral ◽  
Integral Operators ◽  
Fractional Integral Operator ◽  
Differentiable Mapping ◽  
Fractional Integral Operators

In this paper we first prove a new lemma for differentiable mapping via a fractional integral operator. Then, using lemma, we establish some new Hermite-Hadamard-Fejer type results for convex functions via fractional integral operators. The results presented here would provide extensions of those given in earlier works.

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