Fractional Weighted Ostrowski-Type Inequalities and Their Applications

An important area in the field of applied and pure mathematics is the integral inequality. As it is known, inequalities aim to develop different mathematical methods. Nowadays, we need to seek accurate inequalities for proving the existence and uniqueness of the mathematical methods. The concept of convexity plays a strong role in the field of inequalities due to the behavior of its definition and its properties. Furthermore, there is a strong correlation between convexity and symmetry concepts. Whichever one we work on, we can apply it to the other one due the strong correlation produced between them, especially in the last few years. In this study, by using a new identity, we establish some new fractional weighted Ostrowski-type inequalities for differentiable quasi-convex functions. Further, further results for functions with a bounded first derivative are given. Finally, in order to illustrate the efficiency of our main results, some applications to special means are obtain. The obtained results generalize and refine certain known results.

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

Acta et Commentationes Universitatis Tartuensis de Mathematica ◽

10.12697/acutm.2019.23.05 ◽

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.

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

Filomat ◽

10.2298/fil1806193l ◽

2018 ◽

Vol 32 (6) ◽

pp. 2193-2206 ◽

Cited By ~ 2

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.

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Hermite-Hadamard type inequalities via new exponential type convexity and their applications

Filomat ◽

10.2298/fil2106803b ◽

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.

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

Journal of Function Spaces and Applications ◽

10.1155/2012/980438 ◽

2012 ◽

Vol 2012 ◽

pp. 1-14 ◽

Cited By ~ 21

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.

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

Mathematica ◽

10.24193/mathcluj.2021.2.12 ◽

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.

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Hermite-Hadamard inequalities for generalized convex functions in interval-valued calculus

AIMS Mathematics ◽

10.3934/math.2022236 ◽

2021 ◽

Vol 7 (3) ◽

pp. 4266-4292

Author(s):

Jorge E. Macías-Díaz ◽

◽

Muhammad Bilal Khan ◽

Muhammad Aslam Noor ◽

Abd Allah A. Mousa ◽

...

Keyword(s):

Integral Inequality ◽

Convex Functions ◽

The Other ◽

Integral Inequalities ◽

Generalized Convex Functions ◽

Type Integral ◽

The Subject ◽

Harmonically Convex Functions ◽

Interval Valued

<abstract> <p>The importance of convex and non-convex functions in the study of optimization is widely established. The concept of convexity also plays a key part in the subject of inequalities due to the behavior of its definition. The principles of convexity and symmetry are inextricably linked. Because of the considerable association that has emerged between the two in recent years, we may apply what we learn from one to the other. In this study, first, Hermite-Hadamard type inequalities for LR-$ p $-convex interval-valued functions (LR-$ p $-convex-<italic>I</italic>-<italic>V</italic>-<italic>F</italic>) are constructed in this study. Second, for the product of p-convex various Hermite-Hadamard (<italic>HH</italic>) type integral inequalities are established. Similarly, we also obtain Hermite-Hadamard-Fejér (<italic>HH</italic>-Fejér) type integral inequality for LR-$ p $-convex-<italic>I</italic>-<italic>V</italic>-<italic>F</italic>. Finally, for LR-$ p $-convex-<italic>I</italic>-<italic>V</italic>-<italic>F</italic>, various discrete Schur's and Jensen's type inequalities are presented. Moreover, the results presented in this study are verified by useful nontrivial examples. Some of the results reported here for be LR-$ p $-convex-<italic>I</italic>-<italic>V</italic>-<italic>F</italic> are generalizations of prior results for convex and harmonically convex functions, as well as $ p $-convex functions.</p> </abstract>

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Hermite-Hadamard and simpson-like type inequalities for differentiable p-quasi-convex functions

Filomat ◽

10.2298/fil1719945i ◽

2017 ◽

Vol 31 (19) ◽

pp. 5945-5953 ◽

Cited By ~ 7

Author(s):

İmdat İsçan ◽

Sercan Turhan ◽

Selahattin Maden

Keyword(s):

Convex Functions ◽

Real Numbers ◽

Absolute Value ◽

Special Means ◽

Quasi Convexity

In this paper, we give a new concept which is a generalization of the concepts quasi-convexity and harmonically quasi-convexity and establish a new identity. A consequence of the identity is that we obtain some new general inequalities containing all of the Hermite-Hadamard and Simpson-like type for functions whose derivatives in absolute value at certain power are p-quasi-convex. Some applications to special means of real numbers are also given.

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

Advances in Difference Equations ◽

10.1186/s13662-021-03382-0 ◽

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.

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A Fractional SAIDR Model in the Frame of Atangana–Baleanu Derivative

Fractal and Fractional ◽

10.3390/fractalfract5020032 ◽

2021 ◽

Vol 5 (2) ◽

pp. 32

Author(s):

Esmehan Uçar ◽

Sümeyra Uçar ◽

Fırat Evirgen ◽

Necati Özdemir

Keyword(s):

Existence And Uniqueness ◽

Laplace Transformation ◽

Cell Phones ◽

Mobile Network ◽

The Other ◽

Banach Fixed Point Theorem ◽

Propagation Models ◽

Computer Worms ◽

Computer Viruses ◽

The Stability

It is possible to produce mobile phone worms, which are computer viruses with the ability to command the running of cell phones by taking advantage of their flaws, to be transmitted from one device to the other with increasing numbers. In our day, one of the services to gain currency for circulating these malignant worms is SMS. The distinctions of computers from mobile devices render the existing propagation models of computer worms unable to start operating instantaneously in the mobile network, and this is particularly valid for the SMS framework. The susceptible–affected–infectious–suspended–recovered model with a classical derivative (abbreviated as SAIDR) was coined by Xiao et al., (2017) in order to correctly estimate the spread of worms by means of SMS. This study is the first to implement an Atangana–Baleanu (AB) derivative in association with the fractional SAIDR model, depending upon the SAIDR model. The existence and uniqueness of the drinking model solutions together with the stability analysis are shown through the Banach fixed point theorem. The special solution of the model is investigated using the Laplace transformation and then we present a set of numeric graphics by varying the fractional-order θ with the intention of showing the effectiveness of the fractional derivative.

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Research on SUE DTA Model with Constant Demand Based on Probit Model

Advanced Materials Research ◽

10.4028/www.scientific.net/amr.374-377.2605 ◽

2011 ◽

Vol 374-377 ◽

pp. 2605-2609

Author(s):

Lei Shi ◽

Li Gao

Keyword(s):

Logit Model ◽

Existence And Uniqueness ◽

Probit Model ◽

The Other ◽

A Algorithm ◽

Model Based

Logit model is among the most important model in SUE DTA study. A lot of work have been done based on Logit model. As the other very important SUE DTA model, Probit model has not been the focus of many researcher. This paper presents a SUE model based on Probit model, which aims at building up the Probit model with constant demand. The existence and uniqueness of the model is presented, Finally, a algorithm is given.

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