scholarly journals On modified convex interval valued functions and related inclusions via the interval valued generalized fractional integrals in extended interval space

2021 ◽  
Vol 6 (5) ◽  
pp. 4638-4663
Author(s):  
Manar A. Alqudah ◽  
◽  
Artion Kashuri ◽  
Pshtiwan Othman Mohammed ◽  
Muhammad Raees ◽  
...  
Keyword(s):  
Fractional Integrals ◽  
Interval Space ◽  
Interval Valued

scholarly journals New Hermite–Hadamard Inequalities in Fuzzy-Interval Fractional Calculus and Related Inequalities

Symmetry ◽  
2021 ◽  
Vol 13 (4) ◽  
pp. 673
Author(s):  
Muhammad Bilal Khan ◽  
Pshtiwan Othman Mohammed ◽  
Muhammad Aslam Noor ◽  
Y. S. Hamed
Keyword(s):  
Order Relation ◽  
Fractional Integrals ◽  
Order Relations ◽  
Inequality Theory ◽  
Real World Applications ◽  
Mathematical Problems ◽  
Interval Space ◽  
Fuzzy Order ◽  
Interval Valued ◽  
Fuzzy Interval

It is a familiar fact that inequalities have become a very popular method using fractional integrals, and that this method has been the driving force behind many studies in recent years. Many forms of inequality have been studied, resulting in the introduction of new trend in inequality theory. The aim of this paper is to use a fuzzy order relation to introduce various types of inequalities. On the fuzzy interval space, this fuzzy order relation is defined level by level. With the help of this relation, firstly, we derive some discrete Jensen and Schur inequalities for convex fuzzy interval-valued functions (convex fuzzy-IVF), and then, we present Hermite–Hadamard inequalities (-inequalities) for convex fuzzy-IVF via fuzzy interval Riemann–Liouville fractional integrals. These outcomes are a generalization of a number of previously known results, and many new outcomes can be deduced as a result of appropriate parameter and real valued function selections. We hope that our fuzzy order relations results can be used to evaluate a number of mathematical problems related to real-world applications.

scholarly journals Hermite–Hadamard-type inequalities for the interval-valued approximately h-convex functions via generalized fractional integrals

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Dafang Zhao ◽  
Muhammad Aamir Ali ◽  
Artion Kashuri ◽  
Hüseyin Budak ◽  
Mehmet Zeki Sarikaya
Keyword(s):  
Convex Functions ◽  
Fractional Integrals ◽  
Special Cases ◽  
Definition Of ◽  
The Given ◽  
Class Of Functions ◽  
Interval Valued ◽  
New Inequalities

Abstract In this paper, we present a new definition of interval-valued convex functions depending on the given function which is called “interval-valued approximately h-convex functions”. We establish some inequalities of Hermite–Hadamard type for a newly defined class of functions by using generalized fractional integrals. Our new inequalities are the extensions of previously obtained results like (D.F. Zhao et al. in J. Inequal. Appl. 2018(1):302, 2018 and H. Budak et al. in Proc. Am. Math. Soc., 2019). We also discussed some special cases from our main results.

scholarly journals New Hermite–Hadamard-type inequalities for "Equation missing" No EquationSource Format="TEX", only image -convex fuzzy-interval-valued functions

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Muhammad Bilal Khan ◽  
Muhammad Aslam Noor ◽  
Khalida Inayat Noor ◽  
Yu-Ming Chu
Keyword(s):  
Order Relation ◽  
Interval Space ◽  
Fuzzy Order ◽  
Interval Valued ◽  
Fuzzy Interval

AbstractIn this paper, we introduce the non-convex interval-valued functions for fuzzy-interval-valued functions, which are called "Equation missing"-convex fuzzy-interval-valued functions, by means of fuzzy order relation. This fuzzy order relation is defined level-wise through Kulisch–Miranker order relation given on the interval space. By using the "Equation missing"-convexity concept, we present fuzzy-interval Hermite–Hadamard inequalities for fuzzy-interval-valued functions. Several exceptional cases are debated, which can be viewed as useful applications. Interesting examples that verify the applicability of the theory developed in this study are presented. The results of this paper can be considered as extensions of previously established results.

scholarly journals Some Fractional Hermite–Hadamard Type Inequalities for Interval-Valued Functions

Mathematics ◽  
2020 ◽  
Vol 8 (4) ◽  
pp. 534
Author(s):  
Fangfang Shi ◽  
Guoju Ye ◽  
Dafang Zhao ◽  
Wei Liu
Keyword(s):  
Convex Functions ◽  
Fractional Integrals ◽  
Liouville Type ◽  
Special Cases ◽  
The Relationship ◽  
Interval Valued

In this paper, firstly we prove the relationship between interval h-convex functions and interval harmonically h-convex functions. Secondly, several new Hermite–Hadamard type inequalities for interval h-convex functions via interval Riemann–Liouville type fractional integrals are established. Finally, we obtain some new fractional Hadamard–Hermite type inequalities for interval harmonically h-convex functions by using the above relationship. Also we discuss the importance of our results and some special cases. Our results extend and improve some previously known results.

scholarly journals Generalized fractional Hermite-Hadamard type inclusions for co-ordinated convex interval-valued functions

2020 ◽  
Author(s):  
Hasan KARA ◽  
Hüseyin BUDAK ◽  
Muhammad Aamir Ali
Keyword(s):  
Fractional Integrals ◽  
Functions Of Two Variables ◽  
Interval Valued

In this paper, we introduce the notion of generalized fractional integrals for the interval-valued functions of two variables. We establish Hermite-Hadamard type inequalities and some related inequalities for co-ordinated convex interval-valued functions by using the newly defined integrals. It is also proved that the results given in this paper are the strong generalization of already published ones.

scholarly journals Some fuzzy-interval integral inequalities for harmonically convex fuzzy-interval-valued functions

2021 ◽  
Vol 7 (1) ◽  
pp. 349-370
Author(s):  
Muhammad Bilal Khan ◽  
◽  
Muhammad Aslam Noor ◽  
Thabet Abdeljawad ◽  
Bahaaeldin Abdalla ◽  
...  
Keyword(s):  
Order Relation ◽  
Integral Inequalities ◽  
Fuzzy Integral ◽  
Inclusion Relation ◽  
Fuzzy Space ◽  
Interval Space ◽  
Fuzzy Order ◽  
Riemann Integrals ◽  
Interval Valued ◽  
Fuzzy Interval

<abstract> <p>It is well-known fact that fuzzy interval-valued functions (F-I-V-Fs) are generalizations of interval-valued functions (I-V-Fs), and inclusion relation and fuzzy order relation on interval space and fuzzy space are two different concepts. Therefore, by using fuzzy order relation (FOR), we derive inequalities of Hermite-Hadamard (<italic>H</italic>·<italic>H</italic>) and Hermite-Hadamard Fejér (<italic>H</italic>·<italic>H</italic> Fejér) like for harmonically convex fuzzy interval-valued functions by applying fuzzy Riemann integrals. Moreover, we establish the relation between fuzzy integral inequalities and fuzzy products of harmonically convex fuzzy interval-valued functions. The outcomes of this study are generalizations of many known results which can be viewed as an application of a defined new version of inequalities.</p> </abstract>

scholarly journals Some Hadamard–Fejér Type Inequalities for LR-Convex Interval-Valued Functions

2021 ◽  
Vol 6 (1) ◽  
pp. 6
Author(s):  
Muhammad Bilal Khan ◽  
Savin Treanțǎ ◽  
Mohamed S. Soliman ◽  
Kamsing Nonlaopon ◽  
Hatim Ghazi Zaini
Keyword(s):  
Order Relation ◽  
Inclusion Relation ◽  
Hadamard Inequality ◽  
New Class ◽  
Starting Point ◽  
Interval Valued Function ◽  
Fejér Inequality ◽  
Interval Space ◽  
Interval Valued

The purpose of this study is to introduce the new class of Hermite–Hadamard inequality for LR-convex interval-valued functions known as LR-interval Hermite–Hadamard inequality, by means of pseudo-order relation ( ≤p ). This order relation is defined on interval space. We have proved that if the interval-valued function is LR-convex then the inclusion relation “ ⊆ ” coincident to pseudo-order relation “ ≤p ” under some suitable conditions. Moreover, the interval Hermite–Hadamard–Fejér inequality is also derived for LR-convex interval-valued functions. These inequalities also generalize some new and known results. Useful examples that verify the applicability of the theory developed in this study are presented. The concepts and techniques of this paper may be a starting point for further research in this area.

scholarly journals Some fractional Hermite–Hadamard-type inequalities for interval-valued coordinated functions

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Fangfang Shi ◽  
Guoju Ye ◽  
Dafang Zhao ◽  
Wei Liu
Keyword(s):  
Primary Objective ◽  
Fractional Integrals ◽  
Liouville Type ◽  
Interval Valued

AbstractThe primary objective of this paper is establishing new Hermite–Hadamard-type inequalities for interval-valued coordinated functions via Riemann–Liouville-type fractional integrals. Moreover, we obtain some fractional Hermite–Hadamard-type inequalities for the product of two coordinated h-convex interval-valued functions. Our results generalize several well-known inequalities.

scholarly journals Some Integral Inequalities for Generalized Convex Fuzzy-Interval-Valued Functions via Fuzzy Riemann Integrals

2021 ◽  
Vol 14 (1) ◽  
Author(s):  
Muhammad Bilal Khan ◽  
Muhammad Aslam Noor ◽  
Pshtiwan Othman Mohammed ◽  
Juan L. G. Guirao ◽  
Khalida Inayat Noor
Keyword(s):  
Type Inequality ◽  
Order Relation ◽  
Strong Relationship ◽  
Inclusion Relation ◽  
Special Cases ◽  
Interval Space ◽  
Fuzzy Order ◽  
Riemann Integrals ◽  
Interval Valued ◽  
Fuzzy Interval

AbstractIn this study, we introduce the new concept of $$h$$ h -convex fuzzy-interval-valued functions. Under the new concept, we present new versions of Hermite–Hadamard inequalities (H–H inequalities) are called fuzzy-interval Hermite–Hadamard type inequalities for $$h$$ h -convex fuzzy-interval-valued functions ($$h$$ h -convex FIVF) by means of fuzzy order relation. This fuzzy order relation is defined level wise through Kulisch–Miranker order relation defined on fuzzy-interval space. Fuzzy order relation and inclusion relation are two different concepts. With the help of fuzzy order relation, we also present some H–H type inequalities for the product of $$h$$ h -convex FIVFs. Moreover, we have also established strong relationship between Hermite–Hadamard–Fej´er (H–H–Fej´er) type inequality and $$h$$ h -convex FIVF. There are also some special cases presented that can be considered applications. There are useful examples provided to demonstrate the applicability of the concepts proposed in this study. This paper's thoughts and methodologies could serve as a springboard for more research in this field.

Hermite‐Hadamard‐type inequalities for interval‐valued coordinated convex functions involving generalized fractional integrals

2020 ◽  
Vol 44 (1) ◽  
pp. 104-123 ◽  
Author(s):  
Hasan Kara ◽  
Muhammad Aamir Ali ◽  
Hüseyin Budak
Keyword(s):  
Convex Functions ◽  
Fractional Integrals ◽  
Interval Valued
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