scholarly journals On Hermite–Hadamard-Type Inequalities for Coordinated h-Convex Interval-Valued Functions

Mathematics ◽  
2021 ◽  
Vol 9 (19) ◽  
pp. 2352 ◽  
Author(s):  
Dafang Zhao ◽  
Guohui Zhao ◽  
Guoju Ye ◽  
Wei Liu ◽  
Silvestru Sever Dragomir
Keyword(s):  
Convex Functions ◽  
New Concepts ◽  
The Relationship ◽  
Interval Valued

This paper is devoted to establishing some Hermite–Hadamard-type inequalities for interval-valued functions using the coordinated h-convexity, which is more general than classical convex functions. We also discuss the relationship between coordinated h-convexity and h-convexity. Furthermore, we introduce the concepts of minimum expansion and maximum contraction of interval sequences. Based on these two new concepts, we establish some new Hermite–Hadamard-type inequalities, which generalize some known results in the literature. Additionally, some examples are given to illustrate our 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.

New concepts on the structure of the neuronal networks: The miniaturization and hierarchical organization of the central nervous system*

1984 ◽  
Vol 4 (2) ◽  
pp. 93-98 ◽  
Author(s):  
Luigi F. Agnati ◽  
Kjell Fuxe
Keyword(s):  
Central Nervous System ◽  
Nervous System ◽  
Neuronal Networks ◽  
Hierarchical Organization ◽  
Memory Storage ◽  
Information Handling ◽  
New Concepts ◽  
The Central Nervous System ◽  
Local Circuits ◽  
The Relationship

The hypothesis is introduced that miniaturization of neuronal circuits in the central nervous system and the hierarchical organization of the various levels, where information handling can take place, may be the key to understand the enormous capability of the human brain to store engrams as well as its astonishing capacity to reconstruct and organize engrams and thus to perform highly sophisticated integrations. The concept is also proposed that in order to understand the relationship between the structural and functional plasticity of the central nervous system it is necessary to postulate the existence of memory storage at the network level, at the local circuit level, at the synaptic level, at the membrane level, and finally at the molecular level. Thus, memory organization is similar to the hierarchical organization of the various levels, where information handling takes place in the nervous system. In addition, each higher level plays a role in the reconstruction and organization of the engrams stored at lower levels. Thus, the trace of the functionally stored memory (i.e. its reconstruction and organization at various levels of storage) will depend not only on the chemicophysical changes in the membranes of the local circuits but also on the organization of the local circuits themselves and their associated neuronal networks.

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 On the Hermite–Hadamard inequalities for interval-valued coordinated convex functions

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Dafang Zhao ◽  
Muhammad Aamir Ali ◽  
Ghulam Murtaza ◽  
Zhiyue Zhang
Keyword(s):  
Convex Functions ◽  
Interval Valued

Abstract In this work, we introduce the notion of interval-valued coordinated convexity and demonstrate Hermite–Hadamard type inequalities for interval-valued convex functions on the co-ordinates in a rectangle from the plane. Moreover, we prove Hermite–Hadamard inequalities for the product of interval-valued convex functions on coordinates. Our results generalize several other well-known inequalities given in the existing literature on this subject.

scholarly journals Fractional Hermite–Hadamard type inequalities for interval-valued functions

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Xuelong Liu ◽  
Gouju Ye ◽  
Dafang Zhao ◽  
Wei Liu
Keyword(s):  
Convex Functions ◽  
Harmonically Convex Functions ◽  
Interval Valued

Abstract We introduce the concept of interval harmonically convex functions. By using two different classes of convexity, we get some further refinements for interval fractional Hermite–Hadamard type inequalities. Also, some examples are presented.

scholarly journals Post-quantum Hermite–Hadamard type inequalities for interval-valued convex functions

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Muhammad Aamir Ali ◽  
Hüseyin Budak ◽  
Ghulam Murtaza ◽  
Yu-Ming Chu
Keyword(s):  
Convex Functions ◽  
Fundamental Properties ◽  
Interval Valued ◽  
New Inequalities

AbstractIn this research, we introduce the notions of $(p,q)$ ( p , q ) -derivative and integral for interval-valued functions and discuss their fundamental properties. After that, we prove some new inequalities of Hermite–Hadamard type for interval-valued convex functions employing the newly defined integral and derivative. Moreover, we find the estimates for the newly proved inequalities of Hermite–Hadamard type. It is also shown that the results proved in this study are the generalization of some already proved research in the field of Hermite–Hadamard inequalities.

scholarly journals Some Modifications of Pairwise Soft Sets and Some of Their Related Concepts

Mathematics ◽  
2021 ◽  
Vol 9 (15) ◽  
pp. 1781
Author(s):  
Samer Al Ghour
Keyword(s):  
Topological Space ◽  
Sufficient Conditions ◽  
Soft Sets ◽  
New Concepts ◽  
Bitopological Spaces ◽  
The Relationship ◽  
Soft Topological Space

In this paper, we first define soft u-open sets and soft s-open as two new classes of soft sets on soft bitopological spaces. We show that the class of soft p-open sets lies strictly between these classes, and we give several sufficient conditions for the equivalence between soft p-open sets and each of the soft u-open sets and soft s-open sets, respectively. In addition to these, we introduce the soft u-ω-open, soft p-ω-open, and soft s-ω-open sets as three new classes of soft sets in soft bitopological spaces, which contain soft u-open sets, soft p-open sets, and soft s-open sets, respectively. Via soft u-open sets, we define two notions of Lindelöfeness in SBTSs. We discuss the relationship between these two notions, and we characterize them via other types of soft sets. We define several types of soft local countability in soft bitopological spaces. We discuss relationships between them, and via some of them, we give two results related to the discrete soft topological space. According to our new concepts, the study deals with the correspondence between soft bitopological spaces and their generated bitopological spaces.

Fear, history, stigma, and bias in the COVID-19 pandemic

2020 ◽  
Vol 18 (7) ◽  
pp. 177-182
Author(s):  
Kevin Kupietz, PhD ◽  
Lesley Gray, MPH
Keyword(s):  
Emergency Management ◽  
Disease Outbreaks ◽  
Social Effects ◽  
Evidence Based ◽  
Stigma And Discrimination ◽  
Emergency Managers ◽  
Global Pandemic ◽  
New Concepts ◽  
History Of ◽  
The Relationship

Introduction: The greatest enemy of a global pandemic is not the virus itself, but the fear, rumor, and stigma that envelopes people. This article explores the context and history of fear and stigma relating to pandemic, summarizing key actions to mitigate the harms during an active pandemic.Method: Our article draws from accounts in literature and journalist accounts documenting the relationship between infectious diseases and major disease outbreaks that have garnered fear and stigmatization. Results: Fear, stigma, and discrimination are not new concepts for pandemics. These social effects run the risk of diverting attention from the presenting disease and government responses. Reactions to fear, stigma, and discrimination risk sabotaging effective efforts to contain, manage, and eradicate the disease.Conclusion: Emergency managers have an important role in dispelling myths, disseminating appropriate and evidence-based information without exacerbating fears. Knowledge about the roots of fear and bias along with a good understanding of historical plagues and pandemics is vital to ensure those in the field of emergency management can effectively manage irrational fears.

New concepts of interval-valued intuitionistic (S, T)-fuzzy graphs

2016 ◽  
Vol 30 (4) ◽  
pp. 1893-1901 ◽  
Author(s):  
Hossein Rashmanlou ◽  
R.A. Borzooei
Keyword(s):  
Fuzzy Graphs ◽  
New Concepts ◽  
Interval Valued

scholarly journals O potrzebie rekonstrukcji przestrzeni badawczej w nauce o stosunkach międzynarodowych. Refleksje natury polityczno-normatywnej, systemowej i metaforycznej

2018 ◽  
pp. 25-38 ◽  
Author(s):  
Teresa ŁOŚ-NOWAK
Keyword(s):  
International Relations ◽  
Internal State ◽  
Current Theory ◽  
International Affairs ◽  
New Concepts ◽  
International Environment ◽  
The Social ◽  
The World ◽  
New Institutions ◽  
The Relationship

The world of the 21st century provides an intriguing space for academic reflection, offering new challenges and stimulating new concepts of international relations. In this context there emerges the significant question of the essence and direction of these concepts. They may entail deconstruction followed by a reconstruction of the research space in this field. Astrategy of resetting cannot be excluded here, either. Assuming that reconstruction is the appropriate solution there are significant issues of its scope and direction. If a total reset is considered rational we need to address the issue of what it should involve. This is a difficult question for researchers into international relations because it would mean that the hitherto achievements of this subject are being questioned. The post-positivist approach of numerous researchers, which manifests their response to the positivist methodology in the field of international relations, has not so far produced a unified methodological formula or a relatively coherent theory of international relations. Questions concerning the function of science, the nature of the social world (ontology) and the relationship between knowledge and the world (epistemology) remain open. Therefore, it may be worth going back to M. Wight’s provocative thesis that it is impossible to construct a reasonable theory of international relations, mainly owing to the dichotomy of the two fields of research that – in his opinion – cannot be overcome, namely the dichotomy of the ‘international’ (the realm of external affairs of states) and ‘internal’ (the realm of internal affairs within state), which are mutually exclusive because of their specificity; and once again ask the questions of how sensible the thesis of the dichotomy of both these environments is in a world that is strongly conditioned by the cross-border actors, interdependence and globalization. While the separateness of the ‘internal’ and ‘external’ state environments was, for Wight, an important obstacle, making it impossible to construct an academic theory explaining international relations, at the same time the current theory regarding their exclusivity in the context of the internalization of international affairs and the externalization of conditions inside states seems unsustainable. This phenomenon currently allows us to explain the imperative for combining these two environments, overlapping them …breaking down the old, established orders as a result of the now clearly visible phenomena and processes of the ‘internal state’ merging into the ‘international environment’ and vice versa, the disappearance of the traditional functions of borders, the weakening of old institutions and structures for steering the international environment as well as replacing them with entirely new institutions and structures.

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