scholarly journals Fuzzy Mixed Variational-Like and Integral Inequalities for Strongly Preinvex Fuzzy Mappings

Symmetry ◽  
2021 ◽  
Vol 13 (10) ◽  
pp. 1816
Author(s):  
Muhammad Bilal Khan ◽  
Hari Mohan Srivastava ◽  
Pshtiwan Othman Mohammed ◽  
Juan L. G. Guirao
Keyword(s):  
Optimality Conditions ◽  
Critical Role ◽  
Fuzzy Optimization ◽  
Strong Relationship ◽  
The Other ◽  
Hadamard Inequality ◽  
New Class ◽  
Invex Set ◽  
Tight Connection ◽  
The Subject

It is a familiar fact that convex and non-convex fuzzy mappings play a critical role in the study of fuzzy optimization. Due to the behavior of its definition, the idea of convexity plays a significant role in the subject of inequalities. The concepts of convexity and symmetry have a tight connection. We may use whatever we learn from one to the other, thanks to the significant correlation that has developed between both in recent years. Our aim is to consider a new class of fuzzy mappings (FMs) known as strongly preinvex fuzzy mappings (strongly preinvex-FMs) on the invex set. These FMs are more general than convex fuzzy mappings (convex-FMs) and preinvex fuzzy mappings (preinvex-FMs), and when generalized differentiable (briefly, G-differentiable), strongly preinvex-FMs are strongly invex fuzzy mappings (strongly invex-FMs). Some new relationships among various concepts of strongly preinvex-FMs are established and verified with the support of some useful examples. We have also shown that optimality conditions of G-differentiable strongly preinvex-FMs and the fuzzy functional, which is the sum of G-differentiable preinvex-FMs and non G-differentiable strongly preinvex-FMs, can be distinguished by strongly fuzzy variational-like inequalities and strongly fuzzy mixed variational-like inequalities, respectively. In the end, we have established and verified a strong relationship between the Hermite–Hadamard inequality and strongly preinvex-FM. Several exceptional cases are also discussed. These inequalities are a very interesting outcome of our main results and appear to be new ones. The results in this research can be seen as refinements and improvements to previously published findings.

scholarly journals Integral Inequalities for Generalized Harmonically Convex Functions in Fuzzy-Interval-Valued Settings

Symmetry ◽  
2021 ◽  
Vol 13 (12) ◽  
pp. 2352
Author(s):  
Muhammad Bilal Khan ◽  
Pshtiwan Othman Mohammed ◽  
José António Tenreiro Machado ◽  
Juan L. G. Guirao
Keyword(s):  
Critical Role ◽  
Fuzzy Optimization ◽  
Order Relation ◽  
Riemann Integral ◽  
New Class ◽  
Tight Connection ◽  
The Subject ◽  
Fuzzy Order ◽  
Interval Valued ◽  
Fuzzy Interval

It is a well-known fact that convex and non-convex fuzzy mappings play a critical role in the study of fuzzy optimization. Due to the behavior of its definition, the idea of convexity also plays a significant role in the subject of inequalities. The concepts of convexity and symmetry have a tight connection. We may use whatever we learn from both the concepts, owing to the significant correlation that has developed between both in recent years. In this paper, we introduce a new class of harmonically convex fuzzy-interval-valued functions which is known as harmonically h-convex fuzzy-interval-valued functions (abbreviated as harmonically h-convex F-I-V-Fs) by means of fuzzy order relation. This fuzzy order relation is defined level-wise through Kulisch–Miranker order relation defined on interval space. Some properties of this class are investigated. BY using fuzzy order relation and h-convex F-I-V-Fs, Hermite–Hadamard type inequalities for harmonically are developed via fuzzy Riemann integral. We have also obtained some new inequalities for the product of harmonically h-convex F-I-V-Fs. Moreover, we establish Hermite–Hadamard–Fej’er inequality for harmonically h-convex F-I-V-Fs via fuzzy Riemann integral. These outcomes are a generalization of a number of previously known results, as well as many new outcomes can be deduced as a result of appropriate parameter “θ” and real valued function “∇” selections. For the validation of the main results, we have added some nontrivial examples. We hope that the concepts and techniques of this study may open new directions for research.

scholarly journals Some Inequalities for LR-$$\left({h}_{1}, {h}_{2}\right)$$-Convex Interval-Valued Functions by Means of Pseudo Order Relation

2021 ◽  
Vol 14 (1) ◽  
Author(s):  
Muhammad Bilal Khan ◽  
Muhammad Aslam Noor ◽  
Khalida Inayat Noor ◽  
Kottakkaran Sooppy Nisar ◽  
Khadiga Ahmed Ismail ◽  
...  
Keyword(s):  
Applied Mathematics ◽  
Critical Role ◽  
Order Relation ◽  
Strong Relationship ◽  
New Class ◽  
Starting Point ◽  
Interval Valued Function ◽  
Fejér Inequality ◽  
Definition Of ◽  
Interval Valued

AbstractIn both theoretical and applied mathematics fields, integral inequalities play a critical role. Due to the behavior of the definition of convexity, both concepts convexity and integral inequality depend on each other. Therefore, the relationship between convexity and symmetry is strong. Whichever one we work on, we introduced the new class of generalized convex function is known as LR-$$\left({h}_{1}, {h}_{2}\right)$$ h 1 , h 2 -convex interval-valued function (LR-$$\left({h}_{1}, {h}_{2}\right)$$ h 1 , h 2 -IVF) by means of pseudo order relation. Then, we established its strong relationship between Hermite–Hadamard inequality (HH-inequality)) and their variant forms. Besides, we derive the Hermite–Hadamard–Fejér inequality (HH–Fejér inequality)) for LR-$$\left({h}_{1}, {h}_{2}\right)$$ h 1 , h 2 -convex interval-valued functions. Several exceptional cases are also obtained which can be viewed as its applications of this new concept of convexity. Useful examples are given that verify the validity of the theory established in this research. This paper’s concepts and techniques may be the starting point for further research in this field.

scholarly journals A New Version of the Hermite–Hadamard Inequality for Riemann–Liouville Fractional Integrals

Symmetry ◽  
2020 ◽  
Vol 12 (4) ◽  
pp. 610 ◽  
Author(s):  
Pshtiwan Othman Mohammed ◽  
Iver Brevik
Keyword(s):  
Bessel Functions ◽  
Applied Mathematics ◽  
Critical Role ◽  
Strong Relationship ◽  
Fractional Integrals ◽  
Mathematical Methods ◽  
Digamma Function ◽  
Hadamard Inequality ◽  
The Past ◽  
Riemann Integrals

Integral inequalities play a critical role in both theoretical and applied mathematics fields. It is clear that inequalities aim to develop different mathematical methods. Thus, the present days 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. There is a strong relationship between convexity and symmetry. Whichever one we work on, we can apply it to the other one due the strong correlation produced between them, especially in the past few years. In this article, we firstly point out the known Hermite–Hadamard (HH) type inequalities which are related to our main findings. In view of these, we obtain a new inequality of Hermite–Hadamard type for Riemann–Liouville fractional integrals. In addition, we establish a few inequalities of Hermite–Hadamard type for the Riemann integrals and Riemann–Liouville fractional integrals. Finally, three examples are presented to demonstrate the application of our obtained inequalities on modified Bessel functions and q-digamma function.

scholarly journals Optimality criteria in set-valued optimization

2003 ◽  
Vol 75 (2) ◽  
pp. 221-232 ◽  
Author(s):  
C. S. Lalitha ◽  
J. Dutta ◽  
Misha G. Govil
Keyword(s):  
Optimality Conditions ◽  
Optimization Problem ◽  
Convex Set ◽  
Necessary Optimality Conditions ◽  
Optimality Criteria ◽  
New Class ◽  
Invex Set

AbstractThe main aim of this paper is to obtain optimality conditions for a constrained set-valued optimization problem. The concept of Clarke epiderivative is introduced and is used to derive necessary optimality conditions. In order to establish sufficient optimality criteria we introduce a new class of set-valued maps which extends the class of convex set-valued maps and is different from the class of invex set-valued maps.

scholarly journals A Class of SemilocalE-Preinvex Functions and Its Applications in Nonlinear Programming

2012 ◽  
Vol 2012 ◽  
pp. 1-19
Author(s):  
Hehua Jiao ◽  
Sanyang Liu ◽  
Xinying Pai
Keyword(s):  
Nonlinear Programming ◽  
Optimality Conditions ◽  
Convex Functions ◽  
Convex Set ◽  
Basic Properties ◽  
New Class ◽  
Duality Results ◽  
Invex Set ◽  
Preinvex Functions ◽  
Class Of Functions

A kind of generalized convex set, called as local star-shapedE-invex set with respect toη,is presented, and some of its important characterizations are derived. Based on this concept, a new class of functions, named as semilocalE-preinvex functions, which is a generalization of semi-E-preinvex functions and semilocalE-convex functions, is introduced. Simultaneously, some of its basic properties are discussed. Furthermore, as its applications, some optimality conditions and duality results are established for a nonlinear programming.

Golgi Apparatus and Melanogenesis: Ultrastructural Study of a Human Cellular Blue Nevus (Melanocytoma)

1973 ◽  
Vol 31 ◽  
pp. 380-381
Author(s):  
S.R. Allegra
Keyword(s):  
Endoplasmic Reticulum ◽  
Golgi Apparatus ◽  
Ultrastructural Study ◽  
The Other ◽  
Blue Nevus ◽  
Normal Complement ◽  
Golgi Vesicles ◽  
Golgi System ◽  
The Subject ◽  
Cellular Blue Nevus

The respective roles of the ribo somes, endoplasmic reticulum, Golgi apparatus and perhaps nucleus in the synthesis and maturation of melanosomes is still the subject of some controversy. While the early melanosomes (premelanosomes) have been frequently demonstrated to originate as Golgi vesicles, it is undeniable that these structures can be formed in cells in which Golgi system is not found. This report was prompted by the findings in an essentially amelanotic human cellular blue nevus (melanocytoma) of two distinct lines of melanocytes one of which was devoid of any trace of Golgi apparatus while the other had normal complement of this organelle.

“Channeling” the powers of God’s Word

2010 ◽  
Vol 4 (2) ◽  
pp. 135-156 ◽  
Author(s):  
Dorothea E. Schulz
Keyword(s):  
The Other ◽  
Border Zone ◽  
Focus Attention ◽  
Spiritual Power ◽  
New Materials ◽  
God's Word ◽  
Audio Recordings ◽  
Heated Debate ◽  
The Subject ◽  
The One

Starting with the controversial esoteric employment of audio recordings by followers of the charismatic Muslim preacher Sharif Haidara in Mali, the article explores the dynamics emerging at the interface of different technologies and techniques employed by those engaging the realm of the Divine. I focus attention on the “border zone” between, on the one hand, techniques for appropriating scriptures based on long-standing religious conventions, and, on the other, audio recording technologies, whose adoption not yet established authoritative and standardized forms of practice, thereby generating insecurities and becoming the subject of heated debate. I argue that “recyclage” aptly describes the dynamics of this “border zone” because it captures the ways conventional techniques of accessing the Divine are reassessed and reemployed, by integrating new materials and rituals. Historically, appropriations of the Qur’an for esoteric purposes have been widespread in Muslim West Africa. These esoteric appropriations are at the basis of the considerable continuities, overlaps and crossovers, between scripture-related esoteric practices on one side, and the treatment by Sharif Haidara’s followers of audio taped sermons as vessels of his spiritual power, on the other.

The problem of woman’s emansipation in the feuilleton “Amazonia: a very inept story” by Mykola Chirsky

2020 ◽  
pp. 71-76
Author(s):  
Iryna Rusnak
Keyword(s):  
Scientific Understanding ◽  
The Other ◽  
Literary Studies ◽  
Ethical Guidelines ◽  
Compositional Structure ◽  
Urgent Task ◽  
The Subject ◽  
The One ◽  
Artistic Heritage

The author of the article analyses the problem of the female emancipation in the little-known feuilleton “Amazonia: A Very Inept Story” (1924) by Mykola Chirsky. The author determines the genre affiliation of the work and examines its compositional structure. Three parts are distinguished in the architectonics of associative feuilleton: associative conception; deployment of a “small” topic; conclusion. The author of the article clarifies the role of intertextual elements and the method of constantly switching the tone from serious to comic to reveal the thematic direction of the work. Mykola Chirsky’s interest in the problem of female emancipation is corresponded to the general mood of the era. The subject of ridicule in provocative feuilleton is the woman’s radical metamorphoses, since repulsive manifestations of emancipation becomes commonplace. At the same time, the writer shows respect for the woman, appreciates her femininity, internal and external beauty, personality. He associates the positive in women with the functions of a faithful wife, a caring mother, and a skilled housewife. In feuilleton, the writer does not bypass the problem of the modern man role in a family, but analyses the value and moral and ethical guidelines of his character. The husband’s bad habits receive a caricatured interpretation in the strange behaviour of relatives. On the one hand, the writer does not perceive the extremes brought by female emancipation, and on the other, he mercilessly criticises the male “virtues” of contemporaries far from the standard. The artistic heritage of Mykola Chirsky remains little studied. The urgent task of modern literary studies is the introduction of Mykola Chirsky’s unknown works into the scientific circulation and their thorough scientific understanding.

MUNDANE MIRACLES IN AWADH. ENCOUNTERS WITH THE REVEALED AND THE HIDDEN

2020 ◽  
pp. 130-140
Author(s):  
Maxim B. Demchenko ◽  
Keyword(s):  
The Other ◽  
Local People ◽  
Natural Phenomena ◽  
Mughal Empire ◽  
The Public ◽  
British Raj ◽  
The Subject ◽  
Other World ◽  
Better Than

The sphere of the unknown, supernatural and miraculous is one of the most popular subjects for everyday discussions in Ayodhya – the last of the provinces of the Mughal Empire, which entered the British Raj in 1859, and in the distant past – the space of many legendary and mythological events. Mostly they concern encounters with inhabitants of the “other world” – spirits, ghosts, jinns as well as miraculous healings following magic rituals or meetings with the so-called saints of different religions (Hindu sadhus, Sufi dervishes),with incomprehensible and frightening natural phenomena. According to the author’s observations ideas of the unknown in Avadh are codified and structured in Avadh better than in other parts of India. Local people can clearly define if they witness a bhut or a jinn and whether the disease is caused by some witchcraft or other reasons. Perhaps that is due to the presence in the holy town of a persistent tradition of katha, the public presentation of plots from the Ramayana epic in both the narrative and poetic as well as performative forms. But are the events and phenomena in question a miracle for the Avadhvasis, residents of Ayodhya and its environs, or are they so commonplace that they do not surprise or fascinate? That exactly is the subject of the essay, written on the basis of materials collected by the author in Ayodhya during the period of 2010 – 2019. The author would like to express his appreciation to Mr. Alok Sharma (Faizabad) for his advice and cooperation.

De-Finition

2019 ◽  
Vol 95 (2) ◽  
pp. 231-245
Author(s):  
Erik Ode
Keyword(s):  
Educational Research ◽  
The Other ◽  
Political Perspective ◽  
The World ◽  
The Subject ◽  
Scientific Terms

Abstract De-Finition. Poststructuralist Objections to the Limitation of the Other The metaphysic tradition always tried to structure the world by definitions and scientific terms. Since poststructuralist authors like Derrida, Foucault and Deleuze have claimed the ›death of the subject‹ educational research cannot ignore the critical objections to its own methods. Definitions and identifications may be a violation of the other’s right to stay different and undefined. This article tries to discuss the scientific limitations of the other in a pedagogical, ethical and political perspective.

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