On Cauchy–Schwarz inequality for N-tuple diamond-alpha integral

Hu, Ximei; Tian, Jing-Feng; Chu, Yu‐Ming; Lu, Yao

doi:10.1186/s13660-020-2283-4

Cited by 19 publications

(5 citation statements)

References 32 publications

(29 reference statements)

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“…As we all know, analytic inequality plays a very important role in mathematics and in other parts of science (see for example, [4][5][6]) since it offers certain computable and accurate bounds for given complicated functions. As far as the complete elliptic integral of the first kind is concerned, there are at least two kinds of bounds for K (r).…”

Section: Introductionmentioning

confidence: 99%

A Rational Approximation for the Complete Elliptic Integral of the First Kind

2020

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Section: Introductionmentioning

confidence: 99%

A Rational Approximation for the Complete Elliptic Integral of the First Kind

2020

Self Cite

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“…These mathematicians contributed significantly to fractional calculus and its many applications. For further information on fractional calculus, see [15][16][17][18][19][20][21][22][23][24][25][26][27]. In the modern era, fractional calculus is frequently used to describe a variety of phenomena, such as the fractional conservation of mass, and the fractional Schrodinger equation in quantum theory.…”

Section: Introductionmentioning

confidence: 99%

New Versions of Fuzzy-Valued Integral Inclusion over p-Convex Fuzzy Number-Valued Mappings and Related Fuzzy Aumman’s Integral Inequalities

Alreshidi,

Khan,

Breaz

et al. 2023

Symmetry

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It is well known that both concepts of symmetry and convexity are directly connected. Similarly, in fuzzy theory, both ideas behave alike. It is important to note that real and interval-valued mappings are exceptional cases of fuzzy number-valued mappings (FNVMs) because fuzzy theory depends upon the unit interval that make a significant contribution to overcoming the issues that arise in the theory of interval analysis and fuzzy number theory. In this paper, the new class of p-convexity over up and down (UD) fuzzy relation has been introduced which is known as UD-p-convex fuzzy number-valued mappings (UD-p-convex FNVMs). We offer a thorough analysis of Hermite–Hadamard-type inequalities for FNVMs that are UD-p-convex using the fuzzy Aumann integral. Some previous results from the literature are expanded upon and broadly applied in our study. Additionally, we offer precise justifications for the key theorems that Kunt and İşcan first deduced in their article titled “Hermite–Hadamard–Fejer type inequalities for p-convex functions”. Some new and classical exceptional cases are also discussed. Finally, we illustrate our findings with well-defined examples.

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“…In perspective on the broad utilization of such frameworks, numerous scientists went to the examination of the hypothetical parts of fractional differential conditions. Specifically, there was unique consideration regarding demonstrating the integral inequalities for fractional systems enhanced with an assortment of classical and non-classical (nonlocal) operators with the guide of advance strategies for functional investigation, see [5,6,7,8,9,10,11,12,13,14,15,16,17,18,59,60,61,62,63,64,65]. Fractional integral inequalities involving convex functions played a significant role in the mathematical analysis due to their prominent features and convenient characterizations.…”

Section: Introductionmentioning

confidence: 99%

Some new generalizations for exponentially (s, m)-preinvex functions considering generalized fractional integral operators

Safdar

Attique

2021

Punjab Univ. j. math.

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The generalized fractional integral has been one of the most useful operators for modelling non-local behaviors by fractional differential equations. It is considered, for several integral inequalities by introducing the concept of exponentially (s, m)-preinvexity. These variants derived via an extended Mittag-Leffler function based on boundedness, continuity and Hermite-Hadamard type inequalities. The consequences associated with fractional integral operators are more general and also present the results for convexity theory. Moreover, we point out that the variants are useful in solving the problems of science, engineering and technology where the Mittag-Leffler function occurs naturally.

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On Cauchy–Schwarz inequality for N-tuple diamond-alpha integral

Abstract: In this paper, we present some new Cauchy-Schwarz inequalities for N-tuple diamond-alpha integral on time scales. The obtained results improve and generalize some Cauchy-Schwarz type inequalities given by many authors. MSC: 26D15

Cited by 19 publications

References 32 publications

A Rational Approximation for the Complete Elliptic Integral of the First Kind

A Rational Approximation for the Complete Elliptic Integral of the First Kind

New Versions of Fuzzy-Valued Integral Inclusion over p-Convex Fuzzy Number-Valued Mappings and Related Fuzzy Aumman’s Integral Inequalities

Some new generalizations for exponentially (s, m)-preinvex functions considering generalized fractional integral operators

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