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Search Results (3)

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Keywords = (s,m)-convex function in the second sense

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19 pages, 928 KiB  
Article
Properties of Convex Fuzzy-Number-Valued Functions on Harmonic Convex Set in the Second Sense and Related Inequalities via Up and Down Fuzzy Relation
by Muhammad Bilal Khan, Željko Stević, Abdulwadoud A. Maash, Muhammad Aslam Noor and Mohamed S. Soliman
Axioms 2023, 12(4), 399; https://doi.org/10.3390/axioms12040399 - 20 Apr 2023
Cited by 3 | Viewed by 1561
Abstract
In this paper, we provide different variants of the Hermite–Hadamard (H⋅H) inequality using the concept of a new class of convex mappings, which is referred to as up and down harmonically s-convex fuzzy-number-valued functions (UDH [...] Read more.
In this paper, we provide different variants of the Hermite–Hadamard (H⋅H) inequality using the concept of a new class of convex mappings, which is referred to as up and down harmonically s-convex fuzzy-number-valued functions (UDH s-convex FNVM) in the second sense based on the up and down fuzzy inclusion relation. The findings are confirmed with certain numerical calculations that take a few appropriate examples into account. The results deal with various integrals of the 2ρσρ+σ type and are innovative in the setting of up and down harmonically s-convex fuzzy-number-valued functions. Moreover, we acquire classical and new exceptional cases that can be seen as applications of our main outcomes. In our opinion, this will make a significant contribution to encouraging more research. Full article
(This article belongs to the Special Issue Editorial Board Members’ Collection Series: Fuzzy Modeling, Optimization and Computational Intelligence)
19 pages, 361 KiB  
Article
Some Novel Inequalities for LR-(k,h-m)-p Convex Interval Valued Functions by Means of Pseudo Order Relation
by Vuk Stojiljković, Rajagopalan Ramaswamy, Ola A. Ashour Abdelnaby and Stojan Radenović
Fractal Fract. 2022, 6(12), 726; https://doi.org/10.3390/fractalfract6120726 - 9 Dec 2022
Cited by 17 | Viewed by 1991
Abstract
In this paper, a new type of convexity is defined, namely, the left–right-(k,h-m)-p IVM (set-valued function) convexity. Utilizing the definition of this new convexity, we prove the Hadamard inequalities for noninteger Katugampola integrals. These inequalities generalize the noninteger Hadamard inequalities for a convex [...] Read more.
In this paper, a new type of convexity is defined, namely, the left–right-(k,h-m)-p IVM (set-valued function) convexity. Utilizing the definition of this new convexity, we prove the Hadamard inequalities for noninteger Katugampola integrals. These inequalities generalize the noninteger Hadamard inequalities for a convex IVM, (p,h)-convex IVM, p-convex IVM, h-convex, s-convex in the second sense and many other related well-known classes of functions implicitly. An apt number of numerical examples are provided as supplements to the derived results. Full article
(This article belongs to the Special Issue Mathematical Inequalities in Fractional Calculus and Applications)
10 pages, 235 KiB  
Article
Sandor Type Fuzzy Inequality Based on the (s,m)-Convex Function in the Second Sense
by Haiping Ren, Guofu Wang and Laijun Luo
Symmetry 2017, 9(9), 181; https://doi.org/10.3390/sym9090181 - 4 Sep 2017
Cited by 2 | Viewed by 5483
Abstract
Integral inequalities play critical roles in measure theory and probability theory. Given recent profound discoveries in the field of fuzzy set theory, fuzzy inequality has become a hot research topic in recent years. For classical Sandor type inequality, this paper intends to extend [...] Read more.
Integral inequalities play critical roles in measure theory and probability theory. Given recent profound discoveries in the field of fuzzy set theory, fuzzy inequality has become a hot research topic in recent years. For classical Sandor type inequality, this paper intends to extend the Sugeno integral. Based on the (s,m)-convex function in the second sense, a new Sandor type inequality is proposed for the Sugeno integral. Examples are given to verify the conclusion of this paper. Full article
(This article belongs to the Special Issue Fuzzy Sets Theory and Its Applications)
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