New Hermite–Hadamard and Jensen inequalities for log-$$s$$-convex fuzzy-interval-valued functions in the second sense

Лю, Пэйдэ; Khan, Muhammad Bilal; Noor, Muhammad Aslam; Noor, Khalida İnayat

doi:10.1007/s40747-021-00379-w

Cited by 37 publications

(13 citation statements)

References 32 publications

(44 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…They demonstrated the validity of characterizations with help of examples, and improved the previous results provided by Li and Noor [27]. We refer to the readers for further analysis of literature on the applications and properties of variational-like inequalities and generalized convex fuzzy mappings, see [2,9,16,[30][31][32][33][34][35][36][37][38][39][40][41][42][43][44][45][46][47] and the references therein.…”

Section: Introductionsupporting

confidence: 67%

Higher-Order Strongly Preinvex Fuzzy Mappings and Fuzzy Mixed Variational-Like Inequalities

Khan¹,

Noor²,

Noor³

et al. 2021

IJCIS

Self Cite

View full text Add to dashboard Cite

A family of fuzzy mappings is called higher-order strongly preinvex fuzzy mappings (HOS-preinvex fuzzy mappings), which take the place of generalization of the notion of nonconvexity is introduced through the "fuzzy-max" order among fuzzy numbers. This family properly includes the family of preinvex fuzzy mappings and is included in the family of quasi preinvex fuzzy mappings. With the support of examples, we have discussed some special cases. Some properties are derived and relations among the HOS-preinvex fuzzy mappings, HOS-invex fuzzy mappings, and fuzzy HOS-monotonicity are obtained under some mild conditions. Then, we have shown that optimality conditions of generalized differentiable HOS-preinvex fuzzy mappings and for the sum of generalized differentiable (briefly, G-differentiable) preinvex fuzzy mappings and nongeneralized differentiable HOSpreinvex fuzzy mappings can be distinguished by HOS-fuzzy variational-like inequalities and HOS-fuzzy mixed variational-like inequalities, respectively which can be viewed as novel applications. These inequalities are very interesting outcome of our main results and appear to be new ones. Several exceptional cases are debated. Presented results in this paper can be considered and development of previously established results.

show abstract

Section: Introductionsupporting

confidence: 67%

Higher-Order Strongly Preinvex Fuzzy Mappings and Fuzzy Mixed Variational-Like Inequalities

Khan¹,

Noor²,

Noor³

et al. 2021

IJCIS

Self Cite

View full text Add to dashboard Cite

show abstract

“…Khan et al also presented the new class of convex fuzzy mappings known as (χ 1 , χ 2 )-convex fuzzy-interval-valued functions ((χ 1 , χ 2 )-convex F-I-V•F) and obtained the new version of H-H inequalities for (χ 1 , χ 2 )-convex F-I-V•Fs. Moreover, Khan et al introduced new notions of generalized convex F-I-V•Fs, and derived new fractional H-H type and H-H type inequalities for convex F-I-V•Fs [27][28][29][30][31][32]. For more analysis and applications of F-I-V•Fs, see [33][34][35][36][37][38][39][40][41][42][43][44][45][46][47][48][49][50] and the references therein.…”

Section: Introductionmentioning

confidence: 99%

Riemann–Liouville Fractional Integral Inequalities for Generalized Pre-Invex Functions of Interval-Valued Settings Based upon Pseudo Order Relation

et al. 2022

Self Cite

View full text Add to dashboard Cite

The concepts of convex and non-convex functions play a key role in the study of optimization. So, with the help of these ideas, some inequalities can also be established. Moreover, the principles of convexity and symmetry are inextricably linked. In the last two years, convexity and symmetry have emerged as a new field due to considerable association. In this paper, we study a new version of interval-valued functions (I-V·Fs), known as left and right χ-pre-invex interval-valued functions (LR-χ-pre-invex I-V·Fs). For this class of non-convex I-V·Fs, we derive numerous new dynamic inequalities interval Riemann–Liouville fractional integral operators. The applications of these repercussions are taken into account in a unique way. In addition, instructive instances are provided to aid our conclusions. Meanwhile, we’ll discuss a few specific examples that may be extrapolated from our primary findings.

show abstract

“…wherẽis a convex fuzzy-IVF. We urge the readers to [32][33][34][35][36][37][38][39][40][41][42] and the citations therein for further review of related literature on the implementations and characterization of fuzzy-interval, inequalities and generalized convex fuzzy mappings.…”

Section: Introductionmentioning

confidence: 99%

Harmonically Convex Fuzzy-Interval-Valued Functions and Fuzzy-Interval Riemann–Liouville Fractional Integral Inequalities

Sana¹,

Khan²,

Noor³

et al. 2021

IJCIS

Self Cite

View full text Add to dashboard Cite

It is well known that the concept of convexity establishes strong relationship with integral inequality for single-valued and interval-valued function. The single-valued function and interval-valued function both are special cases of fuzzy interval-valued function. The aim of this paper is to introduce a new class of convex fuzzy interval-valued functions, which is called harmonically convex fuzzy interval-valued functions (harmonically convex fuzzy-IVFs) by means of fuzzy order relation and to investigate this new class via fuzzy-interval Riemann-Liouville fractional operator. With the help of fuzzy order relation and fuzzyinterval Riemann-Liouville fractional, we derive some integrals inequalities of Hermite-Hadamard (H-H) type and Hermite-Hadamard-Fejér (H-H Fejér) type as well as some product inequities for harmonically convex fuzzy-IVFs. Our results represent a significant improvement and refinement of the known results. We hope that these interesting outcomes may open a new direction for fuzzy optimization, modeling and interval-valued function.

show abstract

New Hermite–Hadamard and Jensen inequalities for log-$$s$$-convex fuzzy-interval-valued functions in the second sense

Cited by 37 publications

References 32 publications

Higher-Order Strongly Preinvex Fuzzy Mappings and Fuzzy Mixed Variational-Like Inequalities

Higher-Order Strongly Preinvex Fuzzy Mappings and Fuzzy Mixed Variational-Like Inequalities

Riemann–Liouville Fractional Integral Inequalities for Generalized Pre-Invex Functions of Interval-Valued Settings Based upon Pseudo Order Relation

Harmonically Convex Fuzzy-Interval-Valued Functions and Fuzzy-Interval Riemann–Liouville Fractional Integral Inequalities

Contact Info

Product

Resources

About