Some new generalized $ \kappa $–fractional Hermite–Hadamard–Mercer type integral inequalities and their applications

Vivas-Cortez, Miguel; Awan, Muhammad Uzair; Javed, Muhammad Zakria; Kashuri, Artion; Noor, Muhammad Aslam; Noor, Khalida İnayat

doi:10.3934/math.2022177

Cited by 14 publications

(6 citation statements)

References 16 publications

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“…For this we consider the above mentioned assumptions and s ∈ (0, 1] and ω ∈ (0 (34), respectively. Clearly one can see that the inequalities (21) and (34) hold good by varying both the parameters s and ω.…”

Section: Numerical Examples and Visual Analysismentioning

confidence: 96%

“…For more work on Jensen-Mercer-type inequalities, see [18][19][20][21][22]. Over time, the researchers have extended the definition of convex mappings to obtain different variants of Hermite-Hadamard inequality.…”

Section: Introductionmentioning

confidence: 99%

“…In the above figures, the red and purple surfaces show the right and left sides of inequalities (a) (21) and (b)(34), respectively. Clearly one can see that the inequalities(21) and(34) hold good…”

mentioning

confidence: 98%

See 2 more Smart Citations

On Fractional Ostrowski-Mercer-Type Inequalities and Applications

Ramzan,

Awan,

Vivas-Cortez

et al. 2023

Symmetry

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The objective of this research is to study in detail the fractional variants of Ostrowski–Mercer-type inequalities, specifically for the first and second order differentiable s-convex mappings of the second sense. To obtain the main outcomes of the paper, we leverage the use of conformable fractional integral operators. We also check the numerical validations of the main results. Our findings are also validated through visual representations. Furthermore, we provide a detailed discussion on applications of the obtained results related to special means, q-digamma mappings, and modified Bessel mappings.

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Section: Numerical Examples and Visual Analysismentioning

confidence: 96%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

On Fractional Ostrowski-Mercer-Type Inequalities and Applications

Ramzan,

Awan,

Vivas-Cortez

et al. 2023

Symmetry

View full text Add to dashboard Cite

show abstract

“…In this section, we briefly review some basic definitions. The k-analog of gamma, beta and hypergeometric functions was first introduced in [7,8,18] by Daiz and also demonstrated several of these characteristics. Numerous researchers investigated a variety of findings on these functions [2,[11][12][13][14].…”

Section: Preliminariesmentioning

confidence: 99%

K-Humbert confluent hypergeometric functions Φ 1 , k , Φ 2 , k , and Φ 3 , k

Arshad,

Usman,

Iqbal

et al. 2024

J. Math. Computer Sci.

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The main aim of this work is to introduce the k-Humbert confluent hypergeometric functions Φ 1,k , Φ 2,k , Φ 3,k and developed some formulae by using the idea of k-calculus. k-Humbert confluent hypergeometric functions are an extension of the classical confluent hypergeometric functions, incorporating an additional parameter, k, which enriches their analytical properties and applicability in diverse mathematical contexts. We introduce new results by applying q-derivative operator on k-Humbert confluent hypergeometric functions Φ 1,k , Φ 2,k , and Φ 3,k . Contiguous function relations of various types, (q, k)-recurrence relations, and q-derivatives formulae are constructed.

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“…In [26] authors described a new generalized fractional operator utilizing interval domain and delivered some new generalized integral containments. Recently Vivas-Cortez et al [27] defined the γ-cr convex mappings and provided its applications in integral inequalities like Jensen's and H-H inequalities. Recently, Bin-Mohsin et al [28] introduced a novel unified class of interval valued convex mappings and established some fresh fractional versions of classical trapezium type inequalities.…”

Section: Introductionmentioning

confidence: 99%

On Family of Totally Ordered Interval Valued ConvexMappings and Applications

Cortez,

Awan,

Javed

et al. 2024

Preprint

Self Cite

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Inequalities have been examined from multiple viewpoints to identify novel developments and ramifications.One of the prominent strategies in the following area is the development of new unified representationsinvolving various rectified forms of convexity and fractional calculus. Numerous fundamental inequalities,like Hermite-Hadamard, Ostrowski’s, and H¨older’s types, have been assessed in recent years regarding set-valued maps based on various ordering relations. In the progressive article, we define a novel family ofconvex mappings incorporating center-radius relations and quasi-means. The effectiveness of this class isdemonstrated by the fact that by specifying various values of H and ω, we obtain various known and newclasses of I.V. convexity connecting with cr-ordering relations. Furthermore, we construct new genericversions of the Jensen’s like inequalities Hermite-Hadamard(H-H) inequality, Hermite-Hadamard-Fejer(H-H-F) inequality, and product form H-H inequality deploying the freshly proposed class of I.V. convexity andclassical R-L fractional operators. The validation of obtained results is explained with the help of graphicalillustrations and numerical examples. Also, we provide the applications to special means and informationtheory. Mathematics Subject Classification (2010): 26A33; 26A51; 26D07; 26D10; 26D15; 26D20.

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Some new generalized $ \kappa $–fractional Hermite–Hadamard–Mercer type integral inequalities and their applications

Cited by 14 publications

References 16 publications

On Fractional Ostrowski-Mercer-Type Inequalities and Applications

On Fractional Ostrowski-Mercer-Type Inequalities and Applications

K-Humbert confluent hypergeometric functions Φ 1 , k , Φ 2 , k , and Φ 3 , k

On Family of Totally Ordered Interval Valued ConvexMappings and Applications

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