Certain fractional conformable inequalities for the weighted and the extended Chebyshev functionals

Tassaddiq, Asifa; Rahman, Gauhar; Nisar, Kottakkaran Sooppy; Samraiz, Muhammad

doi:10.1186/s13662-020-2543-0

Cited by 17 publications

(14 citation statements)

References 27 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Chebyshev-type inequalities and Minkowski-type inequalities involving generalized conformable integrals can be found in the work of Nisar et al [42,43]. Recently, Tassaddiq et al [63] proposed certain inequalities for the weighted and extended Chebyshev functionals by using fractional conformable integrals. Nisar et al [40] presented some new classes of inequalities for an n (n ∈ N) family of positive continuous and decreasing functions via generalized conformable fractional integrals.…”

Section: Theorem 11 Let φ : [X 1 X 2 ] → R Be An Absolutely Continmentioning

confidence: 99%

On generalized fractional integral inequalities for the monotone weighted Chebyshev functionals

et al. 2020

Self Cite

View full text Add to dashboard Cite

In this paper, we establish the generalized Riemann-Liouville (RL) fractional integrals in the sense of another increasing, positive, monotone, and measurable function Ψ. We determine certain new double-weighted type fractional integral inequalities by utilizing the said integrals. We also give some of the new particular inequalities of the main result. Note that we can form various types of new inequalities of fractional integrals by employing conditions on the function Ψ given in the paper. We present some corollaries as particular cases of the main results.

show abstract

Section: Theorem 11 Let φ : [X 1 X 2 ] → R Be An Absolutely Continmentioning

confidence: 99%

On generalized fractional integral inequalities for the monotone weighted Chebyshev functionals

et al. 2020

Self Cite

View full text Add to dashboard Cite

show abstract

“…Multiplying (27) by F 1 (θ, ρ) (where F 1 (θ, ρ) is defined in (26)) and integrating the resultant estimates with respect to ρ over (1, θ)…”

Section: Remarkmentioning

confidence: 99%

“…In [25,26], Nisar et al proposed generalized Chebyshev-type inequalities and certain Minkowski's type inequalities by employing generalized conformable integrals. Recently, Tassaddiq et al [27] investigated certain inequalities for the weighted and the extended Chebyshev functionals by using fractional conformable integrals. Nisar et al [28] established certain new inequalities for a class of n(n ∈ N) positive continuous and decreasing functions by employing generalized conformable fractional integrals.…”

Section: Introductionmentioning

confidence: 99%

Certain Hadamard Proportional Fractional Integral Inequalities

2020

Self Cite

View full text Add to dashboard Cite

In this present paper we study the non-local Hadmard proportional integrals recently proposed by Rahman et al. (Advances in Difference Equations, (2019) 2019:454) which containing exponential functions in their kernels. Then we establish certain new weighted fractional integral inequalities involving a family of n ( n ∈ N ) positive functions by utilizing Hadamard proportional fractional integral operator. The inequalities presented in this paper are more general than the inequalities existing in the literature.

show abstract

“…It is well known that the Čebyšev inequality (1) has wild applications in the fields of pure and applied mathematics [1][2][3][4][5][6][7][8][9][10]. Recently, the generalizations and variants for the Čebyšev inequality (1) have attracted the attention of many researchers [11][12][13][14][15][16][17][18][19][20].…”

Section: Introductionmentioning

confidence: 99%

On New Modifications Governed by Quantum Hahn’s Integral Operator Pertaining to Fractional Calculus

Rashid

Khalid

Rahman

et al. 2020

Journal of Function Spaces

Self Cite

View full text Add to dashboard Cite

In the article, we present several generalizations for the generalized Čebyšev type inequality in the frame of quantum fractional Hahn’s integral operator by using the quantum shift operator σΨqς=qς+1−qσς∈l1,l2,σ=l1+ω/1−q,0<q<1,ω≥0. As applications, we provide some associated variants to illustrate the efficiency of quantum Hahn’s integral operator and compare our obtained results and proposed technique with the previously known results and existing technique. Our ideas and approaches may lead to new directions in fractional quantum calculus theory.

show abstract

Certain fractional conformable inequalities for the weighted and the extended Chebyshev functionals

Abstract: The main aim of this present paper is to establish fractional conformable inequalities for the weighted and extended Chebyshev functionals. We present some special cases of our main result in terms of the Riemann-Liouville fractional integral operator and classical inequalities.

Cited by 17 publications

References 27 publications

On generalized fractional integral inequalities for the monotone weighted Chebyshev functionals

On generalized fractional integral inequalities for the monotone weighted Chebyshev functionals

Certain Hadamard Proportional Fractional Integral Inequalities

On New Modifications Governed by Quantum Hahn’s Integral Operator Pertaining to Fractional Calculus

Contact Info

Product

Resources

About