Some new generalized Ostrowski type inequalities with new error bounds

Amjad, Junaid; Qayyum, Ather; Fahad, Shah; Arslan, Muhammad

doi:10.55059/ijm.2022.1.2/23

Cited by 4 publications

(3 citation statements)

References 11 publications

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“…Finally, by using the functional properties of the abstract space, in which these derivatives belong to, these identities can be converted into Ostrowski's like inequalities. Some of these studies can be found in Alshanti, 2018Alshanti, , 2019Alshanti and Milovanovic, 2020;Alshanti, 2021;Amjad et al, 2022;Liu et al, 2016;Dragomir and Sofo, 2000;Liu and Park, 2017a;Liu and Lu, 2015;Liu and Park, 2017b;Al-Zoubi et al, 2019). Also, for more rigorous related approaches, we refer the reader to (Milovanović, 2017;Milovanović and Pečarić, 1976;Milovanović, 1975;Milovanovic, 1977;Vasić and Milovanović, 1976;Ðorđević and Milovanović, 1975).…”

Section: Introductionmentioning

confidence: 99%

Perturbed Trapezoid Like Inequalities

Alshanti

Batiha

Alshanty

et al. 2023

Sci. Technol. Indones

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In our current research article, based on a general configuration of a 3-step Peano kernel, new versions of integral inequality of Ostrowski’s type are developed for differentiable mappings that have second derivatives belong to L∞. Then we utilized these versions to generate new perturbed trapezoid like inequalities. These new perturbed trapezoid like inequalities are proposed with error bounds smaller than and similar to those reported by previous studies. Moreover, some of the obtained perturbed trapezoid like inequalities reveal the relationship between the Euler-Maclaurin summation and the trapezoidal rule. Finally, certain implementations to numerical composite quadrature rules are provided for completeness.

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Section: Introductionmentioning

confidence: 99%

Perturbed Trapezoid Like Inequalities

Alshanti

Batiha

Alshanty

et al. 2023

Sci. Technol. Indones

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“…Mappings play a vital role in the field of inequalities (see of example [17][18][19][20]). The mappings which have Lipschitzís constant equal to 1 are called as non-expansive mappings.…”

Section: Introductionmentioning

confidence: 99%

Generalization of Fixed Point Approximation of Contraction and Suzuki Generalized Non-Expansive Mappings in Banach Domain

Muhammad¹,

Asghar²,

Aslam³

et al. 2022

Int. J. Anal. Appl.

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By principal motivation from the results of the new iterative scheme that produces faster results than K-iteration. In this article, we study generalized results by a new iteration scheme to approximate fixed points of generalized contraction and Suzuki non-expansive mappings. We establish strong convergence results of generalized contraction mappings of closed convex Banach space and also deduce data dependent results. Furthermore, we prove some weak and strong convergence theorems in the sense of generalized Suzuki non-expansive mapping by applying condition (C).

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“…Some latest work done by S. Fahad et al [13]. Further works done by Iftikhar et al [14], Mustafa et al [15] and J. Amjad et al [16]. Let the functional S ( f ; ω; ȃ, ĉ) via weighted version represent the deviation of f ( ŝ) over [ ȃ, ĉ] defined as:…”

Section: Introductionmentioning

confidence: 99%