A novel comprehensive analysis on generalized harmonically ψ‐convex with respect to Raina's function on fractal set with applications

The pivotal proposal of this work is to present a new class of harmonically convex functions, namely, generalized harmonically ψ‐convex functions based on the fractal set technique for establishing inequalities of Hermite–Hadamard type, Pachpatte type, and certain related variants with respect to th...

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Bibliographic Details
Published in:Mathematical methods in the applied sciences 2023-05, Vol.46 (7), p.8018-8042
Main Authors: Chu, Yu‐ming, Rashid, Saima, Singh, Jagdev
Format: Article
Language:English
Subjects:
fractal set
Fractals
Fractional calculus
harmonically convex function
Hermite–Hadamard inequality
Inequalities
Raina's function
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Summary:The pivotal proposal of this work is to present a new class of harmonically convex functions, namely, generalized harmonically ψ‐convex functions based on the fractal set technique for establishing inequalities of Hermite–Hadamard type, Pachpatte type, and certain related variants with respect to the Raina's function. With the aid of an auxiliary identity correlated with Raina's function, by generalized Hölder inequality, two Hermite–Hadamard‐type local fractional integral inequalities for generalized harmonically ψ‐convex functions are apprehended. The proposed technique provides the results by giving some special values to the parameters or imposing restrictive assumptions and is completely feasible for recapturing the existing results in the relative literature. To determine the computational efficiency of offered scheme, some numerical applications are discussed. The results of the scheme show that the approach is straightforward to apply and computationally very user‐friendly and accurate.
ISSN:0170-4214
1099-1476
DOI:10.1002/mma.7346