Some integral inequalities for p-convex functions

In this paper, a new type of convexity is defined, namely, the left–right-(k,h-m)-p IVM (set-valued function) convexity. Utilizing the definition of this new convexity, we prove the Hadamard inequalities for noninteger Katugampola integrals. These inequalities generalize the noninteger Hadamard inequalities for a convex IVM, (p,h)-convex IVM, p-convex IVM, h-convex, s-convex in the second sense and many other related well-known classes of functions implicitly. An apt number of numerical examples are provided as supplements to the derived results.

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“…If F * = F * with h(ξ ) = 1 and m = 1, p = 1, then the left-right-(k,h-m)-p-convex IVM reduces to the a p-convex function, see [45].…”

Section: Resultsmentioning

confidence: 99%

Some Novel Inequalities for LR-(k,h-m)-p Convex Interval Valued Functions by Means of Pseudo Order Relation

et al. 2022

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“…For the numerical methods, generalizations and other aspects of harmonic variational inequalities, see [11,29,30,33]. Iscan [13] and Noor et al [9,32,[34][35][36]40] have derived several Hermite-Hadamard type integral inequalities for the harmonic convex functions and their variant forms. It is amazing that the harmonic means have applications in electrical circuits.…”

Section: Introductionmentioning

confidence: 99%

Some New Classes of Harmonic Hemivariational Inequalities

Noor,

Noor

2023

EJMS

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Some new classes of harmonic hemivariational inequalities are introduced and investigated in this paper. It has been shown that the optimality conditions of the sum of two harmonic convex functions can be characterized by the harmonic hemivariational inequalities. Several special cases such as harmonic complementarity problems and related harmonic problems are discussed. The auxiliary principle technique is applied to suggest and analyze some iterative schemes for harmonic hemivariational inequalities. We prove the convergence of these iterative methods under some weak conditions. Our method of proof of the convergence criteria is simple compared to other techniques. Results obtained in this paper continue to hold for new and known classes of harmonic variational inequalities and related optimization problems. The ideas and techniques of this paper may inspire further research in various branches of pure and applied sciences.

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