Some New Generalized Inequalities of Hardy Type Involving Several Functions on Time Scale Nabla Calculus

Saied, Ahmed I.; AlNemer, Ghada; Zakarya, Mohammed; Cesarano, Clemente; Rezk, Haytham M.

doi:10.3390/axioms11120662

Cited by 6 publications

(5 citation statements)

References 11 publications

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“…For more information about Hardy's inequality on time scales delta calculus, we suggest reading [21][22][23][24][25][26][27][28][29][30].…”

Section: Introductionmentioning

confidence: 99%

Exploring Generalized Hardy-Type Inequalities via Nabla Calculus on Time Scales

Rezk,

Mohammed,

Balogun

et al. 2023

Symmetry

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In this research, we aim to explore generalizations of Hardy-type inequalities using nabla Hölder’s inequality, nabla Jensen’s inequality, chain rule on nabla calculus and leveraging the properties of convex and submultiplicative functions. Nabla calculus on time scales provides a unified framework that unifies continuous and discrete calculus, making it a powerful tool for studying various mathematical problems on time scales. By utilizing this approach, we seek to extend Hardy-type inequalities beyond their classical continuous or discrete settings to a more general time scale domain. As specific instances of our discoveries, we have the integral inequalities previously established in the existing literature.

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“…For more information about Hardy's inequality on time scales delta calculus, we suggest reading [21][22][23][24][25][26][27][28][29][30].…”

Section: Introductionmentioning

confidence: 99%

Exploring Generalized Hardy-Type Inequalities via Nabla Calculus on Time Scales

Rezk,

Mohammed,

Balogun

et al. 2023

Symmetry

Self Cite

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“…where H f (x) = 1 For these reasons, Hardy's inequality, both in discrete and continuous case, has attracted a lot of interest of researchers, and there are many papers and monographs dedicated to its development; here, we mention, e.g., [2][3][4][5][6][7][8][9][10][11][12][13].…”

Section: Introductionmentioning

confidence: 99%

Generalizations of Hardy-Type Inequalities by Montgomery Identity and New Green Functions

Himmelreich

Pečarić

Pokaz

et al. 2023

Axioms

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“…For more details about the dynamic inequalities on time scales, see [5][6][7][8][9][10][11][12]. The organization of the paper as follows.…”

Section: Introductionmentioning

confidence: 99%

Novel Integral Inequalities on Nabla Time Scales with C-Monotonic Functions

et al. 2023

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Through the paper, we present several inequalities involving C-monotonic functions with C≥1, on nabla calculus via time scales. It is known that dynamic inequalities generate many different inequalities in different calculus. The main results will be proved by applying the chain rule formula on nabla calculus. As a special case for our results, when T=R, we obtain the continuous analouges of inequalities that had previously been proved in the literature. When T=N, the results, to the best of the authors’ knowledge, are essentially new. Symmetrical properties of C-monotonic functions are critical in determining the best way to solve inequalities.

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Some New Generalized Inequalities of Hardy Type Involving Several Functions on Time Scale Nabla Calculus

Cited by 6 publications

References 11 publications

Exploring Generalized Hardy-Type Inequalities via Nabla Calculus on Time Scales

Exploring Generalized Hardy-Type Inequalities via Nabla Calculus on Time Scales

Generalizations of Hardy-Type Inequalities by Montgomery Identity and New Green Functions

Novel Integral Inequalities on Nabla Time Scales with C-Monotonic Functions

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