The Jensen-Mercer Inequality with Infinite Convex Combinations

Pavić, Zlatko

doi:10.36753/mathenot.559241

Cited by 6 publications

(3 citation statements)

References 8 publications

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“…w k x k , since the above inequality holds for arbitrary value of n, infinite convex combination ∞ k=1 w k x k converges in I and then affine combination a + b − ∞ k=1 w k x k converges in I, see for example [33], so it must be true as n tends to ∞, i.e.,…”

Section: )mentioning

confidence: 99%

Improvement and generalization of some results related to the class of harmonically convex functions and applications

Baloch¹,

Mughal²,

Chu³

et al. 2020

J. Math. Computer Sci.

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Discrete Jensen-type inequality for a harmonically convex function was established by Dragomir in [S. S. Dragomir, RGMIA Monographs, Victoria University, (2015)]. In [I. A. Baloch, A. H. Mughal, Y. M. Chu, M. De la Sen, Accepted in Aims Mathematics], Baloch et al. presented a variant of discrete Jensen-type inequality for harmonically convex functions. Moreover, they established a Jensen-type inequality for harmonically h-convex functions, and then they proved the variant of Jensen-type inequality for harmonically h-convex functions. Our results generalize and improve some earlier results in the literature (for example see [

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Section: )mentioning

confidence: 99%

Improvement and generalization of some results related to the class of harmonically convex functions and applications

Baloch¹,

Mughal²,

Chu³

et al. 2020

J. Math. Computer Sci.

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show abstract

“…For more details, see [3]. Pavić [4] obtained a generalized version of Jensen-Mercer's inequality in the following way:…”

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confidence: 99%

A Quantum Calculus View of Hermite–Hadamard–Jensen–Mercer Inequalities with Applications

et al. 2022

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In this paper, we derive some new quantum estimates of generalized Hermite–Hadamard–Jensen–Mercer type of inequalities, essentially using q-differentiable convex functions. With the help of numerical examples, we check the validity of the results. We also discuss some special cases which show that our results are quite unifying. To show the efficiency of our main results, we offer some interesting applications to special means.

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“…For more details, see [15]. Pavić [16] obtained a generalized version of the Jensen-Mercer's inequality in the following way:…”

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confidence: 99%

Fractional Jensen-Mercer Type Inequalities Involving Generalized Raina’s Function and Applications

et al. 2022

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The aim of this paper is to derive some new generalized fractional analogues of Mercer type inequalities, essentially using the convexity property of the functions and Raina’s function. We also discuss several new special cases which show that our results are, to an extent, unifying. In order to illustrate the significance of our results, we offer some interesting applications of our results to special means, error bounds, and q-digamma functions.

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The Jensen-Mercer Inequality with Infinite Convex Combinations

Abstract: The paper deals with discrete forms of double inequalities related to convex functions of one variable. Infinite convex combinations and sequences of convex combinations are included. The double inequality form of the Jensen-Mercer inequality and its variants are especially studied.

Cited by 6 publications

References 8 publications

Improvement and generalization of some results related to the class of harmonically convex functions and applications

Improvement and generalization of some results related to the class of harmonically convex functions and applications

A Quantum Calculus View of Hermite–Hadamard–Jensen–Mercer Inequalities with Applications

Fractional Jensen-Mercer Type Inequalities Involving Generalized Raina’s Function and Applications

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