Relative Strongly Exponentially Convex Functions

Noor, Muhammad Aslam; Noor, Khalida İnayat; Rassias, Themistocles M.

doi:10.1007/978-3-030-61732-5_16

Cited by 11 publications

(13 citation statements)

References 21 publications

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“…We now define the concept of exponentially convex function, which is mainly due to Antczak [3], Dragomir [6] and Noor et al [17].…”

Section: Definition 1 ([8]) a Function Fmentioning

confidence: 99%

“…An important class of convex functions, which is called an exponentially convex functions, was introduced and studied by Antczak in [3], Dragomir et al in [6] and Noor et al in [17]. In [1], Alirezai and Mathar have investigated their mathematical properties along with their potential applications in statistics and information theory, see [1,19].…”

Section: Introductionmentioning

confidence: 99%

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Integral inequalities for exponentially harmonically convex functions via fractional integral operators

Rashid¹,

Akdemir²,

Noor³

et al. 2021

MMN

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“…We now define the concept of exponentially convex function, which is mainly due to Antczak [3], Dragomir [6] and Noor et al [17].…”

Section: Definition 1 ([8]) a Function Fmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Integral inequalities for exponentially harmonically convex functions via fractional integral operators

Rashid¹,

Akdemir²,

Noor³

et al. 2021

MMN

Self Cite

View full text Add to dashboard Cite

“…For the applications of exponentially convex functions and strongly exponentially convex functions in different field of statistics, information theory and mathematical sciences, see [1,2,5], [24]- [28] and the references therein.…”

Section: Introductionmentioning

confidence: 99%

New inequalities for strongly exponentially generalized functions with applications

Kashuri

Liko

2022

Proyecciones (Antofagasta)

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The aim of this paper is to introduce a new class of functions called strongly exponentially generalized (m, ν1, ν2, g1, g2). Some new integral inequalities of trapezium-type for strongly exponentially generalized (m, ν1, ν2, g1, g2) functions with modulus c via Riemann-Liouville fractional integral are established. Also, some new estimates with respect to trapezium-type integral inequalities for strongly exponentially generalized (m, ν1, ν2, g1, g2) functions with modulus c via general fractional integrals are obtained. We show that the strongly exponentially generalized (m, ν1, ν2, g1, g2) functions with modulus c includes several other classes of functions. At the end, some new error estimates for trapezoidal quadrature formula are provided as well. This results may stimulate further research in different areas of pure and applied sciences.

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“…Pal and Wong [23] provided the application of exponentially convex functions in information, optimization, statistical theory and related areas. For other aspects of exponentially convex functions and their generalizations, see [2,5,12,14,16,18,19,[21][22][23]33].…”

Section: Introductionmentioning

confidence: 99%

Generalized Petrovic’s Inequalities for Coordinated Exponentially m-Convex Functions

Iqbal¹,

Noor

Noor³

et al. 2021

ijaa

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In this paper, we introduce a new class of convex function, which is called coordinated exponentially m-convex functions. Some new Petrović's type inequalities for exponentially m-convex functions and coordinated exponentially m-convex functions are derived. Lagrange-type and Cauchy-type mean value theorems for exponentially m−convex and coordinated exponentially m-convex functions are also derived. Several special cases are discussed. We also prove the Lagrange type and Cauchy type mean value theorems for exponentially m-convex and coordinated exponentially m−convex functions. Results proved in this paper may stimulate further research in different areas of pure and applied sciences.

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Relative Strongly Exponentially Convex Functions

Cited by 11 publications

References 21 publications

Integral inequalities for exponentially harmonically convex functions via fractional integral operators

Integral inequalities for exponentially harmonically convex functions via fractional integral operators

New inequalities for strongly exponentially generalized functions with applications

Generalized Petrovic’s Inequalities for Coordinated Exponentially m-Convex Functions

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