Exponentially Convex Functions on the Coordinates and Novel Estimations via Riemann-Liouville Fractional Operator

Akdemir, Ahmet Ocak; Aslan, Sinan; Dokuyucu, Mustafa Ali; Çelik, Ercan

doi:10.1155/2023/4310880

Cited by 5 publications

(1 citation statement)

References 19 publications

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“…This interesting class of functions is defined as follows ( mentioned in ( [6]). For more information, see the papers [1][2][3][4][5] and [22]- [24]. Another aspect due to which the convexity theory has attracted many researchers 400 E. G ÜL, A. YALC ¸IN is its close relationship with theory of inequalities.…”

Section: Introductionmentioning

confidence: 99%

Some integral inequalities through tempered fractional integral operator

Gül,

Yalçın

2024

Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat.

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Section: Introductionmentioning

confidence: 99%

Some integral inequalities through tempered fractional integral operator

Gül,

Yalçın

2024

Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat.

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Existence of positive weak solutions for stationary fractional Laplacian problem by using sub-super solutions

Guefaifia,

Boulaaras,

Jan

2024

Georgian Mathematical Journal

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In this work, we establish a theorem concerning the extension of positive weak solutions for a stationary fractional Laplacian problem featuring weight functions that change sign. Additionally, we introduce novel conditions to ensure the existence of a positive solution for the given problem. These conditions are derived utilizing the approach of sub-super solutions, thereby extending and complementing existing results in the literature.

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Initialization of the difference of convex functions optimization algorithm for nonconvex quadratic problems

Achour,

Rahmoune,

Ouchenane

et al. 2024

Filomat

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The Difference of Convex functions Algorithm (DCA) is used to solve nonconvex optimization problems over a certain convex set, specifically quadratic programming ones, generally by finding approximate solutions. DCA efficiency depends on two basic parameters that directly affect the speed of its convergence towards the optimal solution. The first parameter is the selected decomposition and the second is the assigned initial point. The aim of this study was to create a new algorithm that allows overcoming the need for a pre-selected initial estimate of the DCA. To achieve this aim, we performed an experimental study with 107 test problems using an implementation framework with MATLAB. Assessment was based on key performance indicators: (a) the time required to reach the initial point and solution and (b) the number of iterations. We selected three initial points, the first (xlin 0) is the minimum of the linear part of the nonconvex quadratic problem (NCQP), the second (xcvx 0) is the approximate global minimum of the convex part, and the third (xcve 0) is the approximate global minimum of the concave part. We compared between the minimuma computed by DCA for each of the three initial estimates. The results demonstrated clear advantage of the DCA algorithm with (xlin 0). Based on this outcome, we constructed a novel algorithm called Initialized DCA (IDCA) that allows implementation of the DCA with the best initial estimate without the requirement for a pre-determined initial point.

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Exponentially Convex Functions on the Coordinates and Novel Estimations via Riemann-Liouville Fractional Operator

Cited by 5 publications

References 19 publications

Some integral inequalities through tempered fractional integral operator

Some integral inequalities through tempered fractional integral operator

Existence of positive weak solutions for stationary fractional Laplacian problem by using sub-super solutions

Initialization of the difference of convex functions optimization algorithm for nonconvex quadratic problems

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