Characterizations of r-Convex Functions

Zhao, Yingxue; Wang, Shouyang; Uría, Luis Coladas

doi:10.1007/s10957-009-9617-1

Cited by 17 publications

(9 citation statements)

References 13 publications

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“…A function f is r-convex (r-concave) if r > 0 (r < 0). The subject of rconvex attracted the interest of some researchers such as Antczak [3] and Zhao et al [23]. They studied some properties of r-convex that have important applications in mathematical programming and optimization.…”

Section: Definitions and Preliminary Resultsmentioning

confidence: 99%

One Class of Generalized Convex Functions in the Sense of Beckenbach

Badr¹,

Faried²,

Ali³

2022

Int. J. of Appl. Math.

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Section: Definitions and Preliminary Resultsmentioning

confidence: 99%

One Class of Generalized Convex Functions in the Sense of Beckenbach

Badr¹,

Faried²,

Ali³

2022

Int. J. of Appl. Math.

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“…В последнее время наблюдается повышение уровня абстрактности теории выпуклых функций, появляются новые способы характеризации выпуклости (например, в работе [22] устанавливаются аналоги неравенств типа неравенств Эрмита -Адамара для гармоническо-логарифмически выпуклых (log-HG-выпуклых) функций, а в работе [23] -для гармоническо-геометрически выпуклых функций). Одно из концептуальных обобщений понятия выпуклости (r-выпуклость) функции обсуждается в работе [24]. Авторами введено в рассмотрение понятие строгой r-выпуклости, что существенно для приложений.…”

Section: результаты исследованияunclassified

Оn the implementation of a transdisciplinary approach in preparing future mathematics teachers

Kalinin

Панкратова

2022

Obraz. nauka

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Introduction. The disparate study of certain areas and branches of knowledge, characteristic of the disciplinary approach, has largely lost its position, recognising the inevitability of interdisciplinary cooperation. At present, interdisciplinarity is already being comprehended at a new level, creating the prerequisites for the introduction of a transdisciplinary approach to solving complex problems, including in the educational sphere.Aim. The current research aims to present the transdisciplinary teaching means, which are relevant in the process of training future teachers of mathematics, and which are identified on the basis of an analysis of the content of education.Methodology and research methods. General scientific and empirical methods were used to develop the ideological basis of the study. The aforementioned methods allowed the authors to draw up a complete picture of the problem under study, to identify its patterns and trends, to understand the essence. The search and selection of mathematics subject content with transdisciplinary properties was based on a systematic and interdisciplinary approach. At the stage of testing the research hypothesis, the competency-based approach was decisive, and tactical tasks were solved by referring to the activity approach. In addition, the main provisions of the concepts of humanisation and humanitarisation of education, as well as the principles of fundamentalisation of mathematical education, were taken into account.Results and theoretical significance. The expediency of using inequalities and convex functions in the training of future mathematics teachers in the context of a transdisciplinary approach is substantiated. A phased description of the work carried out allows us to trace the methods of reflecting the modern scientific content of the relevant topics, conditions, means and expected results of pedagogical interaction. The theory and methods of teaching mathematics at the university are enriched with a qualitatively new vision of the educational potential of the concepts of inequality and a convex function.Practical significance. The introduction of inequalities and convex functions in the process of future mathematics teachers training at Vyatka State University made it possible to demonstrate the possibilities of a transdisciplinary approach in the development of students’ worldview and the formation of professionally significant students’ competencies. The presented means of implementing the transdisciplinary approach can also be comprehended in teaching students of other areas of training.

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“…Alirazaie and Mahar [1] investigated the impact of exponentially concave functions in information theory. Zhao et al [200] discussed some characterizations of r-convex functions. Awan et al [5] also investigated some classes of exponentially convex functions.…”

Section: Introductionmentioning

confidence: 99%

New Trends in General Variational Inequalities

Noor

Rassias

2020

Acta Appl Math

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It is well known that general variational inequalities provide us with a unified, natural, novel and simple framework to study a wide class of unrelated problems, which arise in pure and applied sciences. In this paper, we present a number of new and known numerical techniques for solving general variational inequalities and equilibrium problems using various techniques including projection, Wiener-Hopf equations, dynamical systems, the auxiliary principle and the penalty function. General variational-like inequalities are introduced and investigated. Properties of higher order strongly general convex functions have been discussed. The auxiliary principle technique is used to suggest and analyze some iterative methods for solving higher order general variational inequalities. Some new classes of strongly exponentially general convex functions are introduced and discussed. Our proofs of convergence are very simple as compared with other methods. Our results present a significant improvement of previously known methods for solving variational inequalities and related optimization problems. Since the general variational inequalities include (quasi) variational inequalities and (quasi) implicit complementarity problems as special cases, these results continue to hold for these problems. Some numerical results are included to illustrate the efficiency of the proposed methods. Several open problems have been suggested for further research in these areas.

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Characterizations of r-Convex Functions

Cited by 17 publications

References 13 publications

One Class of Generalized Convex Functions in the Sense of Beckenbach

One Class of Generalized Convex Functions in the Sense of Beckenbach

Оn the implementation of a transdisciplinary approach in preparing future mathematics teachers

New Trends in General Variational Inequalities

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