• Kyungpook Mathematical Journal
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• 제50권3호
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• pp.371-378
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• 2010

In this paper, we establish new inequalities of Ostrowski's type for functions whose derivatives in absolute value are (${\alpha}$, m)-convex.

• 대한수학회보
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• 제30권2호
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• pp.201-212
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• 1993

It is our purpose in this paper to first establish an inequality in real uniformly smooth Banach spaces with modulus of smoothness of power type q > 1 that generalizes a well known Hilbert space inequality. Using our inequality, we shall then extend the above result of Qihou [15] on the Ishikawa iteration process from Hilbert spaces to these much more general Banach spaces. Furthermore, we shall prove that the Mann iteration process converges strongly to the unique fixed point of a quasi-contractive map in this general setting. No compactness assumption on K is required in our theorems.

• 호남수학학술지
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• 제45권2호
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• pp.340-358
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• 2023

This article establishes an equality for the case of twice-differentiable convex functions with respect to the conformable fractional integrals. With the help of this identity, we prove sundry midpoint-type inequalities by twice-differentiable convex functions according to conformable fractional integrals. Several important inequalities are obtained by taking advantage of the convexity, the Hölder inequality, and the power mean inequality. Using the specific selection of our results, we obtain several new and well-known results in the literature.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제31권1호
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• pp.33-48
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• 2024

In this study, we would like to state two refined results related to Hermite Hadamard type inequality for convex functions with two distinct techniques. Hence our obtained results would be better than the results already established for the class of convex functions. Applications to trapezoidal rule and special means are also discussed.

• 충청수학회지
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• 제25권2호
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• pp.313-318
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• 2012

The power inequality ${\prod}_{k=1}^{N}\;{x}_{k}^{x_{k}}\;{\geq}\;{\prod}_{k=1}^{N}\;{p}_{k}^{x_{k}}$ holds for the points $(x_1,{\ldots},x_N),(p_1,{\ldots},p_N)$ of the simplex. We show this using the analytic method combining Frostman's density theorem with the strong law of large numbers.

• Journal of applied mathematics & informatics
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• 제38권5_6호
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• pp.483-487
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• 2020

In this paper, we have proved a new theorem dealing with 𝜑 - |C, 𝛼|_k summability factors of infinite series under weaker conditions. Also, some new and known results are obtained.

• The Journal of Asian Finance, Economics and Business
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• 제8권4호
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• pp.613-624
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• 2021

This paper analyzes the relationship between income distribution and energy consumption from a Pareto optimal approach. For this purpose, the causality relationship between electricity consumption per capita (kWh) with respect to country groups and energy consumption per capita (kg of oil equivalent) along with gross domestic product per capita was analyzed. In addition to this purpose, a Pareto analysis was conducted to determine the countries with the highest per capita national income, how much of the world total energy they consume, and whether the law of power in the energy and electricity markets exists. Finally, the impact of official development assistance provided to low-income countries by high-income countries on the low-income countries' electricity and energy consumption was analyzed. In other words, it was questioned whether pareto redistribution policies serve the purpose or not. The Engle-Granger causality approach was used in the analysis of the causality relationship between variables. Our analysis indicated that, first, the energy data of the country groups may be inadequate in revealing income inequalities. Second, the existence of Pareto law of power and global income inequality can be explained based on energy data. Finally, Pareto optimal redistribution policies to eliminate income inequality remain inadequate in practice.

• International Journal of Computer Science & Network Security
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• 제24권1호
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• pp.85-94
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• 2024

In this paper, we present the very first time the generalized notion of (α, β, γ, δ) - convex (concave) function in mixed kind, which is the generalization of (α, β) - convex (concave) functions in 1^st and 2^nd kind, (s, r) - convex (concave) functions in mixed kind, s - convex (concave) functions in 1^st and 2^nd kind, p - convex (concave) functions, quasi convex(concave) functions and the class of convex (concave) functions. We would like to state the well-known Ostrowski inequality via SVN-Riemann Integrals for (α, β, γ, δ) - convex (concave) function in mixed kind. Moreover we establish some SVN-Ostrowski type inequalities for the class of functions whose derivatives in absolute values at certain powers are (α, β, γ, δ)-convex (concave) functions in mixed kind by using different techniques including Hölder's inequality and power mean inequality. Also, various established results would be captured as special cases with respect to convexity of function.

• Journal of Electrical Engineering and Technology
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• 제13권3호
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• pp.1099-1109
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• 2018

For practical consideration, economic dispatch (ED) problems in power system have non-smooth cost functions with equality and inequality constraints that makes the problems complex constrained nonlinear optimization problems. This paper proposes a new constraint handling method for equality and inequality constraints which is employed to solve ED problems, where the incremental rate is employed to enhance the modification process. In order to prove the applicability of the proposed method, the study cases are tested based on the classical particle swarm optimization (PSO) and differential evolution (DE) algorithm. The proposed method is evaluated for ED problems using six different test systems: 6-, 15-, 20-, 38-, 110- and 140-generators system. Simulation results show that it can always find the satisfactory solutions while satisfying the constraints.

• Journal of Power Electronics
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• 제11권3호
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• pp.327-334
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• 2011

Single-phase power factor correction (PFC) converter circuits are non-linear systems due to the contribution of their multiplier. This non-linearity causes difficulties in analysis and design. Models that reduce the system to a linear system involve considerable approximation, and produce results that are susceptible to instability problems. In this paper a piecewise affine (PWA) system is introduced for describing the nonlinear averaged model. Then robust output feedback controllers are established in terms of the linear matrix inequality (LMI). Simulation and experiments results show the effectiveness of the proposed control method.