• Journal of applied mathematics & informatics
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• 제30권1_2호
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• pp.147-160
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• 2012

In this paper, we establish some sufficient conditions for the existence of positive solutions for a class of multi-point boundary value problem for fractional functional differential equations involving the Caputo fractional derivative. Our results are based on two fixed point theorems. Two examples are also provided to illustrate our main results.

• Journal of applied mathematics & informatics
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• 제22권1_2호
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• pp.295-306
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• 2006

In this paper, by using the Krasnoselskii fixed point theorem, we study the existence of 2m or 2m + 1 symmetric positive solutions of fourth-order two point boundary value problem y(4)(t) - f(t, y(t), y"(t))= 0, y(0) = y(1) = y'(0) = y"(1)=0.

• 한국경영과학회지
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• 제13권2호
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• pp.59-65
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• 1988

This paper discusses the problem of coordinating aggregate planning and production schedules, minimizing the combined set-up inventory and capacity costs. In this study, by using the relation of fixed production quantity and the number of set-up we develop a heuristirc procedure of solving the discrete demand, fixed production quantity, variable capacity problem. First, we obtain the trade-off between set-up cost and capacity cost, then search the point minimizing the combined inventory and capacity costs.

• Journal of applied mathematics & informatics
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• 제28권5_6호
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• pp.1171-1184
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• 2010

In this paper, by using fixed point theorems in cones, the existence of positive solutions is considered for nonlinear m-point boundary value problem for the following second-order dynamic equations on time scales $({\phi}(u^{\Delta}))^{\nabla}+a(t)f(t,\;u(t))=0$, t $\in$ (0, T), $u(0)=\sum\limits^{m-2}_{i=1}a_iu(\xi_i)$, $\phi(u^{\Delta}(T))=\sum\limits^{m-2}_{i=1}b_i{\phi}(u^{\Delta}(\xi_i))$, where $\phi$ : R $\rightarrow$ R is an increasing homeomorphism and positive homomorphism and ${\phi}(0)=0$. In [27], we obtained the existence results of the above problem for an increasing homeomorphism and positive homomorphism with sign changing nonlinearity. The purpose of this paper is to supplement with a result in the case when the nonlinear term f is nonnegative, and the most point we must point out for readers is that there is only the p-Laplacian case for increasing homeomorphism and positive homomorphism due to the sign restriction. As an application, one example to demonstrate our results are given.

• Kyungpook Mathematical Journal
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• 제53권3호
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• pp.371-383
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• 2013

In this paper, we investigate the uniqueness problem on entire functions sharing fixed points (ignoring multiplicities). Our main results improve and generalize some results due to Zhang [13], Qi-Yang [10] and Dou-Qi-Yang [1].

• Nonlinear Functional Analysis and Applications
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• 제29권1호
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• pp.131-164
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• 2024

In this research, we study a modified relaxed Tseng method with a single projection approach for solving common solution to a fixed point problem involving finite family of τ-demimetric operators and a quasi-monotone variational inequalities in real Hilbert spaces with alternating inertial extrapolation steps and adaptive non-monotonic step sizes. Under some appropriate conditions that are imposed on the parameters, the weak and linear convergence results of the proposed iterative scheme are established. Furthermore, we present some numerical examples and application of our proposed methods in comparison with other existing iterative methods. In order to show the practical applicability of our method to real word problems, we show that our algorithm has better restoration efficiency than many well known methods in image restoration problem. Our proposed iterative method generalizes and extends many existing methods in the literature.

• 대한수학회보
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• 제51권3호
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• pp.773-788
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• 2014

We introduce an iterative process which converges strongly to a common minimum-norm point of solutions of variational inequality problem for a monotone mapping and fixed points of a finite family of relatively nonexpansive mappings in Banach spaces. Our theorems improve most of the results that have been proved for this important class of nonlinear operators.

• Nonlinear Functional Analysis and Applications
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• 제29권1호
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• pp.113-130
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• 2024

In this work, we explore the existence and uniqueness results for a class of boundary value issues for implicit Volterra-Fredholm nonlinear integro-differential equations (IDEs) with Atangana-Baleanu-Riemann fractional (ABR-fractional) that have non-instantaneous multi-point fractional boundary conditions. The findings are supported by Krasnoselskii's fixed point theorem, Gronwall-Bellman inequality, and the Banach contraction principle. Finally, a demonstrative example is provided to support our key findings.

• Journal of applied mathematics & informatics
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• 제35권5_6호
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• pp.551-563
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• 2017

In this paper, by using fixed point theorems in cones, the existence of positive solutions is considered for nonlinear m-point boundary value problem for the following second-order dynamic equations on time scales $$u^{{\Delta}{\nabla}}(t)+a(t)f(t,u(t))=0,\;t{\in}(0,T),\;{\beta}u(0)-{\gamma}u^{\Delta}(0)=0,\;u(T)={\sum_{i=1}^{m-2}}\;a_iu({\xi}_i),\;m{\geq}3$$, where $a(t){\in}C_{ld}((0,T),\;[0,+{\infty}))$, $f{\in}C([0,T]{\times}[0,+{\infty}),\;(-{\infty},+{\infty}))$, the nonlinear term f is allowed to change sign. We obtain several existence theorems of positive solutions for the above boundary value problems. In particular, our criteria generalize and improve some known results [15] and the obtained conditions are different from related literature [14]. As an application, an example to demonstrate our results is given.

• 대한수학회지
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• 제52권6호
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• pp.1179-1194
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• 2015

In this paper, we introduce a new iterative algorithm for finding a common element of the set of solutions of a generalized mixed equilibrium problem related to a continuous monotone mapping, the set of solutions of a variational inequality problem for a continuous monotone mapping, and the set of fixed points of a continuous pseudocontractive mapping in Hilbert spaces. Weak convergence for the proposed iterative algorithm is proved. Our results improve and extend some recent results in the literature.