• Journal of the Chungcheong Mathematical Society
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• v.35 no.1
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• pp.53-67
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• 2022

Nonlinear system of initial value problems involving R-L fractional derivative is studied. Monotone iterative technique coupled with lower and upper solutions is developed for the problem. It is successfully applied to study qualitative properties of solutions of nonlinear system of initial value problem when the function on the right hand side is nondecreasing.

• Journal of applied mathematics & informatics
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• v.7 no.2
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• pp.539-552
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• 2000

In this paper, we established the general comparison principles for IVP of impulsive differential equations with time variables, which strictly extend and improve the precious comparison results obtained by V. Lakes. et.al . and S.K.Kaul([3]-[7]). Whit the general comparison results, we constructed the monotone iterative sequences of solution for IVP of such equations which converges the maximal and minimal and minimal solutions , respectively.

• Kyungpook Mathematical Journal
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• v.48 no.4
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• pp.553-558
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• 2008

The method of upper and lower solutions coupled with monotone iterative technique is used to obtain the results of existence and uniqueness for an anti-periodic boundary value problem of impulsive differential equations with delay.

• Journal of applied mathematics & informatics
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• v.20 no.1_2
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• pp.465-478
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• 2006

In this paper, we introduce a new class of completely generalized strongly nonlinear quasivariational inequalities and establish its equivalence with a class of fixed point problems by using the resolvent operator technique. Utilizing this equivalence, we develop a three-step iterative scheme with errors, obtain a few existence theorems of solutions for the completely generalized non-linear strongly quasivariational inequality involving relaxed monotone, relaxed Lipschitz, strongly monotone and generalized pseudocontractive mappings and prove some convergence and stability results of the sequence generated by the three-step iterative scheme with errors. Our results include several previously known results as special cases.

• Kyungpook Mathematical Journal
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• v.59 no.1
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• pp.191-202
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• 2019

The aim of this paper is to develop a monotone iterative technique by introducing upper and lower solutions to Riemann-Liouville fractional differential equations with deviating arguments and integral boundary conditions. As an application of this technique, existence and uniqueness results are obtained.

• East Asian mathematical journal
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• v.24 no.1
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• pp.1-6
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• 2008

In this paper, we introduce a system of nonlinear variational inclusions involving (A, $\eta$)-monotone mappings in the framework of Hilbert spaces. Based on the generalized resolvent operator technique associated with (A, $\eta$)-monotonicity, the approximation solvability of solutions using an iterative algorithm is investigated. Our results improve and extend the recent ones announced by many others.

• Journal of applied mathematics & informatics
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• v.33 no.3_4
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• pp.401-415
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• 2015

In this paper, we propose a modified proximal point algorithm which consists of a resolvent operator technique step followed by a generalized projection onto a moving half-space for approximating a solution of a variational inclusion involving a maximal monotone mapping and a monotone, bounded and continuous operator in Banach spaces. The weak convergence of the iterative sequence generated by the algorithm is also proved.

• Nonlinear Functional Analysis and Applications
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• v.28 no.1
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• pp.175-203
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• 2023

In this paper, we study an iterative algorithm that is based on inertial proximal and contraction methods embellished with relaxation technique, for finding common solution of monotone variational inclusion, and fixed point problems of pseudocontractive mapping in real Hilbert spaces. We establish a strong convergence result of the proposed iterative method based on prediction stepsize conditions, and under some standard assumptions on the algorithm parameters. Finally, some special cases of general problem are given as applications. Our results improve and generalized some well-known and related results in literature.

• Journal of the Korean Mathematical Society
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• v.57 no.1
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• pp.61-88
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• 2020

In this paper, we investigate the existence of mild solutions for a class of fractional impulsive evolution equation with periodic boundary condition by means of the method of upper and lower solutions and monotone iterative method. Using the theory of Kuratowski measure of noncompactness, a series of results about mild solutions are obtained. Finally, two examples are given to illustrate our results.

• Bulletin of the Korean Mathematical Society
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• v.27 no.2
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• pp.165-172
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• 1990

In this paper, we study a method which speeds up the convergence of monotone iterations and give some numerical examples of the types (2) and (3). In [2] this method has been applied to a system of hyperbolic differential equations with initial and boundary conditions.