• East Asian mathematical journal
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• v.19 no.1
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• pp.91-102
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• 2003

In this paper we prove the existence of mild and strong solutions of nonlinear delay integrodifferential equations with nonlocal conditions. The results are obtained by using the Schauder fixed point theorem and resolvent operator.

• Nonlinear Functional Analysis and Applications
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• v.27 no.4
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• pp.701-707
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• 2022

In this article, we put forward a new type of variational inclusion problem known as resolvent inclusion. An algorithm is given for approximating its solution. The convergence of the algorithm is explained with the help of an example and plots using Matlab.

• Bulletin of the Korean Mathematical Society
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• v.47 no.2
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• pp.263-274
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• 2010

In this paper, a new class of general nonlinear variational inclusions involving H-monotone is introduced and studied in Hilbert spaces. By applying the resolvent operator associated with H-monotone, we prove the existence and uniqueness theorems of solution for the general nonlinear variational inclusion, construct an iterative algorithm for computing approximation solution of the general nonlinear variational inclusion and discuss the convergence of the iterative sequence generated by the algorithm. The results presented in this paper improve and extend many known results in recent literatures.

• Bulletin of the Korean Mathematical Society
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• v.41 no.2
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• pp.241-256
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• 2004

In this paper, we introduce and study a new class of variational inclusions, called the general variational inclusion. We prove the equivalence between the general variational inclusions, the general resolvent equations, and the fixed-point problems, using the resolvent operator technique. This equivalence is used to suggest and analyze a few iterative algorithms for solving the general variational inclusions and the general resolvent equations. Under certain conditions, the convergence analyses are also studied. The results presented in this paper generalize, improve and unify a number of recent results.

• East Asian mathematical journal
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• v.26 no.5
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• pp.703-714
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• 2010

A new class of nonlinear set-valued mixed variational inclusions involving (A, ${\eta}$)-accretive mappings in Banach spaces is introduced and studied, which includes many kind of variational inclusion (inequality) and complementarity problems as special cases. By using the resolvent operator associated with (A, ${\eta}$)-accretive operator due to Lan-Cho-Verma, the existence of solution for this kind of variational inclusion is proved, and a new hybrid proximal point algorithm is established and suggested, the convergence and stability theorems of iterative sequences generated by new iterative algorithms are also given in q-uniformly smooth Banach spaces.

• East Asian mathematical journal
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• v.26 no.5
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• pp.671-680
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• 2010

A system of nonlinear variational inclusions involving general H-monotone operators in Banach spaces is introduced. Using the resolvent operator technique, we suggest an iterative algorithm for finding approximate solutions to the system of nonlinear variational inclusions, and establish the existence of solutions and convergence of the iterative algorithm for the system of nonlinear variational inclusions.

• Journal of the Chungcheong Mathematical Society
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• v.31 no.1
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• pp.13-27
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• 2018

By using of the Banach fixed point theorem, the theory of a strongly continuous semigroup of operators and resolvent operator, we investigate the existence and uniqueness of S-asymptotically ${\omega}-periodic$ mild solutions for some differential (integrodifferential) equations with piecewise constant argument when specially ${\omega}$ is an integer.

• Journal of the Korean Mathematical Society
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• v.44 no.4
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• pp.889-902
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• 2007

An existence theorem for a new class of parametric generalized mixed implicit quasi-variational inclusion problems is established in Hilbert spaces. Further, we study the behavior and sensitivity analysis of the solution set in this class of parametric variational inclusion problems.

• Communications of the Korean Mathematical Society
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• v.26 no.4
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• pp.685-693
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• 2011

General framework for proximal point algorithms based on the notion of (A, ${\eta}$)-maximal monotonicity (also referred to as (A, ${\eta}$)-monotonicity in literature) is developed. Linear convergence analysis for this class of algorithms to the context of solving a general class of nonlinear variational inclusion problems is successfully achieved along with some results on the generalized resolvent corresponding to (A, ${\eta}$)-monotonicity. The obtained results generalize and unify a wide range of investigations readily available in literature.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.20 no.1
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• pp.51-82
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• 2016

In view of ideas for semigroups, fractional calculus, resolvent operator and Banach contraction principle, this manuscript is generally included with existence and controllability (EaC) results for fractional neutral integro-differential systems (FNIDS) with state-dependent delay (SDD) in Banach spaces. Finally, an examples are also provided to illustrate the theoretical results.