• East Asian mathematical journal
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• v.34 no.3
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• pp.265-285
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• 2018

The main purpose of this paper, by using the resolvent operator technique associated with randomly (A, ${\eta}$, m)-accretive operator is to establish an existence and convergence theorem for a class of system of random nonlinear equations with fuzzy mappings in Banach spaces. Our works are improvements and generalizations of the corresponding well-known results.

• East Asian mathematical journal
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• v.14 no.2
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• pp.299-309
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• 1998

• Communications of the Korean Mathematical Society
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• v.32 no.2
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• pp.333-352
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• 2017

In this research work, by using the random resolvent operator techniques associated with random ($A_t$, ${\eta}_t$, $m_t$)-monotone operators, is to established an existence and convergence theorems for a class of fuzzy system of random nonlinear equations with fuzzy mappings in Hilbert spaces. Our results improve and generalized the corresponding results of the recent works.

• Journal of applied mathematics & informatics
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• v.30 no.1_2
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• pp.173-181
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• 2012

In this paper, we study the control problems governed by the semilinear parabolic type equation in Hilbert spaces. Under the Lipschitz continuity condition of the nonlinear term, we can obtain the sufficient conditions for the approximate controllability of nonlinear functional equations with nonlinear monotone hemicontinuous and coercive operator. The existence, uniqueness and a variation of solutions of the system are also given.

• East Asian mathematical journal
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• v.38 no.1
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• pp.129-141
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• 2022

We obtain interior regularity estimates in the weighted Orlicz spaces for viscosity solutions of fully nonlinear uniformly parabolic equations u_t - F(D² u, x, t) = f(x, t) in Q₁ under relaxed structure conditions on the nonlinear operator F.

• East Asian mathematical journal
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• v.26 no.3
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• pp.403-413
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• 2010

In this paper, we consider a doubly nonlinear parabolic equation related to the Leray-Lions operator with Dirichlet boundary condition and initial data given. By exploiting a suitable implicit time-discretization technique, we obtain the existence of global strong solution.

• Bulletin of the Korean Mathematical Society
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• v.51 no.1
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• pp.43-54
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• 2014

This paper is concerned with nonlinear evolution differential equations with infinite delay in Banach spaces. Using Kato's approximating approach, existence and uniqueness of strong solutions are obtained.

• Communications of the Korean Mathematical Society
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• v.11 no.4
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• pp.1003-1013
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• 1996

The existence of a bounded generalized solution on the real line for a nonlinear functional evolution problem of the type $$ (FDE) x'(t) + A(t,x_t)x(t) \ni 0, t \in R $$ in a general Banach spaces is considered. It is shown that (FDE) has a bounded generalized solution on the whole real line with well-known Crandall and Pazy's result and recent results of the functional differential equations involving the operator A(t).

• East Asian mathematical journal
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• v.24 no.3
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• pp.295-304
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• 2008

We approximate a locally unique solution of a nonlinear operator equation containing a non-differentiable operator in a Banach space setting using Newton's method. Sufficient conditions for the semilocal convergence of Newton's method in this case have been given by several authors using mainly increasing sequences [1]-[6]. Here, we use center as well as Lipschitz conditions and decreasing majorizing sequences to obtain new sufficient convergence conditions weaker than before in many interesting cases. Numerical examples where our results apply to solve equations but earlier ones cannot [2], [5], [6] are also provided in this study.

• Communications of the Korean Mathematical Society
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• v.11 no.1
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• pp.117-129
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• 1996

In this paper, some existence theorem of solutins for nonlinear operator equations with probabilistic contractor in probabilistic normed spaces are given.