• Nonlinear Functional Analysis and Applications
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• v.27 no.4
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• pp.813-837
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• 2022

In this paper we consider inverse problem for a general class of nonlinear stochastic differential equations on Hilbert spaces whose generating operators (drift, diffusion and jump kernels) are unknown. We introduce a class of function spaces and put a suitable topology on such spaces and prove existence of optimal generating operators from these spaces. We present also necessary conditions of optimality including an algorithm and its convergence whereby one can construct the optimal generators (drift, diffusion and jump kernel).

• East Asian mathematical journal
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• v.36 no.5
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• pp.571-581
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• 2020

In this paper, an equilibrium problems involving a finite family of maximal monotone operators and inverse-strongly monotone operators are introduced and investigated. A strong convergence theorem of common solutions is obtained in Hilbert spaces.

• Nonlinear Functional Analysis and Applications
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• v.26 no.1
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• pp.105-115
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• 2021

Generalized pseudo-differential operators (PDO) involving fractional Fourier transform associate with the symbol a(x, y) whose derivatives satisfy certain growth condition is defined. The product of two generalized pseudo-differential operators is shown to be a generalized pseudo-differential operator.

• Journal of the Korean Mathematical Society
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• v.37 no.6
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• pp.901-913
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• 2000

This is a summary of results involving the development of a theory of an index of an isolated critical point for densely defined nonlinear operators of type (S(sub)+)(sub)0,L. This index theory is associated with a degree theory, for such operators, whch has been recently developed by the authors.

• Kyungpook Mathematical Journal
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• v.63 no.1
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• pp.45-60
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• 2023

In this paper we suggest an enhanced Geraghty-type contractive mapping for examining the existence properties of classical nonlinear operators with or without prior degenerates. The nonlinear operators are proved to exist with the imposition of the Geraghty-type condition in a non-empty closed subset of complete metric spaces. To showcase some efficacies of the Geraghty-type condition, convergent rate and stability are deduced. The results are used to study some asymptotic properties of perturbed integral and hypergeometric operators. The results also extend and generalize some existing Geraghty-type conditions.

• 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.13 no.1
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• pp.119-130
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• 2000

We give alternative proof of the existence theorem for certain elliptic systems describing competing interactions with nonlinear di usion. The existence of positive solution depends on the sign of the principal eigenvalue of suitable operators of Schr$\ddot{o}$dinger type. If the sign of such operators are both positive, then system has a positive solution. The main tool employed is the fixed point index of compact operator on positive cones.

• Bulletin of the Korean Mathematical Society
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• v.54 no.2
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• pp.607-618
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• 2017

In this paper, we introduce a quadratic stochastic operators on the set of all probability measures of a measurable space. We study the dynamics of the Lebesgue quadratic stochastic operator on the set of all Lebesgue measures of the set [0, 1]. Namely, we prove the regularity of the Lebesgue quadratic stochastic operators.

• Journal of the Korean Mathematical Society
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• v.25 no.2
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• pp.289-301
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• 1988

• 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.