• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.27 no.3
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• pp.160-179
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• 2023

In this paper, we investigate the existence and diameter of the approximate fixed point results on E-metric spaces (not necessarily complete) by using various cyclic contraction mappings, including the B-cyclic contraction, the Bianchini cyclic contraction, the Hardy-Rogers cyclic contraction, and so on. Additionally, we prove the approximate fixed point results for rational type cyclic contraction mappings, which were discussed mainly in [35] and [37], in the setting of E-metric space. Also, a few examples are provided to demonstrate our findings. Subsequently, we discuss some applications of approximate fixed point results in the field of applied mathematics rigorously.

• Journal of applied mathematics & informatics
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• v.9 no.1
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• pp.433-440
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• 2002

In this paper, we first prove the existence of fixed points for fuzzy mappings that satisfy a certain contractive condition. Also, we give a fixed point theorem for generalized contractive fuzzy mapping by using Caristi's by fixed point theorem.

• East Asian mathematical journal
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• v.18 no.2
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• pp.225-233
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• 2002

In this paper, we obtain the common fixed point for fuzzy mappings satisfying an implicit relation. We improve earlier results of this line.

• Journal of the Korean Mathematical Society
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• v.31 no.3
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• pp.333-337
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• 1994

Many authors[3][4][5] constructed and examined some processes for the fixed point of strictly pseudocontractive mapping in various Banach spaces. In fact the fixed point of strictly pseudocontractive mapping is the zero of strongly accretive operators. So the same processes are used for the both circumstances. Reich[3] proved that Mann-iteration precess can be applied to approximate the zero of strongly accretive operator in uniformly smooth Banach spaces. In the above paper he asked whether the fact can be extended to other Banach spaces the duals of which are not necessarily uniformly convex. Recently Schu[4] proved it for uniformly continuous strictly pseudocontractive mappings in smooth Banach spaces. In this paper we proved that Mann-iteration process can be applied to approximate the fixed point of strictly pseudocontractive mapping in certain Banach spaces.

• Communications of the Korean Mathematical Society
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• v.28 no.2
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• pp.319-333
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• 2013

Using the fixed point method, we prove the generalized Hyers-Ulam-Rassias stability of the following functional equation in multi-Banach spaces: $${\sum_{1{\leq}i_<j{\leq}n}}\;f(\frac{r_ix_i+r_jx_j}{k})=\frac{n-1}{k}{\sum_{i=1}^n}r_if(x_i)$$.

• Journal of the Korean Mathematical Society
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• v.39 no.4
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• pp.579-591
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• 2002

New fixed Point results for the (equation omitted) selfmaps ale given. The analysis relies on a factorization idea. The notion of an essential map is also introduced for a wide class of maps. Finally, from a new fixed point theorem of ours, we deduce some equilibrium theorems.

• Kyungpook Mathematical Journal
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• v.62 no.4
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• pp.673-687
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• 2022

In this study, we solve the Cayley inclusion problem and the fixed point problem in real Hilbert space using Tseng's technique with inertial extrapolation in order to obtain more efficient results. We provide a strong convergence theorem to approximate a common solution to the Cayley inclusion problem and the fixed point problem under some appropriate assumptions. Finally, we present a numerical example that satisfies the problem and shows the computational performance of our suggested technique.

• Nonlinear Functional Analysis and Applications
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• v.27 no.4
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• pp.785-795
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• 2022

In this paper, we introduce a Mann-like three step iteration method and show that it can be used to approximate the fixed point of a weak contraction mapping. Furthermore, we prove that this scheme is equivalent to the Mann iterative scheme. A comparison is made with the other third order iterative methods. Results are presented in a table to support our conclusion.

• Journal of applied mathematics & informatics
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• v.33 no.5_6
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• pp.699-721
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• 2015

This paper investigates the existence of mild solution for a fractional integro-differential equations with a deviating argument and nonlocal initial condition in an arbitrary separable Hilbert space H via technique of approximations. We obtain an associated integral equation and then consider a sequence of approximate integral equations obtained by the projection of considered associated nonlocal fractional integral equation onto finite dimensional space. The existence and uniqueness of solutions to each approximate integral equation is obtained by virtue of the analytic semigroup theory via Banach fixed point theorem. Next we demonstrate the convergence of the solutions of the approximate integral equations to the solution of the associated integral equation. We consider the Faedo-Galerkin approximation of the solution and demonstrate some convergenceresults. An example is also given to illustrate the abstract theory.

• Journal of the Korean Mathematical Society
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• v.53 no.1
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• pp.89-114
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• 2016

In this paper, we introduce and study an explicit hybrid relaxed extragradient iterative method to approximate a common solution to generalized mixed equilibrium problem and fixed point problem for a nonexpansive semigroup in Hilbert space. Further, we prove that the sequence generated by the proposed iterative scheme converges strongly to the common solution to generalized mixed equilibrium problem and fixed point problem for a nonexpansive semigroup. This common solution is the unique solution of a variational inequality problem and is the optimality condition for a minimization problem. The results presented in this paper are the supplement, improvement and generalization of the previously known results in this area.