• 대한수학회논문집
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• 제31권4호
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• pp.765-777
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• 2016

In this paper, we propose a new modied Ishikawa iteration for finding a common element of the set of solutions of an equilibrium problem and the set of fixed points of 2-generalized hybrid mappings in a Hilbert space. Our results generalize and improve some existing results in the literature. A numerical example is given to illustrate the usability of our results.

• Nonlinear Functional Analysis and Applications
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• 제26권5호
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• pp.1011-1020
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• 2021

In this paper, first order nonlinear Liouville-Caputo fractional differential equations is studied. The existence and uniqueness of a solution are investigated by using Krasnoselskii and Banach fixed point theorems and the method of lower and upper solutions. Finally, an example is given to illustrate our results.

• Nonlinear Functional Analysis and Applications
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• 제29권3호
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• pp.885-897
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• 2024

The purpose of this paper is to introduce a class of distance altering functions that establish the existence and uniqueness of fixed points of 𝜈-admissible mappings that are subject to a generalized (𝜓, 𝜑)-almost weakly contraction on a generalized b₂-metric space.

• Nonlinear Functional Analysis and Applications
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• 제29권1호
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• pp.209-224
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• 2024

The goal of this study is to instigate various new and novel optimum proximity point theorems using the notion of implicit relation type ℶ-proximal contraction for non-self mappings. An illustrated example is used to demonstrate the validity of the obtained results. Furthermore, some uniqueness results for proximal contractions are also furnished with partial order and graph. Various well-known discoveries in the present state-of-the-art are enhanced, extended, unified, and generalized by our findings. As an application, we generate some fixed point results fulfilling a modified contraction and a graph contraction, using the profundity of the established results.

• Journal of applied mathematics & informatics
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• 제26권1_2호
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• pp.61-73
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• 2008

In this paper common fixed point theorems dealing with compatible mappings of type (P) are established. As a application, the existence and uniqueness of common solution for a system of functional equations arising in dynamic programming is given. The results presented in this paper improve, generalize and unify the corresponding results in this field.

• 대한수학회논문집
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• 제17권1호
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• pp.37-51
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• 2002

Let X be a reflexive Banach space with a uniformly Gateaux differentiable norm, C a nonempty bounded open subset of X, and T a continuous mapping from the closure of C into X which is locally pseudo-contractive mapping on C. We show that if the closed unit ball of X has the fixed point property for nonexpansive self-mappings and T satisfies the following condition: there exists z $\in$ C such that ∥z-T(z)∥<∥x-T(x)∥ for all x on the boundary of C, then the trajectory tlongrightarrowz$_{t}$$\in$C, t$\in$[0, 1) defined by the equation z$_{t}$ = tT(z$_{t}$)+(1-t)z is continuous and strongly converges to a fixed point of T as t longrightarrow 1￣.ow 1￣.

• 대한수학회논문집
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• 제25권1호
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• pp.69-82
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• 2010

In this paper, we propose an iterative scheme for finding a common element of the set of solutions of an equilibrium problem and the set of fixed points of an asymptotically k-strict pseudo-contractive mapping in the setting of real Hilbert spaces. We establish some weak and strong convergence theorems of the sequences generated by our proposed scheme. Our results are more general than the known results which are given by many authors. In particular, necessary and sufficient conditions for strong convergence of our iterative scheme are obtained.

• 대한수학회논문집
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• 제25권4호
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• pp.571-581
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• 2010

Some convergence theorems for approximating to a common fixed point of an infinite family of strictly pseudocontractive mappings of Browder-Petryshyn type are proved in the setting of Banach spaces by using a new composite implicit iterative process with errors. The results presented in the paper generalize and improve the main results of Bai and Kim [1], Gu [4], Osilike [5], Su and Li [7], and Xu and Ori [8].

• 대한수학회논문집
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• 제24권1호
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• pp.41-55
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• 2009

A general common fixed point theorem for two pairs of weakly compatible mappings using an implicit function is proved without any continuity requirement which generalizes the result due to Popa [20, Theorem 3]. In process, several previously known results due to Fisher, Kannan, Jeong and Rhoades, Imdad and Ali, Imdad and Khan, Khan, Shahzad and others are derived as special cases. Some related results and illustrative examples are also discussed. As an application of our main result, we prove an existence theorem for the solution of simultaneous Hammerstein type integral equations.

• 한국수학교육학회지시리즈A:수학교육
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• 제29권1호
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• pp.41-45
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• 1990

S. Z. Wang, B. Y. Li, Z. M. Gao and K. Iseki proved some fixed point theorems on expansion mappings, which correspond some contractive mappings. In a recent paper, B. E. Rhoades generalized the results for in of mappings. In this paper, we obtain the following theorem, which generalizes the result of B. E. Rhoades. THEOREM. Let A, B, S and T be mappings from a complete metric space (X, d) into itself satisfying the following conditions: (1) ${\Phi}$(d(A$\chi$, By))$\geq$d(Sx, Ty) holds for all x and y in X, where ${\Phi}$ : R$\^$+/ \longrightarrowR$\^$+/ is non-decreasing, uppersemicontinuous and ${\Phi}$(t) < t for each t > 0, (2) A and B are surjective, (3) one of A, B, S and T is continuous, and (4) the pairs A, S and B, T are compatible. Then A, B, S and T have a unique common fixed point in X.