• Bulletin of the Korean Mathematical Society
• /
• v.45 no.3
• /
• pp.467-475
• /
• 2008

The aim of the present paper is three fold. Firstly, we obtain common fixed point theorems for a pair of selfmaps satisfying nonexpansive or Lipschitz type condition by using the notion of pointwise R-weak commutativity but without assuming the completeness of the space or continuity of the mappings involved (Theorem 1, Theorem 2 and Theorem 3). Secondly, we generalize the results obtained in first three theorems for four mappings by replacing the condition of noncompatibility of maps with the property (E.A) and using the R-weak commutativity of type $(A_g)$ (Theorem 4). Thirdly, in Theorem 5, we show that if the aspect of noncompatibility is taken in place of the property (E.A), the maps become discontinuous at their common fixed point. We, thus, provide one more answer to the problem posed by Rhoades [11] regarding the existence of contractive definition which is strong enough to generate fixed point but does not forces the maps to become continuous.

• Nonlinear Functional Analysis and Applications
• /
• v.26 no.5
• /
• pp.1045-1057
• /
• 2021

We present some fixed point theorems for ((𝛼₁, 𝛼₂, ⋯, 𝛼_n), p)-nonexpansive mappings in CAT(0) spaces. Moreover the properties of the fixed points set are studied. Many of them have been derived from new condition on these mappings, which makes the nonexpansive mapping T_𝛼 := 𝛼₁T ⊕ 𝛼₂T² ⊕ ⋯ ⊕ 𝛼_nTⁿ.

• Kyungpook Mathematical Journal
• /
• v.32 no.3_spc
• /
• pp.463-475
• /
• 1992

• Journal of applied mathematics & informatics
• /
• v.29 no.1_2
• /
• pp.293-309
• /
• 2011

The purpose of this article is to prove strong convergence theorems for weak relatively nonexpansive mapping which is firstly presented in this article. In order to get the strong convergence theorems for weak relatively nonexpansive mapping, the monotone CQ iteration method is presented and is used to approximate the fixed point of weak relatively nonexpansive mapping, therefore this article apply above results to prove the strong convergence theorems of zero point for maximal monotone operators in Banach spaces. Noting that, the CQ iteration method can be used for relatively nonexpansive mapping but it can not be used for weak relatively nonexpansive mapping. However, the monotone CQ method can be used for weak relatively nonexpansive mapping. The results of this paper modify and improve the results of S.Matsushita and W.Takahashi, and some others.

• Journal of applied mathematics & informatics
• /
• v.26 no.3_4
• /
• pp.785-791
• /
• 2008

In this paper, we give a generalized contractive type condition for a pair of self maps of a metric space and analyze the existence of common fixed points for these maps of a metric space.

• Bulletin of the Korean Mathematical Society
• /
• v.40 no.4
• /
• pp.577-581
• /
• 2003

Some random fixed point theorems for weakly inward multivalued random maps are obtained in Banach spaces.

• Journal of the Chungcheong Mathematical Society
• /
• v.28 no.3
• /
• pp.451-463
• /
• 2015

A continuous and non-decreasing function ${\psi}$ and another continuous function ${\phi}$ with ${\phi}(z)=0{\Leftrightarrow}z=0$ defined on $\mathbb{C}^+=\{x+yi:x,y{\geq}0\}$ are introduced, the ${\psi}-{\phi}$-contractive or expansive type conditions are considered, and the existence theorems of common fixed points for two mappings defined on a complex valued metric space are obtained. Also, Banach contraction principle and a fixed point theorem for a I-expansive type mapping are given on complex valued metric spaces.

• The Pure and Applied Mathematics
• /
• v.31 no.3
• /
• pp.299-310
• /
• 2024

The probabilistic metric space as one of the important generalizations of metric space, was introduced by Menger [16] in 1942. Later, Choi et al. [6] initiated the notion of bicomplex-valued metric spaces (bi-CVMS). Recently, Bhattacharyya et al. [3] linked the concept of bicomplex-valued metric spaces and menger spaces, and initiated menger space with bicomplex-valued metric. Here, in this paper, we have taken probabilistic metric space with bicomplex-valued metric, i.e., bicomplexvalued probabilistic metric space and proved some common fixed point theorems using converse commuting mappings in this space.

• Journal of the Chungcheong Mathematical Society
• /
• v.21 no.3
• /
• pp.327-337
• /
• 2008

In this paper, we prove strong convergence theorems of Halpern iteration for relatively asymptotically nonexpansive mappings in the framework of Banach spaces. Our results extend and improve the recent ones announced by [C. Martinez-Yanes, H. K. Xu, Strong convergence of the CQ method for fixed point iteration processes, Nonlinear Anal. 64 (2006), 2400-2411], [X. Qin, Y. Su, Strong convergence theorem for relatively nonexpansive mappings in a Banach space, Nonlinear Anal. 67 (2007), 1958-1965] and many others.

• Korean Journal of Mathematics
• /
• v.27 no.4
• /
• pp.861-877
• /
• 2019

The aim of this paper is to extend some existing fixed point results for asymptotically regular mappings to fuzzy metric spaces. For this purpose some contractive type conditions with respect to an altering distance function are used. Some new common fixed point results have been derived for such mappings. We provide suitable examples to justify our study.