http://chineseinput.net/에서 pinyin(병음)방식으로 중국어를 변환할 수 있습니다.
변환된 중국어를 복사하여 사용하시면 됩니다.
FIXED POINTS OF BETTER ADMISSIBLE MAPS ON GENERALIZED CONVEX SPACES
Park, Se-Hie Korean Mathematical Society 2000 대한수학회지 Vol.37 No.6
We obtain generalized versions of the Fan-Browder fixed point theorem for G-convex spaces. We define the class B of better admissible multimaps on G-convex spaces and show that any closed compact map in b fro ma locally G-convex uniform space into itself has a fixed point.
STRONG CONVERGENCE IN NOOR-TYPE ITERATIVE SCHEMES IN CONVEX CONE METRIC SPACES
이병수 한국수학교육학회 2015 純粹 및 應用數學 Vol.22 No.2
The author considers a Noor-type iterative scheme to approximate com- mon fixed points of an infinite family of uniformly quasi-sup(fn)-Lipschitzian map- pings and an infinite family of gn-expansive mappings in convex cone metric spaces. His results generalize, improve and unify some corresponding results in convex met- ric spaces [1, 3, 9, 16, 18, 19] and convex cone metric spaces [8].
CONVERGENCE OF A NEW MULTISTEP ITERATION IN CONVEX CONE METRIC SPACES
Gunduz, Birol Korean Mathematical Society 2017 대한수학회논문집 Vol.32 No.1
In this paper, we propose a new multistep iteration for a finite family of asymptotically quasi-nonexpansive mappings in convex cone metric spaces. Then we show that our iteration converges to a common fixed point of this class of mappings under suitable conditions. Our result generalizes the corresponding result of Lee [5] from the closed convex subset of a convex cone metric space to whole space.
THE PROXIMAL POINT ALGORITHM IN UNIFORMLY CONVEX METRIC SPACES
Choi, Byoung Jin,Ji, Un Cig Korean Mathematical Society 2016 대한수학회논문집 Vol.31 No.4
We introduce the proximal point algorithm in a p-uniformly convex metric space. We first introduce the notion of p-resolvent map in a p-uniformly convex metric space as a generalization of the Moreau-Yosida resolvent in a CAT(0)-space, and then we secondly prove the convergence of the proximal point algorithm by the p-resolvent map in a p-uniformly convex metric space.
Dileep Kumar Sharma,Jayesh Tiwari 한국수학교육학회 2022 純粹 및 應用數學 Vol.29 No.4
In the present paper, we introduce the notation of δ-convex rectangular metric spaces with the help of convex structure. We investigate fixed point results concerning Kannan-type contraction and Reich-type contraction in such spaces. We also propound an ingenious example in reference of given new notion.
Kyung Soo Kim 경남대학교 수학교육과 2021 Nonlinear Functional Analysis and Applications Vol.26 No.3
A convergence theorem for a generalized $\varphi$-weakly contractive mapping is proved which satisfy a generalized contraction condition on a complete metrically convex metric space. The result in this paper generalizes the relevant results due to Rhoades [18], Alber and Guerre-Delabriere [1], Khan and Imdad [14], Xue [20] and others. An illustrative example is also furnished in support of our main result.
FIXED POINT THEOREMS IN COMPLEX VALUED CONVEX METRIC SPACES
G. A. Okeke,S. H. Khan,J. K. Kim 경남대학교 수학교육과 2021 Nonlinear Functional Analysis and Applications Vol.26 No.1
Our purpose in this paper is to introduce the concept of complex valued convex metric spaces and introduce an analogue of the Picard-Ishikawa hybrid iterative scheme, recently proposed by Okeke [24] in this new setting. We approximate (common) fixed points of certain contractive conditions through these two new concepts and obtain several corollaries. We prove that the Picard-Ishikawa hybrid iterative scheme [24] converges faster than all of Mann, Ishikawa and Noor [23] iterative schemes in complex valued convex metric spaces. Also, we give some numerical examples to validate our results.
Some common fixed point theorems for weakly compatible mappings
Ć,irić,, Lj.B.,Ume, J.S. Elsevier 2006 Journal of mathematical analysis and applications Vol.314 No.2
<P><B>Abstract</B></P><P>Jungck's [G. Jungck, Compatible mappings and common fixed points, Int. J. Math. Math. Sci. 9 (1986) 771–779] notion of compatible mappings is further extended and used to prove some common fixed point theorems for weakly compatible non-self mappings in complete convex metric spaces. We improve on the method of proof used by Rhoades [B.E. Rhoades, A fixed point theorem for non-self set-valued mappings, Int. J. Math. Math. Sci. 20 (1997) 9–12] and Ahmed and Rhoades [A. Ahmed, B.E. Rhoades, Some common fixed point theorems for compatible mappings, Indian J. Pure Appl. Math. 32 (2001) 1247–1254] and obtain generalization of some known results. In particular, a theorem by Rhoades [B.E. Rhoades, A fixed point theorem for non-self set-valued mappings, Int. J. Math. Math. Sci. 20 (1997) 9–12] is generalized and improved.</P>
Moving averages on convex metric spaces
Kum, S.,Lee, H.,Lim, Y. Academic Press 2015 Journal of mathematical analysis and applications Vol.421 No.2
We show that the moving average induced by a contractive mean on a complete metric space converges. This general scheme of convergence covers the moving arithmetic average studied recently by Bauschke, Sarada and Wang (also by Borwein, Borwein and Sims). Significant portions of the derivation can be carried out in general convex metric spaces, which means that the results have broader applications beyond the setting of Banach spaces.
Altun, Ishak,Turkoglu, Duran Department of Mathematics 2008 Kyungpook mathematical journal Vol.48 No.3
In this paper, we give some fixed point theorems for multivalued maps satisfying an implicit relation on metrically convex spaces. Our results extend and generalize some fixed point theorem in the literature.