Fixed points of a certain class of mappings in uniformly convex Banach spaces (original) (raw)
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Common fixed-point results in uniformly convex Banach spaces
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We introduce a condition on mappings, namely condition (K). In a uniformly convex Banach space, the condition is weaker than quasi-nonexpansiveness and weaker than asymptotic nonexpansiveness. We also present the existence theorem of common fixed points for a commuting pair consisting of a mapping satisfying condition (K) and a multivalued mapping satisfying conditions (E) and (C λ ) for some λ ∈ (0, 1).
Some common fixed point theorems for a family of mappings in metrically convex spaces
Nonlinear Analysis: Theory, Methods & Applications, 2007
In the present paper some common fixed point theorems for a sequence and a pair of nonself-mappings in complete metrically convex metric spaces are proved which generalize such results due to Khan et al. Some fixed point theorems in metrically convex spaces, Georgian Math. J. 7 (3) (2000) 523-530], Assad [N.A. Assad, On a fixed point theorem of Kannan in Banach spaces, Tamkang J. Math. 7 (1976) 91-94], Chatterjea [S.K. Chatterjea, Fixed point theorems, C. R. Acad. Bulgare Sci. 25 (1972) 727-730] and several others. Some related results are also discussed.
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In this article, we recall the definition of a real n-normed space and some basic properties. fixed point theorems for types of Kannan, Chatterge, Zamfirescu, -Weak contraction and - (,)-Weak contraction mappings in Banach spaces.
2012
A Banach space X is said to satisfy property (D) if there exists α ∈ [0,1) such that for any nonempty weakly compact convex subset E of X, any sequence {xn }⊂ E which is regular relative to E, and any sequence {yn }⊂ A(E,{xn}) which is regular relative to E, we have r(E,{yn}) ≤ αr (E,{xn}). A this property is the mild modification of the (DL)-condition. Let X be a Banach space satisfying property (D) and let E be a weakly compact convex subset of X .I fT : E → E is a mapping satisfying condition (E) and (Cλ) for some λ ∈ (0,1). We study the existence of a fixed point for this mapping.
Some New Fixed Point Theorems in 2-BANACH Spaces
Математички билтен/BULLETIN MATHÉMATIQUE DE LA SOCIÉTÉ DES MATHÉMATICIENS DE LA RÉPUBLIQUE MACÉDOINE
S. Ghler ([9]), 1965, defined the 2-normed space, A. White ([3]), 1968, defined the 2-Banach space. Several statements about them are proven in [7]. P. K. Hatikrishnan and K. T. Ravindran in [5] defined the contractive mapping in 2-normed space. M. Kir and H. Kiziltunc in [3] by applying the above theorem, proved the generalizations of R. Kannan ([6]) and S. K. Chatterjea ([10]) theorem. Further generalizations of these results are elaborated in [1] and [11]. In this paper we will generalize the above results by using the class Θ of monotony increasing functions f : [0, +∞) → R such that f −1 (0) = {0} holds true.
Fixed points and their approximation in Banach spaces for certain commuting mappings
Glasgow Mathematical Journal, 1982
1. Let X be a Banach space. Then a self-mapping A of X is said to be nonexpansive provided that ‖AX − Ay‖≤‖X − y‖ holds for all x, y ∈ X. The class of nonexpansive mappings includes contraction mappings and is properly contained in the class of all continuous mappings. Keeping in view the fixed point theorems known for contraction mappings (e.g. Banach Contraction Principle) and also for continuous mappings (e.g. those of Brouwer, Schauderand Tychonoff), it seems desirable to obtain fixed point theorems for nonexpansive mappings defined on subsets with conditions weaker than compactness and convexity. Hypotheses of compactness was relaxed byBrowder [2] and Kirk [9] whereas Dotson [3] was able to relax both convexity and compactness by using the notion of so-called star-shaped subsets of a Banach space. On the other hand, Goebel and Zlotkiewicz [5] observed that the same result of Browder [2] canbe extended to mappings with nonexpansive iterates. In [6], Goebel-Kirk-Shimi obtainedfix...
Some Fixed Point Theorems in 2-BANACH Space
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In this note, we establish some fixed point theorems for a class of mapping in 2-Banach space using the concept of upper semi-continuous mapping from right.
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In the present paper we establish some fixed point theorems in Banach space taking rational expression. Our Result Generalize the result of many authors.
A Generalized Banach Fixed Point Theorem
Bulletin of the Malaysian Mathematical Sciences Society, 2015
Motivated by the recent work of H. Liu and S.Y. Xu, we prove a generalized Banach fixed point theorem for the setting of cone rectangular Banach algebra valued metric spaces without assuming the normality of the underlying cone. Our work generalizes Some recent results in cone rectangular Banach algebra valued metric spaces. An example to illustrate the main result is also presented.