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1
Content available remote General iterative method for solving fixed point problems involving a finite family of demicontractive mappings in Banach spaces
Sow Thierno M. M.
Commentationes Mathematicae
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2019
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Vol. 59, No. 1/2
63--80
EN
The purpose of this paper is to study the general iterative method for demicontractive mappings in Banach spaces. The method gives us a strong convergence iteration for a finite family of demicontractive mappings and also permits us to solve variational inequality problems involving accretive operators without any compactness condition. Finally, we provide some applications, and an illustration of the proposed method is given in l4 spaces. Our results improve many recent results using the general iterative method for finding the fixed points of nonlinear operators.
2
Content available Approximating fixed points of a countable family of strict pseudocontractions in Banach spaces
Cholamjiak P.
Opuscula Mathematica
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2014
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Vol. 34, no. 1
67--79
EN
We prove the strong convergence of the modified Mann-type iterative scheme for a countable family of strict pseudocontractions in q-uniformly smooth Banach spaces. Our results mainly improve and extend the results announced in [Y. Yao, H. Zhou, Y.-C. Liou, Strong convergence of a modified Krasnoselski-Mann iterative algorithm for non-expansive mappings, J. Appl. Math. Comput. 29 (2009), 383–389].
3
Content available remote Remarks on occasionally weakly compatible maps versus occasionally weakly compatible maps
Deepmala, Pathak H. K.
Demonstratio Mathematica
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2014
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Vol. 47, nr 3
695--703
EN
In this paper, we discuss some important and interesting remarks on the concept of occasionally weakly compatible (owc) mappings, which is an active and interesting area of research in the present era. Also, we discuss here the lapses of several authors in quoting the definition of owc maps and provide the corrected proof by including some additional conditions on their results.
4
Content available remote Strict contractive conditions and common fixed point theorems with application
Pant V.
Demonstratio Mathematica
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2013
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Vol. 46, nr 2
405--413
EN
The aim of the present paper is to obtain common fixed point theorems under a strict contractive condition by assuming minimal commutativity conditions. Our theorems extend the results due to Pant and Pant [4]. In the setting of our results, we also provide pair of mappings which ensures the existence of a common fixed point; however, both the mappings are discontinuous at the common fixed point. We, thus, provide one more answer to the problem of Rhoades [10]. In the last section, we apply our results to solve an eigenvalue problem.
5
Content available remote Common fixed points for weakly compatible maps satisfying implicit relations without continuity
Akkouchi M.
Demonstratio Mathematica
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2011
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Vol. 44, nr 1
151--158
EN
The purpose of this paper is to prove a common fixed point theorem for a set of four mappings on a complete metric space, using weak compatibility and a general implicit relation without appeal to continuity. Our results improve and generalize all the results obtained by A. Djoudi in a paper published in 2003.
6
Content available remote Fixed point theorem in 2 non-archimedean Menger PM-Space using weakly L-compatible and weakly M-compatible mappings
Gupta V. K., Jain A., Kushwah J.
Commentationes Mathematicae
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2011
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Vol. 51, [Z] 2
177-187
EN
In the present paper, we extend and generalize the result of Cho et. al. [l]by introducing the notion of weakly L-compatible and weakly M-compatible maps in a 2 non-Archimedean Menger PM-space.
7
Content available remote Selections and common fixed points for some generalized multivalued contractions
Sintamarian A.
Demonstratio Mathematica
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2006
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Vol. 39, nr 3
609-617
EN
We show that some generalized multivalued contractions admit selections which are Caristi type mappings. Another purpose of this paper is to give a common fixed point theorem for two multivalued contractive type mappings defined on a closed ball of a complete metric space with values in the set of all nonempty and closed subsets of this space.
8
Content available remote Fixed points for set and single valued maps without continuity
Djoudi A., Khemis R.
Demonstratio Mathematica
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2005
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Vol. 38, nr 3
739-751
EN
In this paper we prove some common fixed point theorems for single valued and set valued mappings on a metric space. The theorems use minimal type commutativity and strict contractivity conditions with no continuity requirements. The theorems extend previous results on delta-compatible and continuous maps of [1] and [11] to a wider class of weakly compatible mappings not necessarly continuous. Also, a common fixed point theorem which applies to a sequence of set valued mappings is given.
9
Content available remote Common fixed points and best approximation in p-normed spaces
Hussain N., Khan A. R.
Demonstratio Mathematica
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2003
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Vol. 36, nr 3
675--681
EN
A general common fixed point result is obtained for commuting maps on non-starshaped domain in a p-normed space. As applications, we obtain Brosowski-Meinardus type approximation theorems in p-normed spaces which are not necessarily locally convex. Recent approximation results of a number of authors follow as a consequence of our results.
10
Content available remote A unique common fixed point for compatible mappings of type (B) satisfying an implicit relation
Djoudi A.
Demonstratio Mathematica
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2003
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Vol. 36, nr 3
763--770
11
Content available remote A common fixed point theorem for compatible mappings of type (B) in complete metric spaces
Djoudi A.
Demonstratio Mathematica
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2003
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Vol. 36, nr 2
463--470
EN
In the present note we give a common fixed point theorem. The theorem extend the results of Popa [8] to the case of four self mappings which are compatible of type (B) and satisfying a contractive relation.
12
Content available remote Some results on common fixed points and best approximation in p-normed spaces
Khan L., Latif A.
Demonstratio Mathematica
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2001
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Vol. 34, nr 4
831-836
EN
A general common fixed point result is obtained for commuting maps in p-normed spaces. The Brosowski-Meinardus type approximation theorem in p-normed spaces via our main result is derived. These results unify and include the recent work of Jungck and Sessa [6], Khan and Khan [7], Sahab, Khan and Sessa [II], Singh [12] etc.
13
Content available remote Common fixed point theorems with applications to nonlinear integral equations
Pathak H., Mishra S., Kalinde A.
Demonstratio Mathematica
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1999
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Vol. 32, nr 3
547-564
EN
Various definitions of compatible maps are characterized and compared in terms of continuity of maps, fixed points and certain limits. Common fixed point theorems for a new class of compatible maps on complete metric spaces are proved. Subsequently, the main result is applied to prove the existence of solutions of two systems of nonlinear integral equation.
14
Content available remote A fixed point theorem in Banach spaces over topological semifields and an application
Pathak H., Lakshmi V., Tas K., Fisher B.
Demonstratio Mathematica
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1999
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Vol. 32, nr 1
139-143
EN
A fixed point theorem for three mappings on a Banach space x over a topological semifield is proved. An application is given for the solvability of certain non-linear functional equations in X.
15
Content available remote On common fixed point theorems of compatible mappings in Menger spaces
Rashwan R., Hedar A.
Demonstratio Mathematica
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1998
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Vol. 31, nr 3
537-546
16
Content available remote Common fixed points by Ishikawa iterates in metric linear spaces
Rashwan R.
Demonstratio Mathematica
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1998
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Vol. 31, nr 1
19-23
EN
In this paper we obtain a common fixed point theorem for Ishikawa iterates of two self-mappi
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