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1
Content available remote Well-posedness and common fixed points for two pairs of maps using weak contractivity
Akkouchi M.
Demonstratio Mathematica
|
2013
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Vol. 46, nr 2
373--382
EN
In 2006, I. Beg and M. Abbas have studied the existence of coincidence and common fixed points for two mappings satisfying a weak contractive condition. Their results were extended in 2008 by A. Azam and M. Shakeel to the case of three mappings. Recently M. Abbas and D. Dorić employed the contractive conditions introduced in [Q. Zhang and Y. Song, Fixed point theory for generalized ϕ-weak contraction, Appl. Math. Lett. 22(2009), 75-78] and [D. Dorić, Common fixed point for generalized (...)-weak contractions, Appl. Math. Lett. 22 (2009), 1896–1900] to prove a common fixed point theorem for four mappings satisfying generalized weak contractive condition (see Filomat 24:2 (2010), 1–10). In this paper, we generalize this theorem by using the concept of common property (E.A). Our result generalizes and unifies several existing results involving generalized weak contractive conditions. We study also well-posedness of a related fixed point problem.
2
Content available A Meir-Keeler type common fixed point theorem for four mappings
Akkouchi M.
Opuscula Mathematica
|
2011
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Vol. 31, no. 1
5-14
EN
In this paper, we prove a general common fixed point theorem for two pairs of weakly compatible self-mappings of a metric space satisfying a weak Meir-Keeler type contractive condition by using a class of implicit relations. In particular, our result generalizes and improves a result of K. Jha, R.P. Pant, S.L. Singh, by removing the assumption of continuity, relaxing compatibility to weakly compatibility property and replacing the completeness of the space with a set of four alternative conditions for maps satisfying an implicit relation. Also, our result improves the main result of H. Bouhadjera, A. Djoudi.
3
Content available remote Well-posedness of fixed point problem for a hybrid pair of mappings
Akkouchi M., Popa V.
Fasciculi Mathematici
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2011
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Nr 46
5--15
EN
The purpose of this paper is to extend the notion of well-posedness of xed point problem for a mapping to a hybrid pair of mappings. Also, we prove a general common fixed point theorem for a pair of D-mappings for which the xed point problem is well posed.
4
Content available remote Common fixed points for weakly compatible maps satisfying implicit relations without continuity
Akkouchi M.
Demonstratio Mathematica
|
2011
|
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.
5
Content available remote Well-posedness of the fixed point problem for ø-max-contractions
Akkouchi M.
Fasciculi Mathematici
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2010
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Nr 45
5-12
EN
We study the well-posedness of the fixed point problem for self-mappings of a metric space which are ø-max-contractions (see [6]).
6
Content available remote Well-posedness of fixed point problem for mappings satisfying an implicit relation
Akkouchi M., Popa V.
Demonstratio Mathematica
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2010
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Vol. 43, nr 4
923-929
EN
The notion of well-posedness of a fixed point problem has generated much interest to a several mathematicians, for example, F. S. De Blassi and J. Myjak (1989), S. Reich and A. J. Zaslavski (2001), B. K. Lahiri and P. Das (2005) and V. Popa (2006 and 2008). The aim of this paper is to prove for mappings satisfying some implicit relations in orbitally complete metric spaces, that fixed point problem is well-posed.
7
Content available remote Solutions of some functional equations related to the determinant of certain matrices
Akkouchi M., Rhali M.
Demonstratio Mathematica
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2010
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Vol. 43, nr 1
97-106
EN
We solve the functional equation : [....] where K is a field which is not of characteristic 2 and f, g, h : K4 ->o K are unknown functions. We study also a class of functional equations of 2n variables generalizing the two equations above. This work is motivated by a paper of J. K. Chung and P. K. Sahoo published in 2002 and a recent paper of the authors published in 2005.
8
Content available remote Study of some functional equations related to some algebras of matrices
Akkouchi M., Rhali M.
Demonstratio Mathematica
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2005
|
Vol. 38, nr 3
611--622
EN
Let K be the real or complex field. Let 1 < n < p be two positive integers. We denote Mp(K) the usual algebra of p x p-matrices. Let An be an n- dimensional subalgebra of Mp(K). Then there exists an injective linear mapping A : Kn- Mp(K) such that A^") = An' Therefore K" may be equipped with a product denoted * such that (Kn, +,*) is an associative algebra. The aim of this paper is to investigate the general solutions of the functional equation: f(x*y) = f(x) f(y), and its Pexider form f(x*y) = g(x) h(y), for all x, y in Kn, where f,g, h: Kn - K are unknown functions. This work is inspired by the paper [2].
9
Content available remote Utility functions associated to relatively invariant measure on partially ordered locally compact groups
Akkouchi M.
Demonstratio Mathematica
|
2002
|
Vol. 35, nr 4
865-871
EN
Let G be a topological locally compact group (abelian or not) endowed with a left Haar measure and a left translation-invariant and strongly continuous strict partial ordering -< . We consider a positive finite measure v on G, such that this order is v-separable. Then, we associate to each positive relatively invariant measure A on G a class of continuous numerical representations for the order -< .
10
Content available remote Study of a class of nonlinear perturbed optimal control systems
Akkouchi M., Bounabat A.
Demonstratio Mathematica
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2002
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Vol. 35, nr 1
139-146
EN
We are concerned in this paper by a general class of nonlinear perturbed optimal control systems. Their study is based on a nonlinear version of Lax-Milgram theorem. For these systems we prove the existence of the (perturbed) states and optimal controls, and study their behaviour. We apply our general results to some perturbed boundary optimal control systems.
11
Content available remote Some fixed and common fixed point theorems connected to a results of M.S. Khan, M. Swald and S. Sessa
Akkouchi M.
Demonstratio Mathematica
|
2002
|
Vol. 35, nr 1
129-138
EN
The aim of this note is to prove some fixed and common fixed point theorems in complete metric spaces for self-maps verifying generalized contractive conditions close to that one introduced by M. S. Khan, M. Swaleh and S. Sessa in [6]. Moreover our results utilize much weaker conditions on the functions altering the distances between the points. Our main result unifies and improves the main results of papers [I], [4], [6] and [8].
12
Content available remote Fixed point theorems using diameters of level sets and the notion of R.G.I. mapping
Akkouchi M.
Demonstratio Mathematica
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2002
|
Vol. 35, nr 3
621-628
EN
In this paper, we generalize and improve a recent result established by W. A. Kirk and L. M. Saliga (see [3], Theorem 4.3, p. 149) by using a result of W. Walter (see [4]). Indeed, We prove that the conclusions of Kirk-Saliga theorem are not only satisfied but, moreover, they are equivalent for a wide class of contractive gauge functions. Our main result contains also a new equivalent conclusion (see Property (4) in Theorem 2.2 below). As a consequence, we recapture (and improve the results of) a theorem proved by M. Angrisani and M. Clavelli in [2]. Theorem 2.2 completes and improves the main result of[1].
13
Content available remote Some optimal control problems with boundary conditions of Robin type and singular cost functionals
Akkouchi M.
Demonstratio Mathematica
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2001
|
Vol. 34, nr 3
671-680
EN
We are concerned with the study of a class of linear boundary optimal control systems associated to the Laplace operator on a regular bounded domain in the n dimensional Euclidean space obtained by perturbing a singular system. The sets of admissible controls, taken here, are closed convex subsets of the Hilbert space of all square integrable functions on the boundary, verifying some natural conditions. The cost functional, used here, is singular. For these systems, we prove the existence of the (perturbed) states and optimal controls, and study their convergence.
14
Content available remote Common fixed point theorems by altering the distances between the points in bounded complete metric space
Akkouchi M.
Demonstratio Mathematica
|
2000
|
Vol. 33, nr 4
843-850
EN
The aim of this note is to prove some common fixed point theorems in bounded complete metric spaces for self-maps verifying generalized contractive conditions obtained by altering the distances between the points.
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