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Fasciculi Mathematici
2010 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]).
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Opuscula Mathematica
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.[...]
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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 publish[...]
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Demonstratio Mathematica
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 o[...]
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Demonstratio Mathematica
2013 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 contractiv[...]
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Demonstratio Mathematica
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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Demonstratio Mathematica
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 [...]
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Demonstratio Mathematica
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 wi[...]
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Demonstratio Mathematica
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 funct[...]
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Fasciculi Mathematici
2011 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.
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Demonstratio Mathematica
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 mapp[...]
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Demonstratio Mathematica
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. S[...]
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Demonstratio Mathematica
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 gener[...]
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Demonstratio Mathematica
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 produ[...]
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