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.
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].
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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.
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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.
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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.
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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.
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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.
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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.
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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.
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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.
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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.
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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.
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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.
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