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EN
In this manuscript, some fixed point results for fuzzy mappings with rational type contraction in the context of a complete partially ordered complex-valued metric space are established. The derived results generalize some fixed point theorems in the existing literature. An appropriate example is given.
EN
The aim of this paper is to introduce generalized condition (B) in a quasi-partial metric space acknowledging the notion of Künzi et al. [Künzi H.-P. A., Pajoohesh H., Schellekens M. P., Partial quasi-metrics, Theoret. Comput. Sci., 2006, 365, 237-246] and Karapinar et al. [Karapinar E., Erhan M., Öztürk A., Fixed point theorems on quasi-partial metric spaces, Math. Comput. Modelling, 2013, 57, 2442-2448] and to establish coincidence and common fixed point theorems for two weakly compatible pairs of self mappings. In the sequel we also answer a rmatively two open problems posed by Abbas, Babu and Alemayehu [Abbas M., Babu G. V. R., Alemayehu G. N., On common fixed points of weakly compatible mappings satisfying generalized condition (B), Filomat, 2011, 25(2), 9-19]. Further in the setting of a quasi-partial metric space, the results obtained are utilized to establish the existence and uniqueness of a solution of the integral equation and the functional equation arising in dynamic programming. Our results are also justified by explanatory examples supported with pictographic validations to demonstrate the authenticity of the postulates.
3
Content available remote An alternative and easy approach to fixed point results via simulation functions
EN
We discuss, extend, improve and enrich results on simulation functions established by several authors. Furthermore, by using Lemma 2.1 of Radenović et al. [Bull. Iran. Math. Soc., 2012, 38, 625], we get much shorter and nicer proofs than the corresponding ones in the existing literature.
4
Content available remote Generalized altering distances and fixed point for occasionally hybrid mappings
EN
In this work we are interested in the generalization of the result which is in the article [20]. To realize this, we weaken the two conditions that are : weakly altering distance and occasionally weakly compatible, then we neglect the distance altered because of some changes in theorem.
EN
The purpose of this paper is to study convergence of a newly defined modified S-iteration process to a common fixed point of two asymptotically quasi-nonexpansive type mappings in the setting of CAT(0) space. We give a sufficient condition for convergence to a common fixed point and establish some strong convergence theorems for the said iteration process and mappings under suitable conditions. Our results extend and improve many known results from the existing literature.
6
Content available remote Some fixed point theorems using wt-distance in b-metric spaces
EN
Some fixed point theorems using wt-distance in b-metric spaces In this paper we establish some common fixed point theorems by using the concept of wt-distance in a b-metric space. Our results extend and generalize several well known comparable results in the existing literature. Finally, some examples are provided to illustrate our results.
7
Content available remote A generalized common fixed point theorem under an implicit relation
EN
An extended generalization of recent result of Kikina and Kikina (2011) has been established through the notions of weak compatibility and the property E.A., under an implicit-type relation and restricted orbital completeness of the space. The result of this paper also extends and generalizes that of Imdad and Ali (2007).
EN
In this paper, we introduce a new one-step iterative scheme for finding a common fixed point of a countable family of multivalued mappings in a real uniformly convex Banach space. By using the best approximation operators, a necessary and sufficient condition for strong convergence of the proposed method is given. Moreover, we establish some strong convergence theorems of the proposed iterative scheme under some control conditions
9
EN
We prove two generalizations: the first to Das and Naik’s theorem for a pair of compatible maps without continuity; and the next as an extension of our first result to three self-maps on a metric space X without compatibility, under a stronger contraction type inequality and restricting the completeness of X to its subspace. The latter is a significant generalization of a recent result of Pant et al.
10
Content available remote Hybrid fixed point theorems in symmetric spaces via common limit range property
EN
In this paper, we point out that some recent results of Vijaywar et al. (Coincidence and common fixed point theorems for hybrid contractions in symmetric spaces, Demonstratio Math. 45 (2012), 611–620) are not true in their present form. With a view to prove corrected and improved versions of such results, we introduce the notion of common limit range property for a hybrid pair of mappings and utilize the same to obtain some coincidence and fixed point results for mappings defined on an arbitrary set with values in symmetric (semi-metric) spaces. Our results improve, generalize and extend some results of the existing literature especially due to Imdad et al., Javid and Imdad, Vijaywar et al. and some others. Some illustrative examples to highlight the realized improvements are also furnished.
EN
The purpose of this paper is to introduce an implicit iterative process with errors for approximating common fixed point of two finite families of asymptotically nonexpansive mappings in the framework of Banach space. The results presented in this paper extend and generalize the corresponding results of Qin et al. [Convergence analysis of implicit iterative algorithms for asymptotically nonexpansive mappings, Appl. Math. Comp. 210 (2009), 542–550], Thakur [Weak and strong convergence of composite implicititeration process, Appl. Math. Comp. 190 (2007), 965–973] and some others.
EN
The purpose of this paper is to prove common fixed point theorems for a family of mappings in symmetric spaces using the property (E.A) and weak compatibility or occasionally weak compatibility. Our results extend some recent results.
EN
In this paper, we present a common fixed point theorem by altering distances for a contractive condition of integral type in partial metric spaces.
EN
In this paper, we establish the existence of coincidence and unique common fixed points of two pairs of weakly compatible maps satisfying A-contractive condition of integral type.
15
Content available remote Common fixed points for four maps in ordered partial metric spaces
EN
In this paper, we present some common fixed point theorems for four maps in partially ordered partial metric spacess. Our results generalize the main theorems of Abbas, Nazir and Radenovic [1].
16
Content available remote Altering distances, fixed point for occasionally hybrid mappings and applications
EN
The purpose of this paper is to prove a general fixed point theorem by altering distance for two pairs of hybrid occasionally weakly compatible mappings and to reduce the study of fixed points of pairs of mappings satisfying a contractive condition of integral type at the study of fixed point in symmetric spaces by altering distance satisfying an implicit relation.
EN
In this paper, we prove some fixed point theorems for two hybrid pairs of mappings in 2-metric spaces by using some weaker conditions.
EN
Three variants of R-weakly commuting mappings in the realm of uniform spaces are defined. Examples are included to reflect upon the distinctiveness of the notions so defined. Common fixed point theorems concerning these variants of R-weakly commuting mappings in the framework of uniform spaces are obtained. This generalizes several known results in the literature including those of Granas and Dugundji [3], Tarafdar [12] and others. Moreover, as a bi-product we obtain several common fixed point theorems which are well in contrast with a common fixed point theorem of Jungck [4] who proved the same for commuting mappings.
EN
Using compatibility of type (N) and (E-A) property of hybrid pair of mappings we obtain some new coincidence and common fixed point theorems under strict contractive conditions in symmetric (semi-metric) space.
EN
Let C be a bounded, closed, convex subset of a uniformly convex and uniformly smooth Banach space X. We investigate the weak convergence of the generalized Krasnosel'skii-Mann and Ishikawa iteration processes to common fixed points of semigroups of nonlinear mappings Tt: C → C. Each of Tt: is assumed to be pointwise Lipschitzian, that is, there exists a family of functions αt: C → [0, ∞) such that ||Tt(x) — Tt(y)\\ ≤ αt:(x) || - y|| for x,y € C. The paper demonstrates how the weak compactness of C plays an essential role in proving the weak convergence of these processes to common fixed points.
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