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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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In this paper, we introduce the concept of (CLRS)-property for mappings F : X x X → X and S : X → X (wherein X stands for a partial metric space) and utilize the same to prove two common fixed point theorems for two pairs of mappings in partial metric spaces. We also furnish two examples to illustrate our main theorems.
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Content available remote A common fixed point theorem in non-Archimedean Menger pm-spaces
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In the present work, we introduce two types of compatible maps in non-Archimedean Menger PM-spaces and obtain a common fixed point theorem for six maps.
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Content available remote On maps and generalized lambda alfa-sets
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In this paper we introduce and study the concepts of g-lambda alfa-continuous maps, g-lambda alfa-irresolute maps and g-lambda alfa-closed maps by using generalized lambda alfa-sets and generalized Valfa-sets.
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Content available remote Fixed points for set and single valued maps without continuity
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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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Content available remote Fixed points of asymptotically regular noncompatible maps
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EN
The concept of R-weakly commutativity of type A for single-valued mapping is extended to multivalued mappings. The structure of common fixed points and coincidence points of a pair of R-weakly commuting multivalued mappings of type A is also discussed.
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It is shown that the graph of the sum of two Lipschitz mappings of the real line into a normed space of infinite dimension, whose graphs have tangents, need not have a tangent. Moreover, it turns out that the contingent of the graph of their linear combination may depend on the coefficients of that combination in quite "nonlinear" way.
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Content available remote An iterative algorithm for the system of split mixed equilibrium problem
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EN
In this article, a new problem that is called system of split mixed equilibrium problems is introduced. This problem is more general than many other equilibrium problems such as problems of system of equilibrium, system of split equilibrium, split mixed equilibrium, and system of split variational inequality. A new iterative algorithm is proposed, and it is shown that it satisfies the weak convergence conditions for nonexpansive mappings in real Hilbert spaces. Also, an application to system of split variational inequality problems and a numeric example are given to show the efficiency of the results. Finally, we compare its rate of convergence other algorithms and show that the proposed method converges faster.
EN
In this article, fixed point results for self-mappings in the setting of two metrics satisfying F -lipschitzian conditions of rational-type are proved, where F is considered as a semi-Wardowski function with constant τ∈R instead of τ>0 . Two metrics have been considered, one as an incomplete while the other is orbitally complete. The mapping is taken to be orbitally continuous from one metric to another. Some examples are provided to validate our results. For applications, we present existence results for the solutions of a new type of ABC-fractional boundary value problem.
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Content available remote Fixed point theorems for weakly inward multivalued maps on a convex metric space
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EN
We prove the existence of fixed point for weakly contractive multivalued maps satisfying the inwardness condition in the framework of a convex metric space. Fixed point theorems for multivalued contraction mapping taking the closed values are also obtained. These theorems extend several known results.
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Content available remote Remarks on almost locally connected spaces
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EN
Some preservation theorems for almost local connectedness are proved.
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Content available remote Convergence of Picard iterates of nonexpansive mappings
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EN
Let X be a Banach space, C a closed subset of X, and T : C --> C a nonexpansive mapping. Conditions are given which assure that if the fixed point set F(T) of T has nonempty interior then the Picard iterates of the mapping T always converge to a point of F(T). If T is asymptotically regular, it suffices to assume that the closed subsets of X are densely proximinal and that nested spheres in X have compact interfaces. Such spaces include, among others, those which have Rolewicz's property ([beta]). If X has strictly convex norm the asymptotic regularity assumption can be dropped and the nested sphere property holds trivially. Consequently the result holds for all reflexive locally uniformly convex spaces.
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Content available remote Orthogonal stability of the Cauchy equation on balls
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EN
We deal with stability of some functional equations postulated for orthogonal vectors in a ball centered at the origin. The maps considered are defined on a finite dimensional inner product space and take their values in a real sequentially complete linear topological space. The main result establishes the stability of the corresponding conditional Cauchy functional equation and as a consequence we obtain some other stability resuits. Results which do not involve the orthogonality relation are considered in more general structures.
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Content available remote Coincidence point for noncompatible multivalued maps satisfying implicit relation
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In this paper we prove a common coincidence point theorem for single- valued and multivalued mappings satisfying an implicit relation under the condition of R-weak commutativity on metric spaces.
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Content available remote Fixed point results in complete metric spaces
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Using the concept of w-distance, we prove fixed point theorems for multivalued contractive maps. Consequently, we improve and extend the corresponding fixed point results due to Feng and Liu, Nadler and many of others.
EN
We establish here an inequality of Ostrowski type for a random variable whose probability density function belongs to L-infinity[a, b], in terms of the cumulative distribution function and expectation. The inequality is then applied to generalized beta random variable.
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Content available remote A note on the weak convergence of a sequence of successive approximations
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In this paper we discuss the weak convergence of the sequence of successive approximations for a generalized para-nonexpansive mapping in a reflexive Banach space that satisfies Opial's condition.
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Content available remote Coincidence points for multivalued maps on non-starsharped domain
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We improve recent results of Shahzad [Demonstratio Math. 36 (2003), 427-431].
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The new concept of weak commutativity of type (KB) is used to prove some fixed point theorems for set and single-valued mappings. We show that continuity of any mapping is not necessary for the existence of common fixed point. We also show that completeness of the whole space can be replaced by a weaker condition.
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