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Open AccessAdvances on the fixed point results via simulation function involving rational terms
In this paper, we propose two new contractions via simulation function that involves rational expression in the setting of partial b-metric space. The obtained results not only extend, but also generalize and ...
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Article
Hyers–Ulam and Hyers–Ulam–Rassias Stability of First-Order Nonlinear Dynamic Equations
We investigate Hyers–Ulam and Hyers–Ulam–Rassias stability of first-order nonlinear dynamic equations for functions defined on a time scale with values in a Banach space.
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Open AccessOn fixed point theory in topological posets, extended quasi-metric spaces and an application to asymptotic complexity of algorithms
In this paper we present a few fixed point results in the framework of topological posets. To this end, we introduce an appropriate notion of completeness and order-continuity. Special attention is paid to the...
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Open AccessProjective contractions, generalized metrics, and fixed points
In 1981, Borsík and Doboš studied the aggregation problem for metric spaces. Thus, they characterized those functions that allow one to merge a collection of metrics providing a single metric as a result (Bors...
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Article
Open AccessThe viscosity technique for the implicit midpoint rule of nonexpansive map**s in Hilbert spaces
The viscosity technique for the implicit midpoint rule of nonexpansive map**s in Hilbert spaces is established. The strong convergence of this technique is proved under certain assumptions imposed on the seq...
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Open AccessErgodicity of the implicit midpoint rule for nonexpansive map**s
We prove a mean ergodic theorem for the implicit midpoint rule for nonexpansivemap**s in a Hilbert space. We obtain weak convergence for the general case andstrong convergence for certain special cases.
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Article
A primal-dual method of partial inverses for composite inclusions
S**arn’s method of partial inverses has found many applications in nonlinear analysis and in optimization. We show that it can be employed to solve composite monotone inclusions in duality, thus opening a ne...
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Open AccessMetric fixed point theory for nonexpansive map**s defined on unbounded sets
It is standard practice in metric fixed point theory to reduce fixed point questions for map**s defined on unbounded sets to the bounded case. Many of these results are couched in a Banach space framework an...
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Open AccessThe implicit midpoint rule for nonexpansive map**s
The implicit midpoint rule (IMR) for nonexpansive map**s is established. The IMR generates a sequence by an implicit algorithm. Weak convergence of this algorithm is proved in a Hilbert space. Applications t...
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Open AccessNew results on the Baire partial quasi-metric space, fixed point theory and asymptoticcomplexity analysis for recursive programs
In Cerdà-Uguet et al. (Theory Comput. Syst. 50:387-399, 2012), a newmathematical fixed point technique, that uses the so-called Baire partial quasi-metricspace, was introduced with the aim of providing the asympt...
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Open AccessG-β-ψ-contractive type map**s in G-metric spaces
In this paper, we introduce G-β-ψ-contractive map**s which are generalizations of α-ψ-contractive map**s in the context of G-metric spaces. Additionally, we prove existence and uniqueness of fixed points of s...
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Open AccessFixed point theorems in generalized metric spaces with applications to computer science
In 1994, Matthews introduced the notion of a partial metric space in order to obtain a suitable mathematical tool for program verification (Matthews in Ann. N.Y. Acad. Sci. 728:183-197, 1994). He gave an appli...
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Open AccessG-β-ψ contractive-type map**s and related fixed point theorems
In this paper, we introduce the notion of generalized G-β-ψ contractive map**s which is inspired by the concept of α-ψ contractive map**s. We showed the existence and uniqueness of a fixed point for such mapp...
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Open AccessCorrection: A fixed point theorem for cyclic generalized contractions in metric spaces. Fixed Point Theory and Applications 2012, 2012:122
The purpose of this short note is to present some corrections and clarifications concerning the proof of the main result given in the above mentioned paper.
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Open AccessBest proximity point results in geodesic metric spaces
In this paper, the existence of a best proximity point for relatively u-continuous map**s is proved in geodesic metric spaces. As an application, we discuss the existence of common best proximity points for a f...
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Open AccessOn fixed point theory in partial metric spaces
In this paper, we continue the study of contractive conditions for map**s in complete partial metric spaces. Concretely, we present fixed point results for weakly contractive and weakly Kannan map**s in su...
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Open AccessA fixed point theorem for cyclic generalized contractions in metric spaces
In this paper, we extend a recent result of V. Pata (J. Fixed Point Theory Appl. 10:299-305, 2011) in the frame of a cyclic representation of a complete metric space.
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Open AccessFixed point theory for cyclic generalized contractions in partial metric spaces
In this article, we give some fixed point theorems for map**s satisfying cyclical generalized contractive conditions in complete partial metric spaces.
