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A basic framework for fixed point theorems: ball spaces and spherical completenessMay 22 2019We systematically develop a general framework in\linebreak which various notions of functions being contractive, as well as of spaces being complete, can be simultaneously encoded. Derived from the notions of ultrametric balls and spherical completeness, ... Moremath.GN54A05, 54H25 (Primary), 03E75, 06A05, 06A06, 06B23, 06B99, 06F20,
12J15, 12J20, 13A18, 47H09, 47H10, 54C10, 54C60, 54E50 (Secondary) Partial quasi-metric completeness via Kannan-type fixed pointsFeb 08 2019In this short note, we obtain partial quasi-metric versions of Kannan's fixed point theorem for self-mappings. Moreover, we use these fixed points results to characterize a certain type of completeness in partial quasi-metric spaces. We have reported ... More Chatterjea type fixed point in Partial $b$-metric spacesFeb 08 2019In this paper, we give and prove two Chatterjea type fixed point theorems on partial $b$-metric space. We propose an extension to the Banach contraction principle on partial $b$-metric space which was already presented by Shukla and also study some related ... More Fixed point on partial metric type spacesSep 07 2018In this paper, we study some new fixed point results for self maps defined on partial metric type spaces. In particular, we give common fixed point theorems in the same setting. Some examples are given which illustrate the results. ($2k+1)^{th}$-order Fixed points in $G$-metric spacesSep 22 2017We establish three major fixed-point theorems for functions satisfying an odd power type contractive condition in G-metric spaces. We first consider the case of a single mapping, followed by that of a triplet of mappings and we conclude by the case of ... More $n$-tuple fixed point in $φ$-ordered $G$-metric spacesSep 22 2017We use three seminal approaches in the study of fixed point theory, the so called $G$-metrics, multidimensional fixed points and partially ordered spaces. More precisely, we extend known results from the theory of quasi-pseudometric spaces to the $G$-metric ... More Some extensions of Banach'\ CP in $G$-metric spacesMar 24 2017We present different extensions of the Banach contraction principle in the $G$-metric space setting. More precisely, we consider mappings for which the contractive condition is satisfied by a power of the mapping and for which the power depends on the ... More Common fixed points via $λ$-sequences in $G$-metric spacesMar 24 2017In this article, we use $\lambda$-sequences to derive common fixed points for a family of self-mappings defined on a complete $G$-metric space. We imitate some existing techniques in our proofs and show that the tools emlyed can be used at a larger scale. ... More Mix-point property in quasi-pseudometric spacesMar 01 2017In this article, we give new results in the startpoint theory for quasi-pseudometric spaces. The results we present provide us with the existence of startpoint (endpoint, fixed point) for multi-valued maps defined on a bicomplete quasi-pseudometric space. ... More New fixed point results on $G$-metric spacesFeb 23 2017In this note, we discuss some fixed point theorems for contractive self mappings defined on a $G$-metric spaces. More precisely, we give fised point theorems for mappings with a contractive iterate at a point. Linear Convergence of Projection AlgorithmsSep 01 2016Projection algorithms are well known for theirs simplicity and flexibility in solving feasibility problems. They are particularly important in practice since softwares involving projection algorithms require minimal implementation and maintenance. In ... More Linear Convergence of Projection AlgorithmsSep 01 2016Oct 25 2017Projection algorithms are well known for their simplicity and flexibility in solving feasibility problems. They are particularly important in practice due to minimal requirements for software implementation and maintenance. In this work, we study linear ... More The forward-backward algorithm and the normal problemAug 07 2016The forward-backward splitting technique is a popular method for solving monotone inclusions that has applications in optimization. In this paper we explore the behaviour of the algorithm when the inclusion problem has no solution. We present a new formula ... More On the finite convergence of a projected cutter methodMay 12 2014Aug 14 2014The subgradient projection iteration is a classical method for solving a convex inequality. Motivated by works of Polyak and of Crombez, we present and analyze a more general method for finding a fixed point of a cutter, provided that the fixed point ... More Firmly nonexpansive mappings in classes of geodesic spacesMar 07 2012Nov 23 2012Firmly nonexpansive mappings play an important role in metric fixed point theory and optimization due to their correspondence with maximal monotone operators. In this paper we do a thorough study of fixed point theory and the asymptotic behaviour of Picard ... More Fixed Points of Averages of Resolvents: Geometry and AlgorithmsFeb 08 2011To provide generalized solutions if a given problem admits no actual solution is an important task in mathematics and the natural sciences. It has a rich history dating back to the early 19th century when Carl Friedrich Gauss developed the method of least ... More $γ$-Radonifying operators -- a surveyNov 19 2009Feb 09 2010We present a survey of the theory of $\gamma$-radonifying operators and their applications to stochastic integration in Banach spaces.