Papers by Zoran Kadelburg
Filomat, 2016
In this paper, we prove existence and uniqueness results for common fixed points of two or three ... more In this paper, we prove existence and uniqueness results for common fixed points of two or three relatively asymptotically regular mappings satisfying the orbital continuity of one of the involved maps on ordered orbitally complete metric spaces under generalized ?-contractive condition. Also, we introduce and use orbitally dominating maps and orbitally weakly increasing maps. We furnish suitable examples to demonstrate the usability of the hypotheses of our results. As an application, we prove the existence of solutions for certain system of integral equations.
Journal of the Egyptian Mathematical Society, 2016
In this paper, we prove a generalization of Chatterjea's fixed point theorem, based on a recent r... more In this paper, we prove a generalization of Chatterjea's fixed point theorem, based on a recent result of Pata. Also, we establish common fixed point results of Pata-type for two maps, as well as a coupled fixed point result in ordered metric spaces. An example is given to show that new results are different from the known ones.
Applied Mathematics Letters, 2009
proved a fixed point theorem for quasi-contractive mappings in cone metric spaces when the underl... more proved a fixed point theorem for quasi-contractive mappings in cone metric spaces when the underlying cone is normal. The aim of this paper is to prove this and some related results without using the normality condition.
The purpose of this new survey paper is, among other things, to collect in one place most of the ... more The purpose of this new survey paper is, among other things, to collect in one place most of the articles on cone (abstract, K-metric) spaces, published after 2007. This list can be useful to young researchers trying to work in this part of functional and nonlinear analysis. On the other hand, the existing review papers on cone metric spaces are updated. The main contribution is the observation that it is usually redundant to treat the case when the underlying cone is solid and non-normal. Namely, using simple properties of cones and Minkowski functionals, it is shown that the problems can be usually reduced to the case when the cone is normal, even with the respective norm being monotone. Thus, we offer a synthesis of the respective fixed point problems arriving at the conclusion that they can be reduced to their standard metric counterparts. However, this does not mean that the whole theory of cone metric spaces is redundant, since some of the problems remain which cannot be treated in this way, which is also shown in the present article.
Gulf Journal of Mathematics
In this paper, we consider fixed point results in the setup of $b$-metric spaces for weakly T-Kan... more In this paper, we consider fixed point results in the setup of $b$-metric spaces for weakly T-Kannan and weakly T-Chatterjea contractive mappings. Thus, we improve and complement recent results established by Z. Mustafa et al.\ [J.\ Inequal.\ Appl.\ 2014, 2014:46] and A. Razani, V. Parvaneh [Russ.\ Math.\ (Izv.\ VUZ), 57 (3), 38--45 (2013)], with much shorter proofs. Moreover, we show that the results of A.H. Ansari et al.\ [J. Inequal.\ Appl.\ 2014, 2014:429] are not generalizations of the known ones. An example is given illustrating our results.
Gulf Journal of Mathematics
In this note, we show how an easy lemma, proved recently by Abkar and Gabeleh, can be applied to ... more In this note, we show how an easy lemma, proved recently by Abkar and Gabeleh, can be applied to obtain Geraghty-type results for best proximity points. In particular, we obtain improvements of some recent best proximity point results and show by an example that these improvements are proper.
Abstract. Several fixed point results are obtained for cyclic mappings satisfying contractive con... more Abstract. Several fixed point results are obtained for cyclic mappings satisfying contractive conditions of Pata-type. Some of them improve existing results in the literature. An example shows a possible usage of the obtained results. 1.
In this paper we obtain improved versions of some common coupled fixed point results for mappings... more In this paper we obtain improved versions of some common coupled fixed point results for mappings in (ordered) G-metric spaces. Examples show that these improvements are proper.
In this paper, we discuss and improve some recent results about contractive and cyclic mappings e... more In this paper, we discuss and improve some recent results about contractive and cyclic mappings established in the framework of C∗-algebravalued b-metric spaces. Our proofs are much shorter than the ones in existing literature. Also, we give two examples that support our approach.
In this paper, we improve some recent coupled fixed point resultsfor single-valued operators in t... more In this paper, we improve some recent coupled fixed point resultsfor single-valued operators in the framework of ordered $b$-metricspaces established by Bota et al. [M-F. Bota, A. Petrusel, G.Petrusel and B. Samet, Coupled fixed point theorems forsingle-valued operators in b-metric spaces, Fixed Point TheoryAppl. (2015) 2015:231]. Also, we prove that Perov-type fixed pointtheorem in ordered generalized $b$-metric spaces is equivalentwith Ran-Reurings-type theorem in ordered $b$-metric spaces.
Filomat, 2017
We prove some common fixed point results for two ?-dominated mappings satisfying some restricted ... more We prove some common fixed point results for two ?-dominated mappings satisfying some restricted contractive conditions on a closed ball of a left (right) K-sequentially complete dislocated quasi metric space. Some examples are given to show the utility of our work. The results of this paper complement, extend and enrich several recent results in the literature.
Fixed Point Theory and Applications, 2016
Very recently, Ma et al. (Fixed Point Theory Appl. 2014:206, 2014) introduced C *-algebra-valued ... more Very recently, Ma et al. (Fixed Point Theory Appl. 2014:206, 2014) introduced C *-algebra-valued metric spaces as a new concept. Also, Ma and Jiang (Fixed Point Theory Appl. 2015:222, 2015), generalizing this concept, introduced C *-algebra-valued b-metric spaces. In both frameworks, these and other authors proved some fixed point results. We show in this paper that all these results (as well as many others) can be directly obtained as consequences of their standard metric or b-metric counterparts.
International Journal of Analysis and Applications, Feb 8, 2014
Recently, E. Karapinar and P. Salimi [Fixed point theorems via auxiliary functions, J. Appl. Math... more Recently, E. Karapinar and P. Salimi [Fixed point theorems via auxiliary functions, J. Appl. Math. 2012, Article ID 792174] have obtained fixed point results for increasing mappings in a partially ordered metric space using three auxiliary functions in the contractive condition. In this paper, these results are extended to 0-complete ordered partial metric spaces with a more general contractive condition. Examples are given showing that these extensions are proper.
Kragujevac Journal of Mathematics, 2015
In this short note we prove the existence of fixed points for nondecreasing mappings in ordered b... more In this short note we prove the existence of fixed points for nondecreasing mappings in ordered b-metric spaces. Our results improve the recent results, established by F. Zabihi and A. Razani [Fixed point theorems for hybrid rational Geraghty contractive mappings in ordered b-metric spaces, Journal of Applied Mathematics, Volume 2014, Article ID 929821, 9 pages], with much more general conditions and shorter proofs. An example is given to show the superiority of our generalization.
Banach Journal of Mathematical Analysis, 2011
The purpose of this paper is to introduce the concept of a cone symmetric space and to investigat... more The purpose of this paper is to introduce the concept of a cone symmetric space and to investigate relationship between (cone) metric spaces and (cone) symmetric spaces. Among other things, we shall also extend some fixed point results from metric spaces to cone metric spaces (Theorem 3.3), and to symmetric spaces (Theorems 3.2 and 3.5) under some new contraction conditions.
Journal of Inequalities and Applications, 2013
Using a combination of techniques introduced by Jleli and Samet (Fixed Point Theory Appl. 2012:21... more Using a combination of techniques introduced by Jleli and Samet (Fixed Point Theory Appl. 2012:210, 2012) and Samet et al. (Int. J. Anal. 2013:917158, 2013) on the one hand, and by Kadelburg et al. (Bull. Math. Anal. Appl. 4:51-63, 2012) on the other hand, we show that several coupled fixed point results in (ordered) G-metric spaces obtained recently are simple consequences of the respective standard (ordered) metric results. The technique can be applied both in symmetric and asymmetric cases. Moreover, we show by an example that the results thus obtained are usually stronger than those presented in the literature. MSC:47H10, 54H25.
Publications de l'Institut Math?matique (Belgrade), 2013
We present some fixed point results for mappings which satisfy Hardy-Rogers rational type, quasic... more We present some fixed point results for mappings which satisfy Hardy-Rogers rational type, quasicontraction type, weak contraction type and generalized f? type cyclic conditions in 0-complete partial metric spaces. Presented results generalize or improve many existing fixed point theorems in the literature. To demonstrate our results, we give throughout the paper some examples. One of the possible applications of our results to well-posed and limit shadowing property of fixed point problems is also presented.
Fixed Point Theory and Applications, 2012
A fixed point theorem is obtained for a monotone self-map in a 0-complete ordered partial metric ... more A fixed point theorem is obtained for a monotone self-map in a 0-complete ordered partial metric space under Hardy-Rogers-type contractive condition. This result improves some recently obtained ones, in the sense that weaker conditions are used. An example shows how this result can be used when the corresponding result in standard metric cannot. The second theorem is concerned with two weakly isotone increasing self-mappings in ordered partial metric spaces. A common fixed point result is obtained without any commutativity or compatibility assumptions.
Filomat, 2013
We deduce coincidence and fixed point theorems under generalized weakly contractive conditions in... more We deduce coincidence and fixed point theorems under generalized weakly contractive conditions in G-metric spaces equipped with partial order. We furnish examples to demonstrate the usage of the results and to distinguish them from the known ones.
Applied Mathematics Letters, 2011
Various Meir-Keeler-type conditions for mappings acting in abstract metric spaces are presented a... more Various Meir-Keeler-type conditions for mappings acting in abstract metric spaces are presented and their connections are discussed. Results about associated symmetric spaces, obtained in [S. Radenović, Z. Kadelburg, Quasi-contractions on symmetric and cone symmetric spaces, Banach J. Math. Anal. 5 (2011), 38-50] are used to show that the regularity condition for the underlying cone can be dropped in some fixed point results that have appeared recently.
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Papers by Zoran Kadelburg