Zoran D. Mitrović

Bio: Zoran D. Mitrović is an academic researcher from University of Banja Luka. The author has contributed to research in topics: Metric space & Fixed point. The author has an hindex of 12, co-authored 83 publications receiving 468 citations. Previous affiliations of Zoran D. Mitrović include Ton Duc Thang University.

Best Proximity Points of MT-Cyclic Contractions with Property UC

Abstract: We initiate the notion of generalized MT- cyclic contraction mappings with respect to an auxiliary function φ and investigate the existence of a best proximity point of such mappings in the setting...

A new survey: Cone metric spaces

Abstract: 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.

Remarks on some fixed point results in b-metric spaces

Abstract: The main purpose of this paper is to generalize, improve and complement several famous results in b-metric spaces. Moreover, an essential estimation of b-quasi-contraction in b-metric spaces is given. We also establish some new results for multi-valued mappings in the metric and b-metric concept. We explore some different proof techniques which provide short proofs of the results.

The Banach and Reich contractions in $$\varvec{b_v(s)}$$-metric spaces

Abstract: In this paper, the concept of \(b_v(s)\)-metric space is introduced as a generalization of metric space, rectangular metric space, b-metric space, rectangular b-metric space and v-generalized metric space. We next give proofs of the Banach and Reich contraction principles in \(b_v(s)\)-metric spaces. Using a new result, we provide short proofs which are different from of the original ones in metric spaces. The results we obtain generalize many known results in fixed point theory. We also provide a solution to an open problem.

Picard sequences in b-metric spaces

Abstract: The purpose of this article is to provide much simpler and shorter proofs of some important results in the framework of b-metric spaces. Namely, we show that the given contractive condition implies b-Cauchyness of the corresponding Picard sequence. The obtained results improve well-known comparable results in the literature.

مستطيلة-ب متري المساحات ومبادئ الانكماش / Rectangular b-metric spaces and contraction principles

Abstract: The concept of rectangular b-metric space is introduced as a generalization of metric space, rectangular metric space and b-metric space. An analogue of Banach contraction principle and Kannan's xed point theorem is proved in this space. Our result generalizes many known results in xed point theory.

Uniqueness of solution for higher-order nonlinear fractional differential equations with multi-point and integral boundary conditions

Abstract: This study is devoted to the development of alternative conditions for existence and uniqueness of nonlinear fractional differential equations of higher-order with integral and multi-point boundary conditions. It uses a novel approach of employing a fixed point theorem based on contractive iterates of the integral operator for the corresponding fixed point problem. We start with developing an existence-uniqueness theorem for self-mappings with contractive iterate in a b-metric-like space. Then, we obtain the unique solvability of the problem under suitable conditions by utilizing an appropriate b-metric-like space.