Discontinuity at fixed point and metric completeness

[EN] In this paper, we prove some new fixed point theorems for a generalized class of Meir-Keeler type mappings, which give some new solutions to the Rhoades open problem regarding the existence of contractive mappings that admit discontinuity at the fixed point. In addition to it, we prove that our theorems characterize completeness of the metric space as well as Cantor's intersection property.Bisht, RK.; Rakocevic, V. (2020). Discontinuity at fixed point and metric completeness. Applied General Topology. 21(2):349-362. https://doi.org/10.4995/agt.2020.13943OJS349362212R. M. T. Bianchini, Su un problema di S. Reich riguardante la teoria dei puntifissi, Boll. Un. Mat. Ital. 5 (1972), 103-108.R. K. Bisht and N. Özgür, Geometric properties of discontinuous fixed point set of $(epsilon-delta)$ contractions and applications to neural networks, Aequat. Math. 94 (2020), 847-863. https://doi.org/10.1007/s00010-019-00680-7R. K. Bisht and R. P. Pant, A remark on discontinuity at fixed points, J. Math. Anal. Appl. 445 (2017), 1239-1242. https://doi.org/10.1016/j.jmaa.2016.02.053R. K. Bisht and R. P. Pant, Contractive definitions and discontinuity at fixed point, Appl. Gen. Topol. 18, no. 1 (2017), 173-182. https://doi.org/10.4995/agt.2017.6713R. K. Bisht and V. Rakocevic , Generalized Meir-Keeler type contractions and discontinuity at fixed point, Fixed Point Theory 19, no. 1 (2018), 57-64. https://doi.org/10.24193/fpt-ro.2018.1.06R. K. Bisht and V. Rakocevic , Fixed points of convex and generalized convex contractions, Rend. Circ. Mat. Palermo, II. Ser., 69, no. 1 (2020), 21-28. https://doi.org/10.1007/s12215-018-0386-2S. K. Chatterjea, Fixed-point theorems, C. R. Acad. Bulgare Sci. 25 (1972), 15-18.Lj. B. Ciric, On contraction type mapping, Math. Balkanica 1 (1971), 52-57.Lj. B. Ciric, A generalization of Banach's contraction principle, Proc. Amer. Math. Soc. 45, no. 2 (1974), 267-273. https://doi.org/10.2307/2040075X. 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Joshi, Caristi type and Meir-Keeler type fixed point theorems, Filomat 33, no. 12 (2019), 3711-3721. https://doi.org/10.2298/FIL1912711PR. P. Pant, Discontinuity and fixed points, J. Math. Anal. Appl. 240 (1999), 284-289. https://doi.org/10.1006/jmaa.1999.6560R. P. Pant, Fixed points of Lipschitz type mappings, preprint.R. P. Pant, N. Özgür, N. Tas, A. Pant and M. C. Joshi, New results on discontinuity at fixed point, J. Fixed Point Theory Appl. (2020) 22:39. https://doi.org/10.1007/s11784-020-0765-0R. P. Pant, N. Y. Özgür and N. Tas, On discontinuity problem at fixed point, Bull. Malays. Math. Sci. Soc. 43 (2020), 499-517. https://doi.org/10.1007/s40840-018-0698-6R. P. Pant, N. Y. Özgür and N. Tas}, Discontinuity at fixed points with applications, Bulletin of the Belgian Mathematical Society-Simon Stevin 25, no. 4 (2019), 571-589.M. Rashid, I. Batool and N. Mehmood, Discontinuous mappings at their fixed points and common fixed points with applications, J. Math. 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Common fixed points of (α − ψ)- generalized rational multivalued contractions in dislocated quasi b-metric spaces and applications

In this paper, the concept of (α − ψ)-generalized rational contraction multivalued operator is introduced and then the existence of common fixed points of such mapping in complete dislocated quasi b-metric spaces is obtained. Some examples are presented to show that the results proved herein are potential generalization and extension of comparable existing results in the literature. We also study Ulam-Hyers stability of fixed point problems of (α − ψ)-generalized rational contraction multivalued operator. We also obtain some common fixed point results for single and multivalued mappings in a complete dq b-metric space endowed with a partial order. As an application, the existence of a continuous solution of an integral equation under appropriate assumptions is obtained.The second author is supported by Grant No. 174025 of the Ministry of Education, Science and Technological Development, Republic of Serbia.http://www.pmf.ni.ac.rs/filomatam2018Mathematics and Applied Mathematic

Development of a SCADA system to monitor and control continuous casting of steel billets

Continuous casting of steel billets, blooms and slabs is one of the dominant processes in the steel making industry. Production of high quality steel with no defects, has become a very important issue in the current highly competitive market conditions. To satisfy quality control standards, steel mills must now incorporate "state of the art" technologies in continuous casting. New techniques from different fields are being applied to the process to assist in casting "perfect" steel. Computers are now essential elements in applying advanced technologies for process and quality improvements. In this work, an attempt has been made to create an intelligent Supervisory Control and Data Acquisition System (SCADA) for the billet casting process. The "brain" of this system consists of an Artificial Intelligence entity that combines low-level numerical processing of sensor inputs with high-level symbol processing, ie. an Expert System The mastered process knowledge and experience, along with intelligent numerical computation, have been captured into a system called "Smart" Mould. This thesis focuses on the evolution of the hardware framework and software support for the SCADA system The concept of intelligent computation as a prerequisite to intelligent process control with respect to the continuous casting of steel billets is also introduced.Applied Science, Faculty ofMining Engineering, Keevil Institute ofGraduat

On a Formula for the Jumps in the Semi-Fredholm Domain

Sin resume

Ordered cone metric spaces and fixed point results

Altun, Ishak/0000-0002-7967-0554WOS: 000281340600002In this paper, we introduce a partial order on a cone metric space and prove a Caristi-type theorem. Furthermore, we prove fixed point theorems for single-valued nondecreasing and weakly increasing mappings, and multi-valued mappings on an ordered cone metric space. (C) 2010 Elsevier Ltd. All rights reserved.Ministry of Science, Technology and Development, Republic of SerbiaThe authors thank the referees for their valuable comments and suggestions. The second author was supported by the Ministry of Science, Technology and Development, Republic of Serbia

Some results in metric fixed point theory

This is a survey of results mainly in metric fixed point theory, including the Darbo–Sadovski˘i theorem using measures of noncompactness. Various different proofs are presented for some of the most important historical results. Furthermore many examples and remarks are added to illustrate the topics of the paper

Quasi-contraction mappings of Ciric and Fisher type via ω-distance

Kada, Suzuki, and Takahashi introduced and studies the concept of ω- distance in xed point theory. In this paper, we generalize and unify Ciric' and Fisher xed points results for quasi-contractions on metric space to ω-distance on complete metric spaces. We also extend some results of Kada, Suzuki and Takahashi, and Suzuki. Our methods of proofs are new and even simpler than the corresponding methods in metric spaces.Keywords: ω-distance, xed point, quasi-contraction