24 research outputs found
Ljubomir B. Ciric (1935-2016)
No full textProfessor Ljubomir B. Ciric, one of the pioneers in the study of fixed point theory and nonlinear analysis in Serbia, died on Saturday, 23th July 2016. Here, we present his brief biography, some comments on main streams of his research work and complete bibliography
On some mappings in metric spaces and fixed points
No full text1991 Mathematics Subject Classifications : Primary 54 H 25. Secondary 47 H 10.
Key words and phrases : Fixed point, metric spaces, Cauchy sequence. Let (X, d) be a metric space and T : X → X a self-mapping on X. For x, y in X put M(x, y) = max{d(x, Tx), d(y, Tsub>y)}, N(x, y) = max {d(x, Tx) + d(y, Ty)]. In this paper mappings which satisfy the following condition :
d (Tx, Ty ≤ a max{d(x, y), M(x, y), N(x, y)} + b min{M(x, y), N(x, y)},
where a≥0, b≥0, are investigated. It is proved that if a + b = 1 and X is complete, then T has a unique fixed point. This result generalizes the recent result of Bogin [1], Ciric [2], Hardy and Rogers [5] and a great number of known generalizations of the Banach contraction principle. Also a remetrization theorem, which is a converse to Banach contraction principle, is established.Cirié Ljubomir B. On some mappings in metric spaces and fixed points. In: Bulletin de la Classe des sciences, tome 6, n°1-6, 1995. pp. 81-89
Common fixed point theorems for families of occasionally weakly compatible mappings
No full textWe prove some common fixed point theorems in probabilistic semi-metric spaces for families of occasionally weakly compatible mappings. We also give a common fixed point theorem for mappings satisfying an integral-type implicit relation
Ciric Type Nonunique Fixed Point Theorems on <i>b</I>-metric Spaces
No full textKARAPINAR, ERDAL/0000-0002-6798-3254; Alsulami, Hamed Hamdan/0000-0001-5188-2830;In this paper, inspired the very interesting results of Ciric [20], we investigate the existing non-unique fixed points of certain operators in the context of b-metric spaces. Our main results unify and cover several existing results on the topic in the literature.Ministry of Education, Science and Technological Development, Republic of Serbia [174025]The third author is supported by Grant No. 174025 of the Ministry of Education, Science and Technological Development, Republic of Serbia
Fixed Point Theorems for Generalized (α<sub>*</Sub> - Ψ)-Ciric Contractive Multivalued Operators in <i>b</I>-metric Spaces
No full textKARAPINAR, ERDAL/0000-0002-6798-3254In this paper we introduce the notion (alpha(*) - psi)- Ciric-type contractive multivalued operator and investigate the existence and uniqueness of fixed point for such a mapping in b-metric spaces. The well-posedness of the fixed point problem and the Ulam-Hyres stability is also studied. (C) 2016 All rights reserved.Romanian National Authority for Scientific Research, CNCS UEFISCDI [PN-II-ID-PCE-2011-3-0094]The first author is supported by a grant of the Romanian National Authority for Scientific Research, CNCS UEFISCDI, project number PN-II-ID-PCE-2011-3-0094
Common fixed points of generalized contractions on partial metric spaces and an application
No full textIn this paper, common fixed point theorems for four mappings satisfying a generalized nonlinear contraction type condition on partial metric spaces are proved. Presented theorems extend the very recent results of I. Altun, F. Sola and H. Simsek [Generalized contractions on partial metric spaces, Topology and its applications 157 (18) (2010) 2778–2785]. As application, some homotopy results for operators on a set endowed with a partial metric are given
A remark on Rhoades fixed point theorem for non-self mappings
No full textLet X be a Banach space, K a non-empty closed subset of X and T:K→X a mapping
satisfying the contractive definition (1.1) below and the condition T(∂K)⫅K. Then T has a unique
fixed point in K. This result improves Theorem of Rhoades [1] and generalizes the corresponding
theorem of Assad [2]
Common fixed points of Ciric-type contractions on partial metric spaces
No full textWe obtain a common fixed point theorem of Boyd-Wong type for four mappings satisfying a Ciric-type contraction on a complete partial metric space. Our result generalizes and unifies, among others, the very recent results of L. CIRIC, B. SAMET, H. AYDI and C. VETRO [Common fixed points of generalized contractions on partial metric spaces and an application, Appl. Math. Comput., 218 (2011), 2398-2406], S. ROMAGUERA [Fixed point theorems for generalized contractions on partial metric spaces, Topology Appl., 159 (2012), 194-199], T. ABDELJAWAD, E. KARAPINAR and K. TAS [Existence and uniqueness of a common fixed point on partial metric spaces, Appl. Math. Lett. 24 (2011), 1900-1904], and D. ILIC, V. PAVLOVIC and V. RAKOCEVIC [Some new extensions of Banach's contraction principle to partial metric space, Appl. Math. Lett. 24 (2011), 1326-1330].The third named author is supported by the Ministry of Science and Innovation of Spain, grant MTM2009-12872-C02-01.Abbas, M.; Altun, I.; Romaguera Bonilla, S. (2013). Common fixed points of Ciric-type contractions on partial metric spaces. Publicationes Mathematicae Debrecen. 82:425-438. https://doi.org/10.5486/PMD.2013.5342S4254388
Special Issue on Ciric type fixed point theorems
No full textProfessor Ljubomir Ćirić was born on August 13, 1935 in Resnik, environmentof the Niš, in Serbia. Primary,secondary and university education Professor Ćirić received in Belgrade, where he completed his Mr Sci and his Dr Sci in 1969. His fields of specialization are Fixed point theory and Nonlinear analysis. He has been founder of different directions in the theory of fixed points, which and in today's time are in the full development. During the past 45 years, he has given significant contributions to these areas. We want point out that his works have been published and cited in prestigious international journals. Two of his work has been cited in the Web of Science over 560 times, each over 250 times. Name Ćirić we can find in the titles over 130 of scientific works of mathematicians from various countries of world. Many mathematical notions and objects are attributed to (and named after) him. These notions and objects include (among other items) "Ćirić’s generalized contractions", “Ljubomir Ćirić quasi-contraction mappings ", "Ćirić's contraction operator", "Ćirić’s multi-valued generalized contractions", “Multivalued Ćirić type mappings”,“Ćirić's maps with a nonunique fixed point”, “Ćirić type non-unique fixed point theorems”, “Ćirić type probabilistic fixed point theorems”, “Ćirić type nonexpansive mappings”, “Ćirić-type almost contractions”, “Nonlinear quasi-contractions of Ćirić-type”, “Ćirić-type δ-contractions”, “Ćirić Quasi Contractive Operator“, “Ćirić typeweak contractions”, “Ćirić-type strong almost contractions”, “Ćirić type cyclic contraction”, “Ćirić-G-Contractions”, “T–Ćirić generalized contractions”, “α-ψ-Ćirić generalized multifunctions”, “Ćirić type I-contractions”, “Prešić - Ćirić type theorems”, “Set-valued Prešić-Ćirić type contractions”,“Ćirić-Suzuki-type inequality”, “Ćirić-Reich-Rus operators”, “Ćirić-Jachymski-Matkowski contraction”, et cetera. All the above words are titles or a part of titles of 130 scientific works. Ćirić is currently Editor-in-Chief of an international journal “Advances in fixed point Theory”, United Kingdom, and a Section editor or a member of the editorial board of many well-known journals in the field of fixed point theory and nonlinear analysis. Fixed point theory is a very powerful and important tool in the study of nonlinear phenomena. The aim of this special issue is to promote contributions in various directions of this theory. Quality research articles, including
Fixed point results for weakly α-admissible pairs
No full textIn this paper, we introduce the concepts of weakly and partially weakly
?-admissible pair of mappings and obtain certain coincidence and fixed point
theorems for classes of weakly ?-admissible contractive mappings in a
b-metric space. As an application, we derive some new coincidence and common
fixed point results in a b-metric space endowed with a binary relation or a
graph. Moreover, an example is provided here to illustrate the usability of
the obtained results.</jats:p
