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Fixed Point Theory: Theory, Computation and Applications

This thematic series is devoted to the latest achievements in fixed point theory, computation and applications. It will reflect both  state-of-the-art
abstract research as well as important recent advances in computation and applications.

One of the most dynamic area of research of the last 50 years, fixed point theory plays a fundamental role in several theoretical and applied areas, such as nonlinear analysis, integral and differential equations and inclusions, dynamic systems theory, mathematics of fractals, mathematical economics (game theory, equilibrium problems, optimization problems) and mathematical modeling. This thematic series will present relevant works related to the theory of fixed points and its various applications to pure, applied and computational mathematics. Special attention will be paid to the most important theories developed by Professor Ioan A. Rus and the Cluj-Napoca Fixed Point Theory School: the Picard operator theory, the fixed point structure theory and other aspects of fixed point theory.

Edited by: Vasile Berinde, Adrian Petrusel and Radu Precup

  1. Content type: Research

    A dislocated cone metric space over Banach algebra is introduced as a generalisation of a cone metric space over Banach algebra as well as a dislocated metric space. Fixed point theorems for Perov-type α-quasi co...

    Authors: Reny George, R Rajagopalan, Hossam A Nabwey and Stojan Radenović

    Citation: Fixed Point Theory and Applications 2017 2017:24

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  2. Content type: Research

    In this paper, we obtain some generalizations of fixed point results for Kannan, Chatterjea and Hardy-Rogers contraction mappings in a new class of generalized metric spaces introduced recently by Jleli and Sa...

    Authors: Youness ElKouch and El Miloudi Marhrani

    Citation: Fixed Point Theory and Applications 2017 2017:23

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  3. Content type: Research

    Rectangular cone b-metric spaces over a Banach algebra are introduced as a generalization of metric space and many of its generalizations. Some fixed point theorems are proved in this space and proper examples...

    Authors: Reny George, Hossam A Nabwey, R Rajagopalan, Stojan Radenović and KP Reshma

    Citation: Fixed Point Theory and Applications 2017 2017:14

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  4. Content type: Research

    In this paper, we use the concept of C-class functions to establish the best proximity point results for a certain class of proximal contractive mappings in S-metric spaces. Our results extend and improve some kn...

    Authors: Arslan Hojat Ansari and Jamnian Nantadilok

    Citation: Fixed Point Theory and Applications 2017 2017:12

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  5. Content type: Research

    Recently, Wardowski (Fixed Point Theory Appl. 2012:94, 2012) introduced a new concept of F-contraction and proved a fixed point theorem which generalizes the Banach contraction principle. Following this direction...

    Authors: Jarosław Górnicki

    Citation: Fixed Point Theory and Applications 2017 2017:9

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  6. Content type: Research

    The aim of this paper is to give a generalized version of Caristi fixed point theorems in pseudo-metric spaces. Our results generalize and improve many of well-known theorems. As an application of our results,...

    Authors: Samih Lazaiz, Karim Chaira, Mohamed Aamri and El Miloudi Marhrani

    Citation: Fixed Point Theory and Applications 2017 2017:3

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  7. Content type: Research

    In this paper, we introduce the notion of diagonal operator, we present the historical roots of diagonal operators and we give some fixed point theorems for this class of operators. Our approaches are based on...

    Authors: Adrian Petruşel, Ioan A Rus and Marcel-Adrian Şerban

    Citation: Fixed Point Theory and Applications 2016 2016:95

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  8. Content type: Review

    The purpose of this survey is to prove that the fixed point results for various multiplicative contractions are in fact equivalent to the corresponding fixed point results in (standard) metric spaces. For exam...

    Authors: Tatjana Došenović, Mihai Postolache and Stojan Radenović

    Citation: Fixed Point Theory and Applications 2016 2016:92

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  9. Content type: Research

    In this paper, we present new fixed point theorems in Banach algebras relative to the weak topology. Our fixed point results are obtained under Leray-Schauder-type boundary conditions. These results improve an...

    Authors: Abdelmjid Khchine, Lahcen Maniar and Mohamed-Aziz Taoudi

    Citation: Fixed Point Theory and Applications 2016 2016:88

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  10. Content type: Research

    We establish existence and uniqueness of fixed points for a new class of mappings, by using R-functions and lower semi-continuous functions in the setting of metric spaces. As consequences of this results, we obt...

    Authors: Antonella Nastasi, Pasquale Vetro and Stojan Radenović

    Citation: Fixed Point Theory and Applications 2016 2016:81

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  11. Content type: Research

    This paper considers the fixed point problem for a nonexpansive mapping on a real Hilbert space and proposes novel line search fixed point algorithms to accelerate the search. The termination conditions for th...

    Authors: Hideaki Iiduka

    Citation: Fixed Point Theory and Applications 2016 2016:77

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  12. Content type: Research

    The purpose of this paper is to establish some fixed point results for cyclic contractions in the setting of dislocated quasi-b-metric spaces. We verify that some previous cyclic contraction results in dislocated...

    Authors: Diana Dolićanin-Ðekić, Tatjana Došenović, Huaping Huang and Stojan Radenović

    Citation: Fixed Point Theory and Applications 2016 2016:74

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  13. Content type: Research

    We show that the result on cyclic weak contractions of Harjani et al. (J. Nonlinear Sci. Appl. 6:279-284, 2013) holds without the assumption of compactness of the underlying space, and also without the assumption...

    Authors: Zoran Kadelburg, Stojan Radenović and Jelena Vujaković

    Citation: Fixed Point Theory and Applications 2016 2016:46

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