research proposal on fixed point theory

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 (Universitatea de Nord din Baia Mare, Romania),  Adrian Petrusel (Babeș-Bolyai University Cluj-Napoca, Romania) and Radu Precup (Babeș-Bolyai University Cluj-Napoca)

Dislocated cone metric space over Banach algebra and α -quasi contraction mappings of Perov type

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...

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On some fixed point theorems in generalized metric spaces

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...

Rectangular cone b-metric spaces over Banach algebra and contraction principle

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...

Best proximity points for proximal contractive type mappings with C -class functions in S -metric spaces

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...

Fixed point theorems for F -expanding mappings

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...

F -cone metric spaces over Banach algebra

Pseudo-metric space and fixed point theorem.

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,...

Strong and weak convergence theorems for split equality generalized mixed equilibrium problem

In this paper, we consider split equality generalized mixed equilibrium problem, which is more general than many problems such as split feasibility problem, split equality problem, split equilibrium problem, a...

Random fixed point theorems in partially ordered metric spaces

We present the random version in partially ordered metric spaces of the classical Banach contraction principle and some of its generalizations to ordered metric spaces.

Contributions to the fixed point theory of diagonal operators

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...

On multiplicative metric spaces: survey

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...

Leray-Schauder-type fixed point theorems in Banach algebras and application to quadratic integral equations

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...

Common fixed points of G -nonexpansive mappings on Banach spaces with a graph

Periodic and fixed points of the leader-type contractions in quasi-triangular spaces, a new iterative scheme for numerical reckoning fixed points of total asymptotically nonexpansive mappings, some fixed point results via r -functions.

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...

Line search fixed point algorithms based on nonlinear conjugate gradient directions: application to constrained smooth convex optimization

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...

A note on recent cyclic fixed point results in dislocated quasi- b -metric spaces

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...

Fixed point results in \(C^{*}\) -algebra-valued metric spaces are direct consequences of their standard metric counterparts

A note on the paper ‘fixed point theorems for cyclic weak contractions in compact metric spaces’.

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...

Fixed Point Theory and Algorithms for Sciences and Engineering

Featured Article: Tykhonov well-posedness of fixed point problems in contact mechanics

History-dependent and almost history-dependent operators represent a special class of nonlinear operators defined on a space of continuous functions. They arise both in functional analysis, solid mechanics, and contact mechanics. 

The author presents two applications in the study of boundary value problems arising in contact mechanics giving the mechanical interpretation of the corresponding convergence results.  

This is a perfect illustration of how fixed point arguments can be successfully used in the variational analysis of mathematical models of contact. 

Relaunch as Fixed Point Theory and Algorithms for Sciences and Engineering

Fixed Point Theory and Algorithms for Sciences and Engineering (formerly Fixed Point Theory and Applications) has been relaunched in 2021. The journal is open for submissions and celebrates its relaunch with Topical Collections on Optimization and Real World Applications  and Contact Mechanics and Engineering Applications . 

This relaunch marks a shift towards a broadened scope with a clear emphasis on applications. See the aims and scope for an overview of all fields covered by the journal.

Key areas are also reflected by the various sections of the journal. Get to know all the sections and the new  editorial board .  

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Relaxed inertial self-adaptive algorithm for the split feasibility problem with multiple output sets and fixed-point problem in the class of demicontractive mappings

Authors: Solomon Gebregiorgis, Poom Kumam and Kanokwan Sitthithakerngkiet

Weak and strong convergence theorems for a new class of enriched strictly pseudononspreading mappings in Hilbert spaces

Authors: Imo Kalu Agwu, Hüseyin Işık and Donatus Ikechi Igbokwe

A general algorithm for convex fair partitions of convex polygons

Authors: Mathilda Campillo, Maria D. Gonzalez-Lima and Bernardo Uribe

On some common fixed point results for two infinite families of uniformly L -Lipschitzian total asymptotically quasi-nonexpansive mappings

Authors: Buraskorn Nuntadilok, Pitchaya Kingkam, Jamnian Nantadilok and Khanitin Samanmit

Ϝ -Contraction of Hardy–Rogers type in supermetric spaces with applications

Authors: Kamaleldin Abodayeh, Syed Khayyam Shah, Muhammad Sarwar, Varaporn Wattanakejorn and Thanin Sitthiwirattham

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Axiom of Infinite Choice, transversal ordered spring spaces and fixed points

Authors: Milan R. Tasković

Fixed points of Suzuki type generalized multivalued mappings in fuzzy metric spaces with applications

Authors: Naeem Saleem, Basit Ali, Mujahid Abbas and Zahid Raza

Fixed points of a new type of contractive mappings in complete metric spaces

Authors: Dariusz Wardowski

A generalized metric space and related fixed point theorems

Authors: Mohamed Jleli and Bessem Samet

Iterative algorithms for solutions of Hammerstein equations in real Banach spaces

Authors: Charles E. Chidume, Abubakar Adamu and Lois C. Okereke

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Aims and scope

In a wide range of mathematical, computational, economical, modeling and engineering problems, the existence of a solution to a theoretical or real world problem is equivalent to the existence of a fixed point for a suitable map or operator. Fixed points are therefore of paramount importance in many areas of mathematics, sciences and engineering.

The theory itself is a beautiful mixture of analysis (pure and applied), topology and geometry. Over the last 60 years or so, the theory of fixed points has been revealed as a very powerful and important tool in the study of nonlinear phenomena. In particular, fixed point techniques have been applied in such diverse fields as biology, chemistry, physics, engineering, game theory and economics.

In numerous cases finding the exact solution is not possible; hence it is necessary to develop appropriate algorithms to approximate the requested result. This is strongly related to control and optimization problems arising in the different sciences and in engineering problems. Many situations in the study of nonlinear equations, calculus of variations, partial differential equations, optimal control and inverse problems can be formulated in terms of fixed point problems or optimization.

The aim of this journal is to report new fixed point results, methods and algorithms as well as their applications in which the indispensability of the fixed point results is highlighted or is the common substrate. It will cover topics such as

·         Applications to Differential Equations and Dynamical Systems

·         Computational Methods

·         Convex and Nonlinear Analysis

·         Fractional Calculus and Fractional Differential Equations

·         Fuzzy Fixed Point Theory

·         Metric Fixed Point Theory

·         Nonlinear Analysis and Partial Differential Equations

·         Numerical Analysis and Optimization

·         Optimization and Control Theory

·         Real World Applications

·         Set-Valued and Variational Analysis

·         Social and Behavioral Sciences

·         Topological Methods in Nonlinear Analysis

This journal will accept high quality articles containing original research results and survey articles of exceptional merit. An article to be published in Fixed Point Theory and Algorithms for Sciences and Engineering must either contain some new applications to real world problems or reveal novel aspects of the theory applicable to new situations.   Fixed Point Theory and Algorithms for Sciences and Engineering  uses continuous article publishing, so your article will be published immediately on the website in a single annual issue.  

Article collections

Metric Fixed Point Theory and Its Applications Edited by: Ishak Altun, Lakshmi Kanta Dey, Erdal Karapinar,  Radu Miculescu

Contact Mechanics and Engineering Applications Edited by: Mircea Sofonea, Weimin Han

Optimization and Real World Applications Edited by: Heinz Bauschke, Yunier Bello-Cruz, Radu Ioan Bot, Robert Csetnek, Alexander Zaslavski

Iterative Methods and Optimization Algorithms: A Dedication to Dr. Hong-Kun Xu Edited by: Ravi Agarwal, Juan Nieto, Adrian Petrusel

Fixed Point Theory: Theory, Computation and Applications Edited by: Vasile Berinde, Adrian Petrusel and Radu Precup

Recent Progress in Fixed Point Theory and Applications (2015) Edited by: Dr Inci Erhan, Prof A. Petrusel, Dr Antonio-Francisco Roldán-López-de-Hierro, Prof Erdal Karapinar

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Annual Journal Metrics

Citation Impact 2023 Source Normalized Impact per Paper (SNIP): 0.832 SCImago Journal Rank (SJR): 0.408

Speed 2023 Submission to first editorial decision (median days): 21 Submission to acceptance (median days): 200

Usage 2023 Downloads: 350,104 Altmetric mentions: 1

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• ISSN: 2730-5422 (electronic)

Fixed Point Theory

• © 2003
• Andrzej Granas 0 ,
• James Dugundji

Département de Mathématiques et Statistique, Université de Montréal, Montréal, Canada Department of Mathematics and Computer Science, University of Warmia and Mazury, Olsztyn, Poland

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• Includes supplementary material: sn.pub/extras

Part of the book series: Springer Monographs in Mathematics (SMM)

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Introduction to Metric Fixed Point Theory

Some fundamental topological fixed point theorems for set-valued maps.

Basic Concepts

• differential equation
• fixed point theory

Table of contents (7 chapters)

Front matter, introduction.

• Andrzej Granas, James Dugundji

Elementary Fixed Point Theorems

Theorem of borsuk and topological transversality, homology and fixed points, leray-schauder degree and fixed point index, the lefschetz-hopf theory, selected topics, back matter, authors and affiliations, département de mathématiques et statistique, université de montréal, montréal, canada.

Andrzej Granas

Department of Mathematics and Computer Science, University of Warmia and Mazury, Olsztyn, Poland

About the authors, bibliographic information.

Book Title : Fixed Point Theory

Authors : Andrzej Granas, James Dugundji

Series Title : Springer Monographs in Mathematics

DOI : https://doi.org/10.1007/978-0-387-21593-8

Publisher : Springer New York, NY

eBook Packages : Springer Book Archive

Copyright Information : Springer Science+Business Media New York 2003

Hardcover ISBN : 978-0-387-00173-9 Published: 26 June 2003

Softcover ISBN : 978-1-4419-1805-5 Published: 29 November 2010

eBook ISBN : 978-0-387-21593-8 Published: 09 March 2013

Series ISSN : 1439-7382

Series E-ISSN : 2196-9922

Edition Number : 1

Number of Pages : XVI, 690

Topics : Topology , Functional Analysis , Operator Theory , Econometrics

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