Some Results on (s − q)-Graphic Contraction Mappings in b-Metric-Like Spaces

In this paper we consider ( s − q ) -graphic contraction mapping in b-metric like spaces. By using our new approach for the proof that a Picard sequence is Cauchy in the context of b-metric-like space, our results generalize, improve and complement several approaches in the existing literature. Moreover, some examples are presented here to illustrate the usability of the obtained theoretical results.

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On Some Recent Results Concerning F-Suzuki-Contractions in b-Metric Spaces

Mathematics ◽

10.3390/math8060940 ◽

2020 ◽

Vol 8 (6) ◽

pp. 940

Author(s):

Ersin Gilić ◽

Diana Dolićanin-Đekić ◽

Zoran D. Mitrović ◽

Dženis Pučić ◽

Hassen Aydi

Keyword(s):

Metric Spaces ◽

New Approach ◽

Contraction Mappings ◽

Picard Sequence ◽

Theoretical Results

The purpose of this manuscript is to provide much simpler and shorter proofs of some recent significant results in the context of generalized F-Suzuki-contraction mappings in b-complete b-metric spaces. By using our new approach for the proof that a Picard sequence is b-Cauchy, our results generalize, complement and improve many known results in the existing literature. Further, some new contractive conditions are provided here to illustrate the usability of the obtained theoretical results.

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SOME FIXED POINT RESULTS FOR CONVEX CONTRACTION MAPPINGS ON F-METRIC SPACES

Facta Universitatis Series Mathematics and Informatics ◽

10.22190/fumi2004939f ◽

2021 ◽

pp. 939

Author(s):

Hamid Faraji ◽

Stojan Radenovic

Keyword(s):

Fixed Point ◽

Contraction Mapping ◽

Fixed Point Theorems ◽

Metric Spaces ◽

Contraction Mappings ◽

Alpha Beta ◽

Theoretical Results

In this paper, we establish some fixed point theorems for convex contraction mappings in F-metric spaces. Also, we introduce the concept of (\alpha,\beta)-convex contraction mapping in F-metric spaces and give some fixed point results for such contractions. Moreover, some examples are given to support our theoretical results.

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Some New Results for Jaggi-W-Contraction-Type Mappings on b-Metric-like Spaces

Mathematics ◽

10.3390/math9161921 ◽

2021 ◽

Vol 9 (16) ◽

pp. 1921

Author(s):

Slobodanka Mitrović ◽

Vahid Parvaneh ◽

Manuel De La Sen ◽

Jelena Vujaković ◽

Stojan Radenović

Keyword(s):

New Approach ◽

Contraction Type ◽

Picard Sequence

In this article, we generalize, improve, unify and enrich some results for Jaggi-W-contraction-type mappings in the framework of b-metric-like spaces. Our results supplement numerous methods in the existing literature, and we created new approach to prove that a Picard sequence is Cauchy in a b-metric-like space. Among other things, we prove Wardowski’s theorem, but now by using only the property (W1). Our proofs in this article are much shorter than ones in recently published papers.

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A new contribution in fuzzy cone metric spaces by strong fixed point techniques with supportive application

Journal of Intelligent & Fuzzy Systems ◽

10.3233/jifs-212188 ◽

2021 ◽

pp. 1-21

Author(s):

Rashwan A. Rashwan ◽

Hasanen A. Hammad ◽

A. Nafea

Keyword(s):

Fixed Point ◽

Contraction Mapping ◽

Metric Spaces ◽

Mixed Monotone Property ◽

Cone Metric Spaces ◽

System Of Integral Equations ◽

Tripled Fixed Point ◽

Fixed Point Techniques ◽

Theoretical Results ◽

Cone Metric

In this manuscript, the concept of a cyclic tripled type fuzzy cone contraction mapping in the setting of fuzzy cone metric spaces is introduced. Also, some theoretical results concerned with tripled fixed points are given without a mixed monotone property in the mentioned space. Moreover, under this concept, some strong tripled fixed point results are obtained. Ultimately, to support the theoretical results non-trivial examples are listed and the existence of a unique solution to a system of integral equations is presented as an application.

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Best approximation and fixed points for rational-type contraction mappings

Journal of Applied Analysis ◽

10.1515/jaa-2019-0021 ◽

2019 ◽

Vol 25 (2) ◽

pp. 205-209

Author(s):

Sumit Chandok

Keyword(s):

Fixed Point ◽

Fixed Point Theorem ◽

Best Approximation ◽

Contraction Mapping ◽

Metric Spaces ◽

Contraction Mappings ◽

Invariant Approximation ◽

Frame Work ◽

Rational Type ◽

Type Contraction

AbstractIn this paper, we prove a fixed point theorem for a rational type contraction mapping in the frame work of metric spaces. Also, we extend Brosowski–Meinardus type results on invariant approximation for such class of contraction mappings. The results proved extend some of the known results existing in the literature.

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Evaluation of the Forward-Backward Sweep Load Flow Method using the Contraction Mapping Principle

International Journal of Electrical and Computer Engineering (IJECE) ◽

10.11591/ijece.v6i6.11303 ◽

2016 ◽

Vol 6 (6) ◽

pp. 3229

Author(s):

Diego Issicaba ◽

Jorge Coelho

Keyword(s):

Distribution System ◽

Existence And Uniqueness ◽

Contraction Mapping ◽

System Analysis ◽

Feasible Solution ◽

Contraction Mapping Principle ◽

Load Flow ◽

Contraction Mapping Theorem ◽

Flow Method ◽

Theoretical Results

<p>This paper presents an assessment of the forward-backward sweep load flow method to distribution system analysis. The method is formally assessed using fixed-point concepts and the contraction mapping theorem. The existence and uniqueness of the load flow feasible solution is supported by an alternative argument from those obtained in the literature. Also, the closed-form of the convergence rate of the method is deduced and the convergence dependence of loading is assessed. Finally, boundaries for error values per iteration between iterates and feasible solution are obtained. Theoretical results have been tested in several numerical simulations, some of them presented in this paper, thus fostering discussions about applications and future works.</p>

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Higher Order of Convergence with Multivalued Contraction Mappings

Journal of Mathematics ◽

10.1155/2020/8867897 ◽

2020 ◽

Vol 2020 ◽

pp. 1-8

Author(s):

Jia-Bao Liu ◽

Asma Rashid Butt ◽

Shahzad Nadeem ◽

Shahbaz Ali ◽

Muhammad Shoaib

Keyword(s):

Fixed Point ◽

Contraction Mapping ◽

Order Of Convergence ◽

Higher Order ◽

Gauge Function ◽

Multivalued Mappings ◽

Contraction Mappings ◽

Multivalued Contraction ◽

Integral Inclusion

In this paper, we establish some theorems of fixed point on multivalued mappings satisfying contraction mapping by using gauge function. Furthermore, we use Q - and R -order of convergence. Our main results extend many previous existing results in the literature. Consequently, to substantiate the validity of proposed method, we give its application in integral inclusion.

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Convergence of stochastic algorithms: from the Kushner–Clark theorem to the Lyapounov functional method

Advances in Applied Probability ◽

10.1017/s0001867800027567 ◽

1996 ◽

Vol 28 (04) ◽

pp. 1072-1094

Author(s):

Jean-Claude Fort ◽

Gilles Pagès

Keyword(s):

Vector Field ◽

Vector Fields ◽

Functional Method ◽

Stochastic Algorithms ◽

Smoothness Assumption ◽

New Approach ◽

The Mean ◽

Path Dependent ◽

Mean Vector ◽

Theoretical Results

In the first part of this paper a global Kushner–Clark theorem about the convergence of stochastic algorithms is proved: we show that, under some natural assumptions, one can ‘read' from the trajectories of its ODE whether or not an algorithm converges. The classical stochastic optimization results are included in this theorem. In the second part, the above smoothness assumption on the mean vector field of the algorithm is relaxed using a new approach based on a path-dependent Lyapounov functional. Several applications, for non-smooth mean vector fields and/or bounded Lyapounov function settings, are derived. Examples and simulations are provided that illustrate and enlighten the field of application of the theoretical results.

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ANTIDEUTERON PRODUCTION AND THE PHYSICS OF COALESCENCE: IMPLICATIONS OF A NEW APPROACH

International Journal of Modern Physics E ◽

10.1142/s0218301302000946 ◽

2002 ◽

Vol 11 (05) ◽

pp. 387-401

Author(s):

BHASKAR DE ◽

S. BHATTACHARYYA ◽

P. GUPTAROY

Keyword(s):

High Energy ◽

Measured Data ◽

New Combination ◽

Coalescence Model ◽

New Approach ◽

Nuclear Collisions ◽

High Energies ◽

Text Production ◽

Theoretical Results

Within the framework of coalescence model, the problem of antideuteron [Formula: see text] production in some high energy nuclear collisions has here been studied with the help of a new combination of models (NCM) outlined in some detail in the text. The totality of the approach, including one useful parametrization, adopted here leads us to obtain finally some theoretical results which are modestly in agreement with the measured data on various aspects of antideuteron production in both Pb + Pb and Au + Au collisions at moderately high energies. The implications of all this are discussed at the end of the paper.

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A classical theory of lattice dynamics

Proceedings of the Royal Society of London Series A - Mathematical and Physical Sciences ◽

10.1098/rspa.1970.0116 ◽

1970 ◽

Vol 317 (1529) ◽

pp. 279-291

Keyword(s):

Potential Energy ◽

Classical Theory ◽

Simple Form ◽

Lattice Dynamics ◽

Total Potential Energy ◽

Potential Functions ◽

New Approach ◽

Total Potential ◽

New Formulation ◽

Theoretical Results

A new formulation of the classical theory of lattice dynamics is presented which correctly reproduces all the features of the quantum theoretical results. This new approach starts with a more detailed description of the various potential functions that contribute to the total potential energy and uses these to define a new set of potential functions that depend on the initial configuration only. The expansion of the total potential energy in powers of nuclear displacements is then found to have a particularly simple form in terms of these configuration dependent potentials.

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