The Picard sequence of a fibration

1976 ◽  
pp. 71-85
Author(s):  
Andy R. Magid
Keyword(s):  
Picard Sequence

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

Mathematics ◽  
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.

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

Mathematics ◽  
2019 ◽  
Vol 7 (12) ◽  
pp. 1190 ◽  
Author(s):  
Manuel De la Sen ◽  
Nebojša Nikolić ◽  
Tatjana Došenović ◽  
Mirjana Pavlović ◽  
Stojan Radenović
Keyword(s):  
Contraction Mapping ◽  
New Approach ◽  
Contraction Mappings ◽  
Graphic Contraction ◽  
Picard Sequence ◽  
Theoretical Results

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.

scholarly journals Some critical remarks on “Some new fixed point results in rectangular metric spaces with an application to fractional-order functional differential equations”

2022 ◽  
Vol 27 (1) ◽  
pp. 163-178
Author(s):  
Mudasir Younis ◽  
Aleksandra Stretenović ◽  
Stojan Radenović
Keyword(s):  
Fixed Point ◽  
Differential Equations ◽  
Fractional Order ◽  
Metric Spaces ◽  
Functional Differential Equations ◽  
Contractive Condition ◽  
Nonlinear Anal ◽  
Model Control ◽  
Functional Differential ◽  
Picard Sequence

In this manuscript, we generalize, improve, and enrich recent results established by Budhia et al. [L. Budhia, H. Aydi, A.H. Ansari, D. Gopal, Some new fixed point results in rectangular metric spaces with application to fractional-order functional differential equations, Nonlinear Anal. Model. Control, 25(4):580–597, 2020]. This paper aims to provide much simpler and shorter proofs of some results in rectangular metric spaces. According to one of our recent lemmas, we show that the given contractive condition yields Cauchyness of the corresponding Picard sequence. The obtained results improve well-known comparable results in the literature. Using our new approach, we prove that a Picard sequence is Cauchy in the framework of rectangular metric spaces. Our obtained results complement and enrich several methods in the existing state-ofart. Endorsing the materiality of the presented results, we also propound an application to dynamic programming associated with the multistage process.

scholarly journals On some F-contraction of Piri-Kumam-Dung-type mappings in metric spaces

2020 ◽  
Vol 68 (4) ◽  
pp. 697-714 ◽  
Author(s):  
Jelena Vujaković ◽  
Stojan Radenović
Keyword(s):  
Metric Space ◽  
Cauchy Sequence ◽  
Metric Spaces ◽  
Complete Metric Space ◽  
Contraction Mappings ◽  
Picard Sequence ◽  
Increasing Function

Introduction/purpose: This paper establishes some new results of Piri-Kumam-Dung-type mappings in a complete metric space.The goal was to improve the already published results. Methods: Using the property of a strictly increasing function as well as the known Lemma formulated in (Radenović et al, 2017), the authors have proved that a Picard sequence is a Cauchy sequence. Results: New results were obtained concerning the F-contraction mappings of S in a complete metric space. To prove it, the authors used only property (W1). Conclusion:The authors believe that the obtained results represent a significant improvement of many known results in the existing literature.

scholarly journals Picard Sequence and Fixed Point Results onb-Metric Spaces

2015 ◽  
Vol 2015 ◽  
pp. 1-6 ◽  
Author(s):  
Marta Demma ◽  
Pasquale Vetro
Keyword(s):  
Fixed Point ◽  
Metric Space ◽  
Metric Spaces ◽  
Multivalued Mappings ◽  
Picard Sequence

We obtain some fixed point results for single-valued and multivalued mappings in the setting of ab-metric space. These results are generalizations of the analogous ones recently proved by Khojasteh, Abbas, and Costache.

scholarly journals On the initial value problem for a class of nonlinear biharmonic equation with time-fractional derivative

2021 ◽  
pp. 1-43
Author(s):  
Anh Tuan Nguyen ◽  
Tomás Caraballo ◽  
Nguyen Huy Tuan
Keyword(s):  
Mild Solution ◽  
Blow Up ◽  
Resolvent Operators ◽  
Initial Value ◽  
Exponential Nonlinearity ◽  
Smoothing Effects ◽  
Singular Initial Data ◽  
Cahn Hilliard Equation ◽  
Picard Sequence ◽  
Time Existence

In this study, we investigate the intial value problem (IVP) for a time-fractional fourth-order equation with nonlinear source terms. More specifically, we consider the time-fractional biharmonic with exponential nonlinearity and the time-fractional Cahn–Hilliard equation. By using the Fourier transform concept, the generalized formula for the mild solution as well as the smoothing effects of resolvent operators are proved. For the IVP associated with the first one, by using the Orlicz space with the function $\Xi (z)={\textrm {e}}^{|z|^{p}}-1$ and some embeddings between it and the usual Lebesgue spaces, we prove that the solution is a global-in-time solution or it shall blow up in a finite time if the initial value is regular. In the case of singular initial data, the local-in-time/global-in-time existence and uniqueness are derived. Also, the regularity of the mild solution is investigated. For the IVP associated with the second one, some modifications to the generalized formula are made to deal with the nonlinear term. We also establish some important estimates for the derivatives of resolvent operators, they are the basis for using the Picard sequence to prove the local-in-time existence of the solution.

scholarly journals On Recent Results Concerning F-Contraction in Generalized Metric Spaces

Mathematics ◽  
2020 ◽  
Vol 8 (5) ◽  
pp. 767 ◽  
Author(s):  
Jelena Vujaković ◽  
Slobodanka Mitrović ◽  
Mirjana Pavlović ◽  
Stojan Radenović
Keyword(s):  
Fixed Point ◽  
Metric Spaces ◽  
Weak Contraction ◽  
New Approach ◽  
Generalized Metric Spaces ◽  
Complete Metric Spaces ◽  
Type Mapping ◽  
Contraction Type ◽  
Picard Sequence ◽  
Open Question

In this manuscript we discuss, consider, generalize, improve and unify several recent results for so-called F-contraction-type mappings in the framework of complete metric spaces. We also introduce ( φ , F ) -weak contraction and establish the corresponding fixed point result. Using our new approach for the proof that a Picard sequence is a Cauchy in metric space, our obtained results complement and enrich several methods in the existing literature. At the end we give one open question for F-contraction of Ćirić-type mapping.

The Picard Sequence of a Fibration

1975 ◽  
Vol 53 (1) ◽  
pp. 37 ◽  
Author(s):  
Andy R. Magid
Keyword(s):  
Picard Sequence

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

Mathematics ◽  
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.

scholarly journals Revisiting and revamping some novel results in F-metric spaces

2021 ◽  
Vol 69 (2) ◽  
pp. 338-354
Author(s):  
Zoran Mitrović ◽  
Mudasir Jounis ◽  
Miloje Rajović
Keyword(s):  
Fixed Point ◽  
Metric Space ◽  
Metric Spaces ◽  
Recent Developments ◽  
Picard Sequence

Introduction/purpose: This article establishes several new contractive conditions in the context of so-called F-metric spaces. The main purpose was to generalize, extend, improve, complement, unify and enrich the already published results in the existing literature. We used only the property (F1) of Wardowski as well as one well-known lemma for the proof that Picard sequence is an F-Cauchy in the framework of F-metric space. Methods: Fixed point metric theory methods were used. Results: New results are enunciated concerning the F-contraction of two mappings S and T in the context of F-complete F-metric spaces. Conclusions: The obtained results represent sharp and significant improvements of some recently published ones. At the end of the paper, an example is given, claiming that the results presented in this paper are proper generalizations of recent developments.

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