Cyclic Picard Operator and Simulation Type Functions

2020 ◽  
Vol Accepted ◽  
Author(s):  
Sumit Chandok
Keyword(s):  
Picard Operator

scholarly journals Ulam–Hyers–Mittag-Leffler stability for tripled system of weighted fractional operator with TIME delay

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Mohammed A. Almalahi ◽  
Satish K. Panchal ◽  
Fahd Jarad ◽  
Thabet Abdeljawad
Keyword(s):  
Fixed Point ◽  
Time Delay ◽  
Fractional Derivatives ◽  
Fixed Point Theorems ◽  
Sufficient Conditions ◽  
Fractional Operator ◽  
Caputo Fractional Derivatives ◽  
Picard Operator

AbstractThis study is aimed to investigate the sufficient conditions of the existence of unique solutions and the Ulam–Hyers–Mittag-Leffler (UHML) stability for a tripled system of weighted generalized Caputo fractional derivatives investigated by Jarad et al. (Fractals 28:2040011 2020) in the frame of Chebyshev and Bielecki norms with time delay. The acquired results are obtained by using Banach fixed point theorems and the Picard operator (PO) method. Finally, a pertinent example of the results obtained is demonstrated.

scholarly journals Suzuki ψF-contractions and some fixed point results

2018 ◽  
Vol 34 (1) ◽  
pp. 93-102
Author(s):  
NICOLAE-ADRIAN SECELEAN ◽  
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Metric Space ◽  
Metric Spaces ◽  
Complete Metric Space ◽  
Continuity Point ◽  
Picard Operator ◽  
Nonlinear Anal ◽  
New Type

The purpose of this paper is to combine and extend some recent fixed point results of Suzuki, T., [A new type of fixed point theorem in metric spaces, Nonlinear Anal., 71 (2009), 5313–5317] and Secelean, N. A. & Wardowski, D., [ψF-contractions: not necessarily nonexpansive Picard operators, Results Math., 70 (2016), 415–431]. The continuity and the completeness conditions are replaced by orbitally continuity and orbitally completeness respectively. It is given an illustrative example of a Picard operator on a non complete metric space which is neither nonexpansive nor expansive and has a unique continuity point.

scholarly journals Existence and Ulam-Hyers stability results for multivalued coincidence problems

Filomat ◽  
2012 ◽  
Vol 26 (5) ◽  
pp. 965-976 ◽  
Author(s):  
Oana Mleşniţe ◽  
Adrian Petruşel
Keyword(s):  
Fixed Point ◽  
Coincidence Point ◽  
Operator Technique ◽  
Picard Operator ◽  
Multivalued Operators ◽  
Weakly Picard Operator ◽  
Stability Results

In this paper, we will present some existence and Ulam-Hyers stability results for fixed point and coincidence point problems with multivalued operators using the weakly Picard operator technique in spaces endowed with vector metrics.

scholarly journals Properties of the solutions of those equations for which the Krasnoselskii iteration converges

2012 ◽  
Vol 28 (2) ◽  
pp. 329-336
Author(s):  
IOAN A. RUS ◽  
Keyword(s):  
Banach Space ◽  
Fixed Points ◽  
Convex Subset ◽  
Data Dependence ◽  
Picard Operator ◽  
Nonempty Convex Subset ◽  
Krasnoselskii Iteration ◽  
Nonempty Convex ◽  
Weakly Picard Operator

Let (X, +, R, →) be a vectorial L-space, Y ⊂ X a nonempty convex subset of X and f : Y → Y be an operator with Ff := {x ∈ Y | f(x) = x} 6= ∅. Let 0 < λ < 1 and let fλ be the Krasnoselskii operator corresponding to f, i.e., fλ(x) := (1 − λ)x + λf(x), x ∈ Y. We suppose that fλ is a weakly Picard operator (see I. A. Rus, Picard operators and applications, Sc. Math. Japonicae, 58 (2003), No. 1, 191-219). The aim of this paper is to study some properties of the fixed points of the operator f: Gronwall lemmas and comparison lemmas (when (X, +, R, →, ≤) is an ordered L-space) and data dependence (when X is a Banach space). Some applications are also given.

scholarly journals A-contraction mappings of integral type in n-normed spaces

2020 ◽  
Vol 31 (4) ◽  
pp. 87
Author(s):  
Salwa Salman Abed ◽  
Hanan Sabah Lazam
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorems ◽  
Normed Spaces ◽  
Integral Type ◽  
Contraction Mappings ◽  
Picard Operator ◽  
Contraction Type

In this article, A-contraction type mappings in integral case are defined on a complete n-normed spaces and the existence of some fixed point theorems are proved in the complete n-normed spaces and given some results on Picard operator. 

scholarly journals Ulam-Hyers stability for partial differential equations

2012 ◽  
Vol 21 (1) ◽  
pp. 73-78
Author(s):  
VASILE L. LAZAR ◽  
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Operator Technique ◽  
Partial Differential ◽  
Picard Operator ◽  
Weakly Picard Operator ◽  
Stability Results

Using the weakly Picard operator technique, we will present some Ulam-Hyers stability results for some partial differential equations.

SELF-SIMILARITY OF SOLUTIONS TO INTEGRAL AND DIFFERENTIAL EQUATIONS WITH RESPECT TO A FRACTAL MEASURE

Fractals ◽  
2019 ◽  
Vol 27 (02) ◽  
pp. 1950014
Author(s):  
H. KUNZE ◽  
D. LA TORRE ◽  
F. MENDIVIL ◽  
E. R. VRSCAY
Keyword(s):  
Integral Equation ◽  
Iterated Function System ◽  
Differential Forms ◽  
Self Similarity ◽  
Similar Measure ◽  
Picard Operator ◽  
Convergence Results ◽  
Iterated Function ◽  
Classical Integral ◽  
Self Similar

In this paper, we study solutions of a variation of a classical integral equation (based on the Picard operator) in which Lebesgue measure is replaced by a self-similar measure [Formula: see text]. Our main interest is in the fractal nature of the solutions and we use Iterated Function System (IFS) tools to investigate the behavior and self-similarity of these solutions. Both the integral and differential forms of the equation are discussed since each brings useful insights. Several convergence results are provided along with illustrative examples that show the applications of the theory when the underlying fractal object is the celebrated Cantor set. Additionally we show that the solution to our integral equation inherits self-similarity from the defining measure [Formula: see text].

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