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 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.

scholarly journals Some Properties of Solutions of a Functional-Differential Equation of Second Order with Delay

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Veronica Ana Ilea ◽  
Diana Otrocol
Keyword(s):  
Differential Equation ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Differential Equations ◽  
Operator Theory ◽  
Functional Differential Equations ◽  
Picard Operator ◽  
Functional Differential ◽  
Weakly Picard Operator ◽  
Stability Results

Existence, uniqueness, data dependence (monotony, continuity, and differentiability with respect to parameter), and Ulam-Hyers stability results for the solutions of a system of functional-differential equations with delays are proved. The techniques used are Perov’s fixed point theorem and weakly Picard operator theory.

scholarly journals Random fixed point theorems for nonexpansive and contractive-type random operators on Banach spaces

1994 ◽  
Vol 7 (4) ◽  
pp. 569-580 ◽  
Author(s):  
Ismat Beg ◽  
Naseer Shahzad
Keyword(s):  
Banach Space ◽  
Fixed Point ◽  
Fixed Point Theorems ◽  
Coincidence Point ◽  
Random Operators ◽  
Random Coincidence ◽  
Random Fixed Point ◽  
Random Fixed Points ◽  
Multivalued Operators ◽  
Contractive Type

The existence of random fixed points. for nonexpansive and pseudocontractive random multivalued operators defined on unbounded subsets of a Banach space is proved. A random coincidence point theorem for a pair of compatible random multivalued operators is established.

Ulam stability for Hilfer type fractional differential inclusions via the weakly Picard operators theory

2017 ◽  
Vol 20 (2) ◽  
Author(s):  
Saïd Abbas ◽  
Mouffak Benchohra ◽  
Adrian Petruşel
Keyword(s):  
Fractional Derivative ◽  
Operator Theory ◽  
Differential Inclusions ◽  
Ulam Stability ◽  
Hilfer Fractional Derivative ◽  
Picard Operator ◽  
Fractional Differential ◽  
Differential Equations And Inclusions ◽  
Weakly Picard Operator ◽  
Stability Results

AbstractConsiderable attention has been recently given to the existence of solutions of initial or boundary value problems for fractional differential equations and inclusions with Hilfer fractional derivative. Motivated by these results, in this paper we will present existence, data dependence and Ulam stability results for some differential inclusions with Hilfer fractional derivative. The results follow as applications of the multi-valued weakly Picard operator theory. An example illustrates the main result of the paper.

scholarly journals Ulam-Hyers stability for operatorial inclusions

2012 ◽  
Vol 21 (1) ◽  
pp. 87-94
Author(s):  
OANA MARIA MLESNITE ◽  
Keyword(s):  
Differential Inclusion ◽  
Coincidence Point ◽  
Stability Theorem ◽  
Point Problem ◽  
Multivalued Operators ◽  
Stability Results

The purpose of the work is to present some Ulam-Hyers stability results for the coincidence point problem associated to single-valued and multivalued operators. As an application, an Ulam-Hyers stability theorem for a differential inclusion.

scholarly journals OCCURRENCE OF STABLE ROUGH FRACTIONAL INTEGRAL INCLUSION

2019 ◽  
pp. 329
Author(s):  
Rabha W. Ibrahim ◽  
Jay Jahangiri
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Fractional Integral ◽  
Operator Method ◽  
Rough Kernel ◽  
Fredholm Type ◽  
Picard Operator ◽  
Integral Inclusion ◽  
Type Integral ◽  
Weakly Picard Operator

In the present paper, we generalize the Fredholm type integral operator, by using the fractional rough kernel. We also deal with the Ulam-Hyers stability for rough fractional integral inclusion and utilize the weakly Picard operator method as well as the generalized Covitz-Nadler fixed point theorem.

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 Existence and Ulam stability for implicit fractional q-difference equations

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Saïd Abbas ◽  
Mouffak Benchohra ◽  
Nadjet Laledj ◽  
Yong Zhou
Keyword(s):  
Fixed Point ◽  
Banach Spaces ◽  
Difference Equations ◽  
Existence And Uniqueness ◽  
Fixed Point Theorems ◽  
Ulam Stability ◽  
Uniqueness Of Solutions ◽  
Stability Results ◽  
Rassias Stability

AbstractThis paper deals with some existence, uniqueness and Ulam–Hyers–Rassias stability results for a class of implicit fractional q-difference equations. Some applications are made of some fixed point theorems in Banach spaces for the existence and uniqueness of solutions, next we prove that our problem is generalized Ulam–Hyers–Rassias stable. Two illustrative examples are given in the last section.

scholarly journals Some New Coupled Coincidence Point and Coupled Fixed Point Results in Partially Ordered Metric-Like Spaces and an Application

2018 ◽  
Vol 2018 ◽  
pp. 1-13 ◽  
Author(s):  
Min Liang ◽  
Chuanxi Zhu ◽  
Zhaoqi Wu ◽  
Chunfang Chen
Keyword(s):  
Fixed Point ◽  
Integral Equations ◽  
Fixed Point Theorems ◽  
Coincidence Point ◽  
Coupled Fixed Point ◽  
Coupled Coincidence Point ◽  
Nonlinear Integral Equations ◽  
Partially Ordered ◽  
Coupled Coincidence

Some new coupled coincidence point and coupled fixed point theorems are established in partially ordered metric-like spaces, which generalize many results in corresponding literatures. An example is given to support our main results. As an application, we discuss the existence of the solutions for a class of nonlinear integral equations.

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