Fixed Point, Data Dependence, and Well‐Posed Problems for Multivalued Nonlinear Contractions
Journal of Function Spaces, Volume 2021, Issue 1, 2021., 2021 The aim of the paper is to discuss data dependence, existence of fixed points, strict fixed points, and well posedness of some multivalued generalized contractions in the setting of complete metric spaces. Using auxiliary functions, we introduce Wardowski type multivalued nonlinear operators that satisfy a novel class of contractive requirements ...
Iram Iqbal +4 more
wiley +1 more source
Fixed Point Theorems for Set-Valued Mappings on TVS-Cone Metric Spaces [PDF]
, 2015 In the context of tvs-cone metric spaces, we prove a Bishop-Phelps and a Caristi's type theorem. These results allow us to prove a fixed point theorem for $(\delta, L)$-weak contraction according to a pseudo Hausdorff metric defined by means of a cone ...
Fierro, Raúl
core +2 more sources
Existence Theorems on Advanced Contractions with Applications
Journal of Function Spaces, Volume 2021, Issue 1, 2021., 2021 In this research article, by introducing a mapping φ defined on [0,∞)4, with some axioms, we define two generalized contractions called FH+φ‐contractions and φHP+‐contractions. We investigate their mutual relation and establish an existence theorem addressing FH+φ‐contractions with some applications.
Sang Og Kim +2 more
wiley +1 more source
Some Random Fixed‐Point Theorems for Weakly Contractive Random Operators in a Separable Banach Space
International Journal of Mathematics and Mathematical Sciences, Volume 2021, Issue 1, 2021., 2021 The aim of this paper is to prove a common random fixed‐point and some random fixed‐point theorems for random weakly contractive operators in separable Banach spaces. A random Mann iterative process is introduced to approximate the fixed point. Finally, the main result is supported by an example and used to prove the existence and the uniqueness of a ...
Kenza Benkirane +3 more
wiley +1 more source
Data dependence results of a new multistep and S-iterative schemes for contractive-like operators [PDF]
, 2012 In this paper, we prove that convergence of a new iteration and S-iteration can be used to approximate to the fixed points of contractive-like operators.
Gursoy, Faik +2 more
core +1 more source
A general class of noninstantaneous impulsive fractional differential inclusions in Banach spaces
Advances in Difference Equations, 2017 In this paper we introduce the concept of a PC-mild solution to a general new class of noninstantaneous impulsive fractional differential inclusions involving the generalized Caputo derivative with the lower bound at zero in infinite dimensional Banach ...
JinRong Wang +3 more
doaj +1 more source
The Theory of Reich's Fixed Point Theorem for Multivalued Operators
Fixed Point Theory and Applications, 2010 The purpose of this paper is to present a theory of Reich's fixed point theorem for multivalued operators in terms of fixed points, strict fixed points, multivalued weakly Picard operators, multivalued Picard operators, data dependence of the fixed ...
Tania Lazăr +3 more
doaj +1 more source
Ulam-Hyers stability for partial differential inclusions
Electronic Journal of Qualitative Theory of Differential Equations, 2012 Using the weakly Picard operator technique, we will present Ulam-Hyers stability results for integral inclusions of Fredholm and Volterra type and for the Darboux problem associated to a partial differential inclusion.
V. Lazar
doaj +1 more source
Convergence and almost sure T-stability for a random iterative sequence generated by a generalized random operator [PDF]
, 2015 The aim of this paper is to introduce the concept of generalized φ-weakly contraction random operators and then to prove the convergence and almost sure T-stability of Mann and Ishikawa-type random iterative schemes.
Abbas, Mujahid, Okeke, G.A.
core +5 more sources
Multivalued Problems, Orthogonal Mappings, and Fractional Integro‐Differential Equation
Journal of Mathematics, Volume 2020, Issue 1, 2020., 2020 In this manuscript, we propose some sufficient conditions for the existence of solution for the multivalued orthogonal ℱ‐contraction mappings in the framework of orthogonal metric spaces. As a consequence of results, we obtain some interesting results.
R. K. Sharma +2 more
wiley +1 more source