Weakly Picard Operators Research Articles

Data Dependence, Strict Fixed Point Results, and Well-Posedness of Multivalued Weakly Picard Operators

In this paper, we introduce the notion of s , r -contractive multivalued weakly Picard operators via simulation functions, named as Z s , r -contractions. We present some related fixed point theorems. We investigate data dependence and strict fixed point results. The well-posedness for such operators is also considered. Moreover, we generalize the results of Moţ and Petruşel. To show the usability of our results, we give some examples and an application to resolve a functional equation arising in dynamical systems.

The influence of theta-function to the class of MWP operators

In this work, taking into account the theta-function, we present a general class of multivalued weakly Picard operators on complete metric space. We also provide an example showing that it includes some earlier classes as properly.

A new approach to multivalued nonlinear weakly Picard operators

The notion of nonlinear (mathcal{F}_{s}, mathcal{L})-contractive multivalued operators is initiated and some related fixed point results are considered. We also give an example to show the validity of obtained theoretical results. Our results generalize many existing ones in the literature.

Some new fixed point results for multi-valued weakly Picard operators

In this paper, we present some extensions of Banach contraction principle for multi-valued maps. Corresponding convergence theorems for the Picard iteration associated to a class of multi-valued operators are obtained in the setting of modular metric spaces. The presented results improve many recent fixed points results in the setting of modular metric spaces and also generalize some classical known results. Moreover, some examples are given.

On a broad category of multivalued weakly Picard operators

On a broad category of multivalued weakly Picard operators

A new perspective for multivalued weakly Picard operators

This research contains some recent developments about multivalued weakly Picard operators on complete metric spaces. In addition, taking into account both multivalued ?-contraction and almost contraction on complete metric spaces, we present a new perspective for multivalued weakly Picard operators. Finally, we give a nontrivial example showing that the investigation of this paper is significant.

Relevant Classes of Weakly Picard Operators

AbstractIn this paper we consider the following problems:(1) Which weakly Picard operators satisfy a retraction- displacement condition? (2) For which weakly Picard operators the fixed point problem is well posed? (3) Which weakly Picard operators have Ostrowski property?Some applications and open problems are also presented.

Multivalued almost F-contractions on complete metric spaces

In the present paper, considering a new concept of multivalued almost F-contraction, we give a general class of multivalued weakly Picard operators on complete metric space. Also, we give some illustrative examples showing that our results are proper generalizations of some previous theorems.

On multivalued weakly Picard operators in partial Hausdorff metric spaces

AbstractWe discuss multivalued weakly Picard operators on partial Hausdorff metric spaces. First, we obtain Kikkawa-Suzuki type fixed point theorems for a new type of generalized contractive conditions. Then, we prove data dependence of a fixed points set theorem. Finally, we present sufficient conditions for well-posedness of a fixed point problem. Our results generalize, complement and extend classical theorems in metric and partial metric spaces.

A fixed point theorem for multi-valued weakly Picard operators in b-metric space

AbstractIn this paper, we establish a fixed point theorem for multi-valued operators in a complete

Existence and data dependence of fixed points for multivalued operators on gauge spaces

The purpose of this note is to present some fixed point and data dependence theorems in complete gauge spaces and in hyperconvex metric spaces for the so-called Meir–Keeler multivalued operators and admissible multivalued a α -contractions. Our results extend and generalize several theorems of Espínola and Kirk [R. Espínola, W.A. Kirk, Set-valued contractions and fixed points, Nonlinear Anal. 54 (2003) 485–494] and Rus, Petruşel, and Sîntămărian [I.A. Rus, A. Petruşel, A. Sîntămărian, Data dependence of the fixed point set of some multivalued weakly Picard operators, Nonlinear Anal. 52 (2003) 1947–1959].

Data dependence of the fixed point set of some multivalued weakly Picard operators

In this paper we study data dependence of the fixed point set for a special class of multivalued weakly Picard operators. Existence and data dependence of the common fixed points for some Reich-type multivalued operators are also proved. Finally, an application to a Fredholm integral inclusion is given.