Krasnosel’skii-type fixed point theorems with applications to Volterra integral equations (original) (raw)
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2016
In this paper, we first state some new fixed point theorems for operators of the form A + B on a bounded closed convex set of a Banach space, where A is a weakly compact and weakly sequentially continuous mapping and B is either a weakly sequentially continuous nonlinear contraction or a weakly sequentially continuous separate contraction mapping. Second, we study the fixed point property for a larger class of weakly sequentially continuous mappings under weaker assumptions and we explore this kind of generalization by looking for the multivalued mapping (I −B)−1A, when I −B may not be injective. To attain this goal, we extend H. Schaefer’s theorem to multivalued mappings having weakly sequentially closed graph. Our results generalize many known ones in the literature, in particular those obtained by C. Avramescu (2004, Electron. J. Qual. Theory Differ. Equ., 17, 1 − 10), C. S. Barroso (2003, Nonlinear Anal., 55, 25 − 31), T.A. Burton (1998, Appl. Math. Lett., 11, 85− 88), Y. Liu an...
Publications de l'Institut Math?matique (Belgrade)
Darbo fixed point theorem is a powerful tool which is used in many fields in mathematics. Because of this feature, many generalizations of this theorem and its relations with other subjects have been investigated. Here we introduce a generalization of an F - contraction of Darbo type mapping and define a new contraction by using both function lasses and uniformly convergent sequences of functions and examine some of its properties. Afterward, we show that the new type of contraction, which we all F-Darbo type contraction, has more general results than many already studied in the literature. Furthermore, we explain the results of F-Darbo type contraction mapping with an interesting example. Finally, we give an application to solve the Volterra-type integral equation with the new type contraction.
In this paper, we establish certain new fixed point results for generalized weak contraction mappings using the concept of a triangular 2 − α − η admissible mappings in the framework of 2-metric spaces. As an application of the obtained results, we prove some fixed point results in partially ordered 2-metric spaces. The presented theorems generalize certain recent results in the literature. Moreover, some examples and an application to integral equations are provided to illustrate the usability of the obtained results.
Some fixed point theorems for weak contraction conditions of integral type
2010
In this paper, we shall establish two fixed point theorems by following the concept of [9, 21] and using weak contractions of the integral type. Our results are generalizations of the classical Banach's fixed point theorem [1, 2, 3, 4, 5, 7, 25] as well as extensions of some other results of Berinde [4, 5, 6, 7], Berinde and Berinde [8], Branciari [9], Chatterjea [10], Kannan [16] and Zamfirescu [24].
Fixed Points for -Graphic Contractions with Application to Integral Equations
Abstract and Applied Analysis, 2013
The aim of this paper is to define modified weak --contractive mappings and to establish fixed point results for such mappings defined on partial metric spaces using the notion of triangular -admissibility. As an application, we prove new fixed point results for graphic weak -contractive mappings. Moreover, some examples and an application to integral equation are given here to illustrate the usability of the obtained results.
Fixed Point Theorems for Manageable Contractions with Application to Integral Equations
Journal of Function Spaces, 2017
In this paper we utilize the concept of manageable functions to define multivalued α⁎-η⁎ manageable contractions and prove fixed point theorems for such contractions. As applications we deduce certain fixed point theorems which generalize and improve Nadler’s fixed point theorem, Mizoguchi-Takahashi’s fixed point theorem, and some other well-known results in the literature. Also, we give an illustrating example showing that our results are a proper generalization of Nadler’s theorem and provide an application to integral equations.