The aim of this work is to modify the notions of α-admissible and α-ψ-contractive mappings and establish new fixed point theorems for such mappings in complete metric spaces. Presented theorems provide main results of Karapinar and Samet (Abstr. Appl. Anal. 2012Anal. :793486, 2012 and Samet et al. (Nonlinear Anal. 75:2154-2165 as direct corollaries. Moreover, some examples and applications to integral equations are given here to illustrate the usability of the obtained results.
Fixed point theorems for multivalued contractive-type and nonexpansive-type maps on complete metric spaces and on certain closed bounded convex subsets of Banach spaces have been proved. They extend some known results due to Browder, Husain and Tarafdar, Karlovitz and Kirk
Samet et al. (Nonlinear Anal. 75:2154-2165, 2012) introduced α-ψ-contractive mappings and proved some fixed point results for these mappings. More recently Salimi et al. (Fixed Point Theory Appl. 2013:151, 2013) modified the notion of α-ψ-contractive mappings and established certain fixed point theorems. Here, we continue to utilize these modified notions for single-valued Geraghty and Meir-Keeler-type contractions, as well as multi-valued contractive mappings. Presented theorems provide main results of Hussain et al.
In this paper, a regularization projection algorithm is investigated for solving common elements of an equilibrium problem, a variational inequality problem and a fixed point problem of a strictly pseudocontractive mapping. Strong convergence theorems are established in the framework of real Hilbert spaces.
Abstract. In this paper we prove coincidence and common fixed points results for single-valued maps / and multivalued /-nonexpansive maps with star-shaped weakly compact domains in Banach spaces, which extend the theorems of [3], [6], [8] and others. Moreover weak convergence and strong convergence results for coincidence point sets have also been proved, extending a result in [1].
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