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۱Some fixed point theorems concerning (ψ,φ)–type contraction in complete metric spaces
اطلاعات انتشار: Journal of Nonlinear Sciences and Applications، نهم،شماره۶، ۲۰۱۶، سال
تعداد صفحات: ۱۰
The purpose of this paper is to introduce the notions of (ψ,φ)–type contractions and (ψ,φ)–type Suzuki contractions and to establish some new fixed point theorems for such kind of mappings in the setting of complete metric spaces. The results presented in the paper are an extension of the Banach contraction principle, Suzuki contraction theorem, Jleli and Samet fixed point theorem, Piri and Kumam fixed point theorem.

۲Viscosity approximation methods for the implicit midpoint rule of asymptotically nonexpansive mappings in Hilbert spaces
اطلاعات انتشار: Journal of Nonlinear Sciences and Applications، نهم،شماره۶، ۲۰۱۶، سال
تعداد صفحات: ۱۱
The purpose of this paper is to introduce the implicit midpoint rule of asymptotically nonexpansive mappings in Hilbert spaces. The strong convergence of this viscosity method is proved under certain assumptions imposed on the sequence of parameters. Moreover, it is shown that the limit solves an additional variational inequality. Applications to nonlinear variational inclusion problem, nonlinear Volterra integral equations, variational inequality problem and hierarchical minimization problems are included. The results presented in the paper extend and improve some recent results announced in the current literature.
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