In this paper we first prove some coincidence and fixed point theorems for nonlinear hybrid generalized contractions on metric spaces. Secondly, using the concept of an asymptotically regular sequence, we give some fixed point theorems for Kannan type multi-valued mappings on metric spaces. Our main results improve and extend several known results proved by other authors.
Let be a nonempty closed convex subset of a real Hilbert space such that , a -strict pseudo-contraction for some such that . Consider the following iterative algorithm given by where is defined by , is the metric projection of onto , is a strongly positive linear bounded self-adjoint operator, is a contraction. It is proved that the sequence generated by the above iterative algorithm converges strongly to a fixed point of , which solves a variational inequality related...
The purpose of this paper is to establish some weak and strong convergence theorems of modified three-step iteration methods with errors with respect to a pair of nonexpansive and asymptotically nonexpansive mappings in uniformly convex Banach spaces. The results presented in this paper generalize, improve and unify a few results due to Chang [1], Liu and Kang [5], Osilike and Aniagbosor [7], Rhoades [8] and Schu [9], [10] and others. An example is included to demonstrate that our results are sharp....
In this paper, we introduce a general iterative scheme to investigate the problem of finding a common element of the fixed point set of a strict pseudocontraction and the solution set of a variational inequality problem for a relaxed cocoercive mapping by viscosity approximate methods. Strong convergence theorems are established in a real Hilbert space.
In this paper, we establish some new versions of coincidence point theorems for single-valued and multi-valued mappings in F-type topological space. As applications, we utilize our main theorems to prove coincidence point theorems and fixed point theorems for single-valued and multi-valued mappings in fuzzy metric spaces and probabilistic metric spaces.
Let be a measurable space and a nonempty bounded closed convex separable subset of -uniformly convex Banach space for some . We prove random fixed point theorems for a class of mappings satisfying: for each , and integer , where are functions satisfying certain conditions and is the value at of the -th iterate of the mapping . Further we establish for these mappings some random fixed point theorems in a Hilbert space, in spaces, in Hardy spaces and in Sobolev spaces ...
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