Non-self Operators Research Articles

A fixed point principle for some nonself operators on large Kasahara spaces

A fixed point principle for some nonself operators on large Kasahara spaces

Fixed point theorems for nonself operators on a large Kasahara space

Fixed point theorems for nonself operators on a large Kasahara space

Common solutions for a monotone variational inequality problem and an infinite family of inverse strongly monotone non-self operators

In this paper, we introduce regularization methods for finding a point, being not only a solution for a monotone variational inequality problem but also a common zero for an infinite family of inverse strongly monotone non-self operators of a closed convex subset in a real Hilbert space. In these methods, only a finite number of the operators is used at each iteration step. Applications to the problem of common fixed point for an infinite family of strictly pseudo-contractive non-self operators and the split feasibility and fixed point problems are considered. As a particular case, a regularization extragradient iterative method without prior knowledge of operator norms for solving the split feasibility problem (SFP) is obtained. Numerical examples are given for illustration.

Best proximity point results for Prešić type nonself operators in $ b $-metric spaces

<abstract><p>The present work is about the existence of best proximity points for Prešić type nonself operators in $ b $-metric spaces. In order to elaborate the results an example is presented. Moreover, some interesting formulations of Prešić fixed point results are also established. In addition a result in double controlled metric type space is also formulated.</p></abstract>

Fixed point results for non-self nonlinear graphic contractions in complete metric spaces with applications

In this paper, we will present some fixed point results for the case of non-self operators satisfying a nonlinear graphic contraction condition in complete metric spaces. Properties of the corresponding fixed point equation are established and some applications are given.

Fixed point theory for nonself generalized contractions in Kasahara spaces

Abstract In this paper we extend some results of V. Berinde, Şt. Măruşter and I.A. Rus (Saturated contraction principles for nonself operators, generalizations and applications, Filomat, 31:11(2017), 3391-3406), which were given in metric spaces, to Kasahara spaces. Some research directions are also presented.

Coincidences of Nonself Operators by a Simpler Algorithm

In this article, we introduce a new class of contractive mappings and study analytical and computational aspects of a special case of Jungck-Khan iterative algorithm generated by this class of mappings. In particular, we improve upon strong convergence, rate of convergence and data dependence results existing in the current literature. Analytical as well numerical illustrative examples are given to support the new results.

Prešić Type Nonself Operators and Related Best Proximity Results

The purpose of this article is to discuss the existence of best proximity points for Pre s ˇ i c ´ -type nonself operators, say T : A k → B . We also give several examples to support our results. As a consequence of our results, we have provided some interesting formulations of Pre s ˇ i c ´ fixed point results.

A viscosity approximation method for nonself operators and equilibrium problems in Hilbert spaces

A viscosity approximation method for nonself operators and equilibrium problems in Hilbert spaces

Common fixed point of Jungck-Kirk-type iterations for non-self operators in normed linear spaces

Abstract In this paper, we introduce Jungck-Kirk-multistep and Jungck-Kirk-multistep-SP iterative schemes and use their strong convergences to approximate the common fixed point of nonself operators in a normed linear Space. The Jungck-Kirk-Noor, Jungck-Kirk-SP, Jungck-Kirk-Ishikawa, Jungck-Kirk-Mann and Jungck-Kirk iterative schemes follow our results as corollaries. We also study and prove stability results of these schemes in a normed linear space. Our results generalize and unify most approximation and stability results in the literature.

Stability and data dependence results for the Jungck--Khan iterative scheme

The Jungck--Khan iterative scheme for a pair of nonself operators contains as a special case Jungck--Ishikawa and Jungck--Mann iterative schemes. In this paper, we establish improved results about convergence, stability, and data dependence for the Jungck--Khan iterative scheme.

Fixed points for non-self operators in gauge spaces

Fixed points for non-self operators in gauge spaces

Fixed point theory for a new type of contractive multivalued operators

The aim of this paper is to discuss some basic problems (data dependence, well-posedness, nonself operators, homotopy results, generalized contractions) of the fixed point theory for a new type contractive multivalued operator. The results complement and extend some very recent results proved by M. Kikkawa and T. Suzuki, as well as, other theorems given by M. Frigon and A. Granas, S. Reich, I.A. Rus, etc.

Fixed points for non-self operators and domain invariance theorems

The purpose of this paper is to discuss some basic problems of the fixed point theory for non-self (single-valued and multivalued) generalized contractions. As consequences, new open operator principles and domain invariance theorems are obtained. The results complement and extend some known results in the literature.