Multi-valued Non-self Mappings Research Articles

Comments on the paper ‘A new contribution to best proximity point theory on quasi metric spaces and an application to nonlinear integral equations’

Just recently M. Aslantas [A new contribution to best proximity point theory on quasi metric spaces and an application to nonlinear integral equations. Optimization. 2022] established a new best proximity point theorem multivalued non-self mappings which satisfy an appropriate contractive condition in the framework of quasi metric spaces. Then he applied the existing result to present an application to the solvability of a class of nonlinear integral equations. In this short note, we show that the best proximity point theorem proved in the aforesaid article is a special case of a fixed point theorem for multivalued contraction type mappings which was studied by J. Marin et al. [Q-functions on quasimetric spaces and fixed points for multivalued maps. Fixed Point Theory Appl. 2011:Article ID 603861].

A contribution to best proximity point theory and an application to partial differential equation

In this work, the main discussion centres on avoiding the use of triangle inequality while proving Cauchy sequence to establish best proximity point theorems for single valued as well as multivalued non-self mappings. We prove such best proximity point theorems in the setting of non-triangular metric spaces and elaborate through examples. In this process host of the existing best proximity results are generalized and improved. To arouse further interest in the subject, we connect this work in solving a specific type of partial differential equation problem.

Fixed point theorems for extended interpolative multi-valued non-self mappings in b-metric space with some application

Fixed point theorems for extended interpolative multi-valued non-self mappings in b-metric space with some application

FIXED POINT THEOREM FOR MULTIVALUED NON-SELF MAPPINGS SATISFYING JS-CONTRACTION WITH AN APPLICATION

In this paper, we present some fixed point results for multivalued non-self mappings. We generalize the fixed point theorem due to Altun and Minak [2] by using Jleli and Sameti [9] \(\vartheta\)-contraction. To validate the results proved here, we provide an appropriate application of our main result.

Fixed point theorem for a sequence of multivalued nonself mappings in metrically convex metric spaces

Abstract In this paper, a common fixed point theorem is demonstrated for a sequence of multivalued mappings which satisfy certain requirements in complete metric spaces. The results proved here will generalize and extend the results due to Ćirić [1]. Suitable examples are given at the end to support the results proved herein.

Existence of common best proximity point for single and multivalued non-self mappings

In this article, we introduce a new concept called proximal E. A property for single and multivalued mappings. We prove existence of proximally coincidence point for such class of mappings. We provide interesting example which illustrates our main results. Finally, we provide sufficient condition for existence of common best proximity point for this class of mappings.

Fixed Point Theorem for Multivalued Non-self Mappings in Partial Symmetric Spaces

Abstract In this paper, we proved a fixed point theorem for multi-valued non-self mappings in partial symmetric spaces. In doing so, we extended and generalized the results in literature by employing a convex structure for multi-valued non-self mappings using Rhoades type contractions. We also provided an illustrative example to support the results.

A novel iteration algorithm for a hybrid pair of total asymptotically non-expansive single-valued and total asymptotically quasi-non-expansive multi-valued non-self mappings in Banach spaces

A novel iteration algorithm for a hybrid pair of total asymptotically non-expansive single-valued and total asymptotically quasi-non-expansive multi-valued non-self mappings in Banach spaces

Approximate best proximity point sequences for C*λ mappings in strictly convex Banach spaces

Let A and B be nonempty subsets of a Banach space X and T : A → B be a non-self mapping. An approximate sequence of best proximity points for the mapping T is a sequence {xn } in A such that lim n →∞ || xn − T xn || → dist(A, B). In the current paper, we survey the existence of approximate best proximity point sequences for single and multivalued non-self mappings in strictly convex Banach spaces. We also introduce a geometric notion on a nonempty and convex pair of subsets of a Banach space, called semi-Opial condition, and establish some new best proximity point theorems.

Iterative Method for Approximating a Common Fixed Point for Family of Multivalued Nonself Mappings in Uniformly Convex Hyperbolic Spaces

In this paper, authors constructed Mann type of iterative method for the finite family of multi valued, nonself and nonexpansive mappings in a uniformly convex hyperbolic space. Authors proved strong convergence theorems of the iterative method, which approximates a common fixed point for the family single valued and multi valued nonexpansive mappings in a complete uniformly convex hyperbolic space which is more general than a complete CAT(0) space and a uniformly convex Banach space. The results in this work extended many results in the literature.

Common fixed points of a pair of multivalued non-self mappings in partial metric spaces

Common fixed points of a pair of multivalued non-self mappings in partial metric spaces

Weak PG-property and best proximity points

Abkar and Gbeleh proved the existence of best proximity points for multivalued nonself mappings on a complete metric space. We generalize/ extend their result by introducing the notion of weak PG-property. We also construct some examples in the support of our results.

Common best proximity point theorem for multivalued mappings in partially ordered metric spaces

In this paper, we prove the existence of a common best proximity point for a pair of multivalued non-self mappings in partially ordered metric spaces. Also, we provide some interesting examples to illustrate our main results.

Ishikawa iterative process for hemicontractive multi-valued non-self mappings in CAT(0) spaces

Our purpose in this paper is to construct Ishikawa iterative scheme formulti-valued non-self mappings in CAT(0) spaces. Then we obtain strong convergence of the scheme to a fixed point of multi-valued hemicontractive non-self mapping in a complete CAT(0) space. In addition, we define pseudocontractive mapping in CAT(0) spaces and show that a pseudocontractive mapping T with \(F(T)\not =\emptyset \) and \(Tp=\{p\}, \forall p\in F(T)\) is hemicontractive mapping. Furthermore, we give an example of hemicontractive mapping which is not pseudocontarctive to show that the converse is not necessarily true. Our theorems improve and unify most of the results in the literature.

Mann and Ishikawa-Type Iterative Schemes for Approximating Fixed Points of Multi-valued Non-Self Mappings

A Mann-type iterative scheme which converges strongly to a fixed point of a multi-valued nonexpansive non-self mapping T is constructed in a real Hilbert space H. We also constructed a Mann-type sequence which converges to a fixed point of a multi-valued quasi-nonexpansive non-self mapping under appropriate conditions. In addition, an Ishikawa-type iterative scheme which approximates the fixed points of multi-valued Lipschitz pseudocontractive non-self mappings is constructed in Banach spaces. The results obtained in this paper improve and extend the known results in the literature.

An extension of Assad-Kirk’s fixed point theorem for multivalued nonself mappings

In the present paper, taking into account the recent developments on the theory of fixed point, we give some fixed point results for multivalued nonself mappings on complete metrically convex metric spaces. Our main result properly includes the famous Assad-Kirk fixed point theorem for nonself mappings. Also, we provide a nontrivial example which shows the motivation for such investigations of multivalued nonself contraction mappings.

Convergence of iterative schemes for solving fixed point problems for multi-valued nonself mappings and equilibrium problems

Convergence of iterative schemes for solving fixed point problems for multi-valued nonself mappings and equilibrium problems

Viscosity Approximation Methods for Nonexpansive Multi-Valued Nonself Mappings and Equilibrium Problems

Abstract In this paper, strong convergence theorems by the viscosity approximation method for nonexpansive multi-valued nonself mappings and equilibrium problems are established under some suitable conditions in a Hilbert space. The obtained results extend and improve the corresponding results existed in the literature.

Best proximity points: global minimization of multivalued non-self mappings

In this article, we give a best proximity point theorem for generalized contractions in metric spaces with appropriate geometric property. We also, give an example which ensures that our result cannot be obtained from a similar result due to Amini-Harandi (Best proximity points for proximal generalized contractions in metric spaces. Optim Lett, 2012). Moreover, we prove a best proximity point theorem for multivalued non-self mappings which generalizes the Mizoguchi and Takahashi’s fixed point theorem for multivalued mappings.

Convergence of a Viscosity Iterative Method for Multivalued Nonself-Mappings in Banach Spaces

Let be a reflexive Banach space having a weakly sequentially continuous duality mapping with gauge function , a nonempty closed convex subset of , and a multivalued nonself-mapping such that is nonexpansive, where . Let be a contraction with constant . Suppose that, for each and , the contraction defined by has a fixed point . Let , and be three sequences in satisfying approximate conditions. Then, for arbitrary , the sequence generated by for all converges strongly to a fixed point of .