Properties of Chmielinski-orthogonality using Kadets-Klee property

The aim of this paper is to study new results of an approximate orthogonality of Birkhoff-James techniques in real Banach space , namely Chiemelinski orthogonality (even there is no ambiguity between the concepts symbolized by orthogonality) and provide some new geometric characterizations which is considered as the basis of our main definitions. Also, we explore relation between two different types of orthogonalities. First of them orthogonality in a real Banach space and the other orthogonality in the space of bounded linear operator . We obtain a complete characterizations of these two orthogonalities in some types of Banach spaces such as strictly convex space, smooth space and reflexive space. The study is designed to give different results about the concept symmetry of Chmielinski-orthogonality for a compact linear operator on a reflexive, strictly convex Banach space having Kadets-Klee property by exploring a new type of a generalized some results with Birkhoff James orthogonality in the space of bounded linear operators. We also exhibit a smooth compact linear operator with a spectral value that is defined on a reflexive, strictly convex Banach space having Kadets-Klee property either having zero nullity or not -right-symmetric.

Approximation of the Solution of Delay Fractional Differential Equation Using AA-Iterative Scheme

The aim of this paper is to propose a new faster iterative scheme (called AA-iteration) to approximate the fixed point of (b,η)-enriched contraction mapping in the framework of Banach spaces. It is also proved that our iteration is stable and converges faster than many iterations existing in the literature. For validity of our proposed scheme, we presented some numerical examples. Further, we proved some strong and weak convergence results for b-enriched nonexpansive mapping in the uniformly convex Banach space. Finally, we approximate the solution of delay fractional differential equations using AA-iterative scheme.

Existence of fixed point and best proximity point of p-cyclic orbital phi-contraction map

In this manuscript, p-cyclic orbital ϕ-contraction map over closed, nonempty, convex subsets of a uniformly convex Banach space X possesses a unique best proximity point if the auxiliary function ϕ is strictly increasing. The given result unifies and extend some existing results in the related literature. We provide an illustrative example to indicate the validity of the observed result.

Coarse infinite-dimensionality of hyperspaces of finite subsets

We consider infinite-dimensional properties in coarse geometry for hyperspaces consisting of finite subsets of metric spaces with the Hausdorff metric. We see that several infinite-dimensional properties are preserved by taking the hyperspace of subsets with at most n points. On the other hand, we prove that, if a metric space contains a sequence of long intervals coarsely, then its hyperspace of finite subsets is not coarsely embeddable into any uniformly convex Banach space. As a corollary, the hyperspace of finite subsets of the real line is not coarsely embeddable into any uniformly convex Banach space. It is also shown that every (not necessarily bounded geometry) metric space with straight finite decomposition complexity has metric sparsification property.

A New Modified Fixed-Point Iteration Process

In this paper, we present a new modified iteration process in the setting of uniformly convex Banach space. The newly obtained iteration process can be used to approximate a common fixed point of three nonexpansive mappings. We have obtained strong and weak convergence results for three nonexpansive mappings. Additionally, we have provided an example to support the theoretical proof. In the process, several relevant results are improved and generalized.

Common Fixed Points of a Subfamily of a Nonexpansive Periodic Evolution Family on a Strictly Convex Banach Space

In this study, we establish some results for strong convergence of a sequence to a common fixed point of a subfamily of a nonexpansive and periodic evolution family of bounded linear operators acting on a closed and bounded subset J of a strictly convex Banach space X . In fact, we generalized the results from semigroups of the operator to an evolution family of operators.

Non-convex proximal pair and relatively nonexpansive maps with respect to orbits

Every non-convex pair $(C, D)$ ( C , D ) may not have proximal normal structure even in a Hilbert space. In this article, we use cyclic relatively nonexpansive maps with respect to orbits to show the presence of best proximity points in $C\cup D$ C ∪ D , where $C\cup D$ C ∪ D is a cyclic T-regular set and $(C, D)$ ( C , D ) is a non-empty, non-convex proximal pair in a real Hilbert space. Moreover, we show the presence of best proximity points and fixed points for non-cyclic relatively nonexpansive maps with respect to orbits defined on $C\cup D$ C ∪ D , where C and D are T-regular sets in a uniformly convex Banach space satisfying $T(C)\subseteq C$ T ( C ) ⊆ C , $T(D)\subseteq D$ T ( D ) ⊆ D wherein the convergence of Kranoselskii’s iteration process is also discussed.

Inertial Accelerated Algorithm for Fixed Point of Asymptotically Nonexpansive Mapping in Real Uniformly Convex Banach Spaces

In this work, we introduce a new inertial accelerated Mann algorithm for finding a point in the set of fixed points of asymptotically nonexpansive mapping in a real uniformly convex Banach space. We also establish weak and strong convergence theorems of the scheme. Finally, we give a numerical experiment to validate the performance of our algorithm and compare with some existing methods. Our results generalize and improve some recent results in the literature.

AN ITERATIVE SCHEME FOR FIXED POINT PROBLEMS

In this paper, we introduce a new three steps iteration process, prove that our newly proposed iterative scheme can be used to approximate the fixed point of a contractive-like mapping and establish some convergence results for our newly proposed iterative scheme generated by a mapping satisfying condition (E) in the framework of uniformly convex Banach space. In addition, with the aid of numerical examples, we established that our newly proposed iterative scheme is faster than the iterative process introduced by Ullah et al., [26], Karakaya et al., [16], Abass et. al. [1] and some existing iterative scheme in literature. More so, the stability of our newly proposed iterative process is presented and we also gave some numerical examples to display the efficiency of our proposed algorithm.