A Relation-Theoretic Metrical Fixed Point Theorem for Rational Type Contraction Mapping with an Application

In this article, we discuss the relation theoretic aspect of rational type contractive mapping to obtain fixed point results in a complete metric space under arbitrary binary relation. Furthermore, we provide an application to find a solution to a non-linear integral equation.

Existence of common fixed points of non-linear semigroups of Enriched Kannan contractive mappings

In this article, we consider the non-linear semigroup of \textit{enriched Kannan} contractive mapping and prove the existence of common fixed point on a non-empty closed convex subset $\mathcal C$ of a real Banach space $\mathscr X$, having uniformly normal structure.

Fixed point theorem with contractive mapping on C*-Algebra valued G-Metric Space

Banach-Caccioppoli Fixed Point Theorem is an interesting theorem in metric space theory. This theorem states that if T : X → X is a contractive mapping on complete metric space, then T has a unique fixed point. In 2018, the notion of C *-algebra valued G-metric space was introduced by Congcong Shen, Lining Jiang, and Zhenhua Ma. The C *-algebra valued G-metric space is a generalization of the G-metric space and the C*-algebra valued metric space, meanwhile the G-metric space and the C *-algebra valued metric space itself is a generalization of known metric space. The G-metric generalized the domain of metric from X × X into X × X × X, the C *-algebra valued metric generalized the codomain from real number into C *-algebra, and the C *-algebra valued G-metric space generalized both the domain and the codomain. In C *-algebra valued G-metric space, there is one theorem that is similar to the Banach-Caccioppoli Fixed Point Theorem, called by fixed point theorem with contractive mapping on C *-algebra valued G-metric space. This theorem is already proven by Congcong Shen, Lining Jiang, Zhenhua Ma (2018). In this paper, we discuss another new proof of this theorem by using the metric function d(x, y) = max{G(x, x, y),G(y, x, x)}.

Revising the Hardy–Rogers–Suzuki-type Z-contractions

The aim of this study is to introduce a new interpolative contractive mapping combining the Hardy–Rogers contractive mapping of Suzuki type and $\mathcal{Z}$ Z -contraction. We investigate the existence of a fixed point of this type of mappings and prove some corollaries. The new results of the paper generalize a number of existing results which were published in the last two decades.

Fixed Point Theorem on Contractive Mapping in Standard 2-Normed Spaces

This paper discussed about the proof of the fixed point theorem on the standard 2-normed spaces by using completeness. The completeness of the standard 2-normed spaces is shown by defining a new norm. Two linear independent vectors on standard 2-normed spaces are used to define the new norm, namely which has been shown to be equivalent to standard norm.

Proving Fixed Point Theorems Employing Fuzzy $(\sigma,\mathcal{Z})$-Contractive Type Mappings

In this article, the concept of fuzzy $(\sigma,\mathcal{Z})$-contractive mapping has been introduced in fuzzy metric spaces which is an improvement over the corresponding concept recently introduced by Shukla et al. [Fuzzy Sets and system. 350 (2018) 85--94]. Thereafter, we utilized our newly introduced concept to prove some existence and uniqueness theorems in $\mathcal{M}$-complete fuzzy metric spaces. Our results extend and generalize the corresponding results of Shukla et al.. Moreover, an example is adopted to exhibit the utility of newly obtained results.

STRONG CONVERGENCE OF IMPLICIT ITERATIVE ALGORITHMS FOR STRICTLY PSEUDO-CONTRACTIVE MAPPINGS

The class of strictly pseudo-contractive mappings is known to have more powerful applications than the class of nonexpansive mappings in solving nonlinear equations such as inverse and equilibrium problems. Motivated by the potency of the class of strictly pseudo-contractive mappings, a generalized viscosity implicit algorithm is constructed for finding their fixed points in the framework of Banach spaces. The strong convergence of the newly constructed sequence to a fixed point of a strictly pseudo-contractive mapping is obtained under some mild conditions on the parameters and the fixed point is shown to solve some variational inequality problems. An example is given to illustrate the convergence analysis of the newly constructed generalized viscosity implicit algorithm for the class of strictly pseudo-contractive mappings. The example also shows that the algorithm and the conditions which are imposed on the parameters are not just optical illusion.

Some New Results of Interpolative Hardy–Rogers and Ćirić–Reich–Rus Type Contraction

In this paper, we present new concepts on completeness of Hardy–Rogers type contraction mappings in metric space to prove the existence of fixed points. Furthermore, we introduce the concept of g -interpolative Hardy–Rogers type contractions in b -metric spaces to prove the existence of the coincidence point. Lastly, we add a third concept, interpolative weakly contractive mapping type, Ćirić–Reich–Rus, to show the existence of fixed points. These results are a generalization of previous results, which we have reinforced with examples.

A Method for Solving the Variational Inequality Problem and Fixed Point Problems in Banach Spaces

The purpose of this research is to modify Halpern iteration’s process for finding a common element of the set of solutions of a variational inequality problem and the set of fixed points of a strictly pseudo contractive mapping in q-uniformly smooth Banach space. We also introduce a new technique to prove a strong convergence theorem for a finite family of strictly pseudo contractive mappings in q-uniformly smooth Banach space. Moreover, we give a numerical result to illustrate the main theorem.