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The purpose of the present this paper is to study and establish some new common and coupled coincidence fixed point results for commuting mappings with prosperity of mixed풢 – monoton in the setting of partially ordered complete 풟* – metric sps. In our paper we extend and generalize several results for a pair of commutative mappings in the literature. Furthermore, suitable examples that support our main results have been introduced. [ABSTRACT FROM AUTHOR]

The main object in Feigenbaum's universality theory is the fixed point g(x) of renormalization transformation in the space of unimodal maps on interval [−1, 1]. The map g(x) is called Feigenbaum's map. In present paper we study the Feigenbaum's unstable separatrix is that is the family of unimodal maps of the interval [−1, 1] with one critical point. It is established implicit formulas for periodic orbits of this family, and the relations between orbits of different maps of this family. [ABSTRACT FROM AUTHOR]

In the current research paper we have defined rationalized Ξ-contraction for four mappings. In b-metric, using simulation function, for rationalized Ξ-contraction fulfilling the weakly compatible condition for four mappings in pairs, fulfilling conjoint limit range property, a unique common fixed point theorem has been proved. The conclusion has been tested by not using the situation of completeness for b-metric space. The outcome is an improvement and generalization of [2, 4, 6] existing in metric space and b-metric spaces. To back-up the result a supporting example is also discussed. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to establish some new common fixed point results for a pair of conditionally sequential absorbing self-mappings satisfying an enriched contraction condition in Banach space by introducing the notion of weaker form of continuity. We have also illustrated an example in support of our main result. Further, to make our result more effective, we have established the existence and the uniqueness of the solution of an Integral equation as an application of our main result with an example. [ABSTRACT FROM AUTHOR]

Altun I. and Turkoglu D. proved some fixed point theorems for two pairs of weakly compatible self-mappings satisfying an implicit relation. In this paper, we extend the results proved by Altun and Turkoglu by using E.A. and (CLR) properties along with weakly compatible property for two pairs of self-maps. [ABSTRACT FROM AUTHOR]

The research of differential equations has a long history, among which there are limited types of equations with definite solutions. However, the solution of a large number of differential equations is ambiguous. The study of bounded and asymptotic properties for solutions of differential equations plays an important role in the qualitative theory and application of differential equations. In this paper, we study the bounded and asymptotic properties of a class of second-order differential equations. By constructing Banach space, cleverly defining the operator, using Schauder-Tikhonov fixed point theory and L'hospital rule, the bounded and asymptotic properties of equation solutions are studied, and the existing results are generalized. Finally, the results can be used to study the asymptotic properties of differential equation solutions. [ABSTRACT FROM AUTHOR]

In this paper, we present some fixed point results for self-mappings satisfying an implicit relation in partial b-metric spaces which are generalization of several previously fixed point theorems in the literature. As an application, we obtained solution of non-linear integral equation. [ABSTRACT FROM AUTHOR]

For a complete extended b-metric space with continuous mapping satisfying the rational type contractive condition, a distinctive common fixed point theorem is established. Our outcome is the extension of several results available in the literature, from metric space to extended b-metric space. In specific, Dass and Gupta[Indian J. Pure Appl. Math. 6, 1455–1458 (1975)], Jaggi[Indian J. Pure Appl. Math. 8, 223–230 (1977)], Alqahtani et.al.[J. Inequal. Appl. Paper No. 220, 11 pp (2019)] and even the well-known Banach contraction mapping theory are extracted. A proper example is also given in sustenance of it. [ABSTRACT FROM AUTHOR]

Due to increasing applications of fixed-point theory and iterative schemes in real life in various directions, we develop a new result for using Das and Debata [1] iterative process with a pair of Zamfirescu operators in ABS ("Arbitrary Banach Space") and verify the convergence of an iteration given by [1]. By this result we extend and refine many existing results. [ABSTRACT FROM AUTHOR]

The theory of convergence of fixed point iteration has been developed a lot over the past years due to its immense significance in real life applications. The evolution of iterative processes has reached from one-step process to recently defined four-step process. Also, the metric spaces have been generalized to Banach spaces but not much work is done in complex valued Banach space. The objective of this paper is to establish a convergence result of a newly defined CUIA iterative process in the framework of complex valued Banach space under contraction mappings. The current work will enhance the already existing literature of complex valued Banach space. The results are supported with suitable example. [ABSTRACT FROM AUTHOR]