Strong Convergence Theorems for Split Common Fixed Point Problem of Bregman Generalized Asymptotically Nonexpansive Mappings in Banach Spaces

Recent studies have highlighted fixed point theorems in the context of bicomplex valued metric spaces, utilizing rational type contractions with coefficients defined by two-variable control functions. In our research, we extend these findings by proposing new theorems for identifying common fixed points within bicomplex valued metric spaces, employing rational type contractions characterized by three-variable control functions as coefficients. We have refined the contraction conditions presented in numerous existing theorems by substituting constants with a limited number of control functions for more versatility in bicomplex valued metric spaces. This advancement broadens the scope of several significant findings in the literature. To demonstrate the efficacy of our results, we offer compelling examples that validate our theorems. Furthermore, we apply our primary findings to effectively address the Urysohn integral equation system, showcasing the practical application of our research.

Section: Introductionmentioning

confidence: 99%

Some theorems on fixed points in bi-complex valued metric spaces with an application to integral equations

Murali,

Muthunagai

2024

“…Also, the Lagrange interpolation is used to estimate the delay argument [49]. Furthermore, the local truncation errors and stability polynomials are calculated [50][51][52].…”

Section: Introductionmentioning

confidence: 99%

Time-Fractional Differential Equations with an Approximate Solution

Alzaki¹,

Jassim²

2022

This paper shows how to use the fractional Sumudu homotopy perturbation technique (SHP) with the Caputo fractional operator (CF) to solve time fractional linear and nonlinear partial differential equations. The Sumudu transform (ST) and the homotopy perturbation technique (HP) are combined in this approach. In the Caputo definition, the fractional derivative is defined. In general, the method is straightforward to execute and yields good results. There are some examples offered to demonstrate the technique's validity and use.

“…The inclusion in both cases are strict. For few older results on the family of nonexpansive mappings, see [6,17,18,19,20,21].…”

Section: Introductionmentioning

confidence: 99%

On Nonexpansive and Expansive Semigroup of Order-Preserving Total Mappings in Waist Metric Spaces

Wahab

Usamot

Alata³

et al. 2022

In this paper, we introduce nonexpansive and expansive semigroup of order-preserving total mappings (ONTn) and (OETn), respectively, to prove some fixed point theorems in waist metric spaces. We examine the existence of mappings that satisfy the conditions ONTn and OETn. We also prove that every semigroup of order-preserving total mappings OTn has fixed point properties and that the set of fixed points is closed and convex. The present study generalised many previous results on semigroup of order-preserving total mappings OTn. Efficacy of the results was justified with some practical examples.