The aim of this paper is to obtain some new important consequences related to coupled coincidence points via C-class functions in the context of a regular partial ordered complete b-metric-like space (for short, RPOCbML space); this space arises from combining the results of b-metric-like space with partial metric space and adding the regularity condition. Finally, we support our theoretical results by some examples and an application about finding an analytical solution for nonlinear integral equations.

In the present paper, the representation, in different domains, of analytic functions by complex conformable fractional derivative bases (CCFDB) and complex conformable fractional integral bases (CCFIB) in Fréchet space are investigated.Results are proved to show that such representation is possible in closed disks, open disks, open regions surrounding closed disks, at the origin, and for all entire functions. Also, some results concerning the growth order and type of CCFDB and CCFIB are determined. Moreover, the T 𝜌 -property of CCFDB and CCFIB is discussed. The obtained results recover some known results when 𝛼 = 1.Finally, some applications to the CCFDB and CCFIB of Bernoulli, Euler, Bessel, and Chebyshev polynomials have been studied.

The purpose of this paper is to determine the existence of tripled fixed point results for the tripled symmetry system of fractional hybrid delay differential equations. We obtain results which support the existence of at least one solution to our system by applying hybrid fixed point theory. Similar types of stability analysis are presented, including Ulam–Hyers, generalized Ulam–Hyers, Ulam–Hyers–Rassias, and generalized Ulam–Hyers–Rassias. The necessary stipulations for obtaining the solution to our proposed problem are established. Finally, we provide a non-trivial illustrative example to support and enhance our analysis.

The goal of this paper is to present a new class of operators satisfying the Prešić-type rational η-contraction condition in the setting of usual metric spaces. New fixed point results are also obtained for these operators. Our results generalize, extend, and unify many papers in this direction. Moreover, two examples are derived to support and document our theoretical results. Finally, to strengthen our paper and its contribution to applications, some convergence results for a class of matrix difference equations are investigated.

This manuscript is devoted to obtaining a quadruple best proximity point for a cyclic contraction mapping in the setting of ordinary metric spaces. The validity of the theoretical results is also discussed in uniformly convex Banach spaces. Furthermore, some examples are given to strengthen our study. Also, under suitable conditions, some quadruple fixed point results are presented. Finally, as applications, the existence and uniqueness of a solution to a system of functional and integral equations are obtained to promote our paper.