In this paper, we prove some fixed points properties and demiclosedness principle for a Banach operator in uniformly convex hyperbolic spaces. We further propose an iterative scheme for approximating a fixed point of a Banach operator and establish some strong and $Delta$-convergence theorems for such operator in the frame work of uniformly convex hyperbolic spaces. The results obtained in this...

In the presented research, uniqueness and existence of a mild solution for fractional system semilinear evolution equations with infinite delay an infinitesimal generator operator are demonstrated. The generalized Liouville–Caputo derivative non-integer-order 1<??2 parameter 0<?<1 used to establish our model. ?-Laplace transform strongly continuous cosine sine families uniformly bounde...

Certain maximum principles can be reformulated to various types of fixed point theorems and conversely, based on Metatheorem due ourselves. Such are Zorn's lemma, Banach contraction principle, Nadler's theorem, Brézis-Browder Caristi's Ekeland's variational Takahashi's nonconvex minimization some others, their variants, generalizations, or equivalent formulations. Consequently, we have many new...

This study is devoted to studying the existence and uniqueness of solutions for Hadamard implicit fractional differential equations with generalized integro-differential boundary conditions by utilizing contraction principle Banach Leray–Schauder fixed point theorems. Moreover, two different approaches, Hyers–Ulam stabilities are also discussed. Different ordinary third order (e.g., initial, an...

*Correspondence: [email protected] 1Theoretical and Computational Science Center (TaCS-Center), Department of Mathematics, Faculty of Science, King Mongkut’s University of Technology Thonburi (KMUTT), 126 Pracha-Uthit Road, Bang Mod, Thung Khru, Bangkok, 10140, Thailand 3Department of Medical Research, China Medical University Hospital, China Medical University, Taichung, 40402, Taiwan Full ...

Meir and Keeler in 1 considered an extension of the classical Banach contraction theorem on a complete metric space. Kirk et al. in 2 extended the Banach contraction theorem for a class of mappings satisfying cyclical contractive conditions. Eldred and Veeramani in 3 introduced the following definition. Let A and B be nonempty subsets of a metric space X. A map T : A ∪ B → A ∪ B, is a cyclic co...

Theory of fractional calculus with singular and non-singular kernels is pioneering has garnered significant interest recently. Fair amount literature on the qualitative properties differential integral equations involving different types operators available. This manuscript aims to analyze stability a class nonlinear equation in terms Atangana-Baleanu-Caputo operator. Sufficient conditions for ...

Abstract We prove and discuss several fixed point results for nonlinear operators, acting on some classes of functions with values in a b-metric space. Thus we generalize extend recent theorem Dung Hang (J Math Anal Appl 462:131–147, 2018), motivated by outcomes Ulam type stability. As simple consequence obtain, particular, that approximate (in sense) eigenvalues linear function spaces, must be...

In this paper, we study the existence of solutions for fractional evolution equations with nonlocalconditions. These results are obtained using Banach contraction xed point theorem. Other resultsare also presented using Krasnoselskii theorem.