The Monotone Contraction Mapping Theorem by Joseph Frank Gordon

“…In this paper, the fixed-point theorem for monotone contraction mappings in the setting of a uniformly convex smooth Banach space is studied. This paper provides a version of the Banach fixed-point theorem in a complete metric space.…”
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Weak Solutions of a Coupled System of Urysohn-Stieltjes Functional (Delayed) Integral Equations by A. M. A. El-Sayed, M. M. A. Al-Fadel

“…We study the existence of weak solutions for the coupled system of functional integral equations of Urysohn-Stieltjes type in the reflexive Banach space E. As an application, the coupled system of Hammerstien-Stieltjes functional integral equations is also studied.…”
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Fixed-Point Theorem for Isometric Self-Mappings by Joseph Frank Gordon

“…That is, it is shown that every isometric self-mapping on a weakly compact convex subset of a strictly convex Banach space has a fixed point.…”
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Controllability of Mild Solution of Nonlocal Conformable Fractional Differential Equations by Mohamed Hannabou, Mohamed Bouaouid, Khalid Hilal

“…The control function u is an element of L20,τ,U with U is a Banach space and B is a bounded linear operator from U into X.…”
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The fixed point index for accretive mapping with K—set contraction perturbation in cones by Yu-Qing Chen

“…Let P be cone Banach space E, A, K are two mappings in P, A accretive, K is K—set contraction, then fixed point index defined for mapping −A+K, some fixed point theorems are also deduced.…”
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Convergence theorems and stability results for Lipschitz strongly pseudocontractive operators by Zeqing Liu, Lili Zhang, Shin Min Kang

“…Suppose that X is an arbitrary real Banach space and T:X→X is a Lipschitz strongly pseudocontractive operator. …”
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Existence of Almost Periodic Solutions for Impulsive Neutral Functional Differential Equations by Junwei Liu, Chuanyi Zhang

“…The existence of piecewise almost periodic solutions for impulsive neutral functional differential equations in Banach space is investigated. Our results are based on Krasnoselskii’s fixed-point theorem combined with an exponentially stable strongly continuous operator semigroup. …”
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Nonlinear Volterra Integral Equation of the Second Kind and Biorthogonal Systems by M. I. Berenguer, D. Gámez, A. I. Garralda-Guillem, M. C. Serrano Pérez

“…The main tools used to establish it are the properties of a biorthogonal system in a Banach space and the Banach fixed point theorem.…”
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Existence theorems for differential inclusions with nonconvex right hand side by Nikolaos S. Papageorgiou

“…In this paper we prove some new existence theorems for differential inclusions with a nonconvex right hand side, which is lower semicontinuous or continuous in the state variable, measurable in the time variable and takes values in a finite or infinite dimensional separable Banach space.…”
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On the extension of positive linear functionals by Ergashboy Muhamadiev, Adel T. Diab

“…The case of a closed subspace of a Banach space is also discussed.…”
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Fixed Point Theorems for Asymptotically Contractive Multimappings by M. Djedidi, K. Nachi

“…We present fixed point theorems for a nonexpansive set-valued mapping from a closed convex subset of a reflexive Banach space into itself under some asymptotic contraction assumptions. …”
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Data Dependence Results for Multistep and CR Iterative Schemes in the Class of Contractive-Like Operators by Vatan Karakaya, Faik Gürsoy, Kadri Doğan, Müzeyyen Ertürk

“…We intend to establish some results on the data dependence of fixed points of certain contractive-like operators for the multistep and CR iterative processes in a Banach space setting. One of our results generalizes the corresponding results of Soltuz and Grosan (2008) and Chugh and Kumar (2011).…”
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Some analogues of Knopp’s core theorem by I. J. Maddox

“…Also, a result is given on infinite matrices of bounded linear operators acting on bounded sequences in a Banach space.…”
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Convoluted Fractional C-Semigroups and Fractional Abstract Cauchy Problems by Zhan-Dong Mei, Ji-Gen Peng, Jing-Huai Gao

“…We present the notion of convoluted fractional C-semigroup, which is the generalization of convoluted C-semigroup in the Banach space setting. We present two equivalent functional equations associated with convoluted fractional C-semigroup. …”
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Strong Convergence Theorems for Solutions of Equilibrium Problems and Common Fixed Points of a Finite Family of Asymptotically Nonextensive Nonself Mappings by Lijuan Zhang, Hui Tong, Ying Liu

“…A strong convergence theorem of common element is established in a uniformly smooth and uniformly convex Banach space.…”
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Comparison between Certain Equivalent Norms Regarding Some Familiar Properties Implying WFPP by Helga Fetter, Berta Gamboa de Buen

“…In a Banach space with a basis we define a similar norm to the norm shown by Lin to make l1 into a space with FPP and make a comparative study of certain geometric properties such as the Opial property, WNS, and uniform nonsquareness of the original space and the space with the new norm.…”
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Hybrid Projection Algorithm for Two Countable Families of Hemirelatively Nonexpansive Mappings and Applications by Zi-Ming Wang, Poom Kumam

“…Strong convergence theorems of iterative sequences are obtained in an uniformly convex and uniformly smooth Banach space. As applications, convex feasibility problems, equilibrium problems, variational inequality problems, and zeros of maximal monotone operators are studied.…”
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Characteristic Functions and Borel Exceptional Values of E-Valued Meromorphic Functions by Zhaojun Wu, Zuxing Xuan

“…The main purpose of this paper is to investigate the characteristic functions and Borel exceptional values of E-valued meromorphic functions from the ℂR={z:|z|<R},   0<R≤+∞ to an infinite-dimensional complex Banach space E with a Schauder basis. Results obtained extend the relative results by Xuan, Wu and Yang, Bhoosnurmath, and Pujari.…”
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Iterative Solutions for the Differential Equation with p-Laplacian on Infinite Interval by Guoying Zhao, Ying Wang

“…This paper systematically investigates a class of fourth-order differential equation with p-Laplacian on infinite interval in Banach space. By means of the monotone iterative technique, we establish not only the existence of positive solutions but also iterative schemes under the suitable conditions. …”
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Characterizations of Nonlinear Lie Derivations of B(X) by Donghua Huo, Baodong Zheng, Hongyu Liu

“…Let X be an infinite dimensional Banach space, and Φ:B(X)→B(X) is a nonlinear Lie derivation. …”
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