Banach space ≈ Banach space
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A new approach to the study of fixed point theory for simulation functions Open
Let (X,d) be a metric space and T: X → X be a mapping. In this work, we\n introduce the mapping ζ:[0,1)x[0,1) → R, called the simulation function and\n the notion of Z-contraction with respect to Z which generalize the Banach\n contraction…
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Geometric median and robust estimation in Banach spaces Open
In many real-world applications, collected data are contaminated by noise\nwith heavy-tailed distribution and might contain outliers of large magnitude.\nIn this situation, it is necessary to apply methods which produce reliable\noutcomes …
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Existence and uniqueness of weak solutions for a class of fractional superdiffusion equations Open
In this paper, we consider the existence and uniqueness of weak solutions for a class of fractional superdiffusion equations with initial-boundary conditions. For a multidimensional fractional drift superdiffusion equation, we just conside…
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MIONet: Learning Multiple-Input Operators via Tensor Product Open
As an emerging paradigm in scientific machine learning, neural operators aim to learn operators, via neural networks, that map between infinite-dimensional function spaces. Several neural operators have been recently developed. However, al…
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Error estimates for DeepONets: a deep learning framework in infinite dimensions Open
DeepONets have recently been proposed as a framework for learning nonlinear operators mapping between infinite-dimensional Banach spaces. We analyze DeepONets and prove estimates on the resulting approximation and generalization errors. In…
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On orthogonal sets and Banach fixed point theorem Open
We introduce the notion of the orthogonal sets and give a real generalization of Banach' fixed point theorem.As an application, we find the existence of solution for a first-order ordinary differential equation.
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Controllability for fractional evolution inclusions without compactness Open
In this paper, we study the existence and controllability for fractional evolution inclusions in Banach spaces. We use a new approach to obtain the existence of mild solutions and controllability results, avoiding hypotheses of compactness…
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New results on controllability of fractional evolution systems with order $ \alpha\in (1,2) $ Open
This paper addresses some interesting results of mild solutions to fractional evolution systems with order in Banach spaces as well as the controllability problem. Firstly, we deduce a new representation of solution operators and give a n…
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Protein generation with evolutionary diffusion: sequence is all you need Open
Deep generative models are increasingly powerful tools for the in silico design of novel proteins. Recently, a family of generative models called diffusion models has demonstrated the ability to generate biologically plausible proteins tha…
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Numerical reckoning fixed points for Suzuki’s generalized nonexpansive mappings via new iteration process Open
In this paper we propose a new three-step iteration process, called M iteration process, for approximation of fixed points. Some weak and strong convergence theorems are proved for Suzuki generalized nonexpansive mappings in the setting of…
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Nonlinear Quasi-hemivariational Inequalities: Existence and Optimal Control Open
In this paper, we investigate a generalized nonlinear quasi-hemivariational inequality (QHI) involving a multivalued map in a Banach space. Under general assumptions, by using a fixed point theorem combined with the theory of nonsmooth ana…
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A General Class of Impulsive Evolution Equations Open
One of the novelty of this paper is the study of a\ngeneral class of impulsive differential equations, which is more\nreasonable to show dynamics of evolution processes in\nPharmacotherapy. This fact reduces many difficulties in applying\n…
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The Role of Neural Network Activation Functions Open
A wide variety of activation functions have been proposed for neural\nnetworks. The Rectified Linear Unit (ReLU) is especially popular today. There\nare many practical reasons that motivate the use of the ReLU. This paper\nprovides new the…
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Hybrid viscosity extragradient method for systems of variational inequalities, fixed points of nonexpansive mappings, zero points of accretive operators in Banach spaces Open
In this paper, we introduce a hybrid viscosity extragradient method for a general system of variational inequalities with solutions being also common fixed points of a countable family of nonexpansive mappings and zeros point of an accreti…
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Deciphering protein evolution and fitness landscapes with latent space models Open
Protein sequences contain rich information about protein evolution, fitness landscapes, and stability. Here we investigate how latent space models trained using variational auto-encoders can infer these properties from sequences. Using bot…
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EnzymeMiner: automated mining of soluble enzymes with diverse structures, catalytic properties and stabilities Open
Millions of protein sequences are being discovered at an incredible pace, representing an inexhaustible source of biocatalysts. Despite genomic databases growing exponentially, classical biochemical characterization techniques are time-dem…
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Lineability: The Search For Linearity In Mathematics Open
Preliminary Notions and Tools Cardinal numbers Cardinal arithmetic Basic concepts and results of abstract and linear algebra Residual subsets Lineability, spaceability, algebrability, and their variants Real Analysis What one needs to know…
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A new iteration scheme for approximating fixed points of nonexpansive mappings Open
In this paper, we introduce a new three-step iteration scheme and establish convergence results for approximation of fixed points of nonexpansive mappings in the framework of Banach space. Further, we show that the new iteration process is…
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Results on the Chebyshev method in banach spaces Open
In this paper, under standard Newton-Kantorovich conditions, we establish the Kantorovich-type convergence theorem for Chebyshev method in Banach spaces.
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Geometric Group Theory Open
The primary focus of this book is to cover the foundations of geometric group theory, including coarse topology, ultralimits and asymptotic cones, hyperbolic groups, isoperimetric inequalities, growth of groups, amenability, Kazhdan's ...
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A class of differential hemivariational inequalities in Banach spaces Open
In this paper we investigate an abstract system which consists of a hemivariational inequality of parabolic type combined with a nonlinear evolution equation in the framework of an evolution triple of spaces which is called a differential …
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Existence and Ulam stability for impulsive generalized Hilfer-type fractional differential equations Open
In this manuscript, we examine the existence and the Ulam stability of solutions for a class of boundary value problems for nonlinear implicit fractional differential equations with instantaneous impulses in Banach spaces. The results are …
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A New Banach Space Defined By Euler Totient Matrix Operator Open
The main object of this paper is to introduce a new Banach space derived by using a matrix operator which is comprised of Euler's totient function.Also, we determine α , β , γ -duals of this space and characterize some matrix classes on th…
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Existence, uniqueness and stability of solutions to second order nonlinear differential equations with non-instantaneous impulses Open
In this paper, we consider a non-instantaneous impulsive system represented by second order nonlinear differential equation with deviated argument in a Banach space X. We used the strongly continuous cosine family of linear operators and B…
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Smoothing properties of bilinear operators and Leibniz-type rules in Lebesgue and mixed Lebesgue spaces Open
We prove that bilinear fractional integral operators and similar multipliers are smoothing in the sense that they improve the regularity of functions. We also treat bilinear singular multiplier operators which preserve regularity and obtai…
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Systems of variational inequalities with hierarchical variational inequality constraints for Lipschitzian pseudocontractions Open
In this paper, we consider the problem of solving a general system of variational inequalities (GSVI) with a hierarchical variational inequality (HVI) constraint for countably many uniformly Lipschitzian pseudocontractive mappings and an a…
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Applications of Hardy Spaces Associated with Ball Quasi-Banach Function Spaces Open
Let X be a ball quasi-Banach function space satisfying some minor assumptions. In this article, the authors establish the characterizations of H-X(R-n), the Hardy space associated with X, via the LittlewoodPaley g-functions and g(lambda)*-…
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A Thought on Generalized Morrey Spaces Open
Morrey spaces can complement the boundedness propertiesof operators that Lebesgue spaces can not handle.Morrey spaces which we have been handling are called classical Morrey spaces.However,classical Morrey spaces are not totally enough to …
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Connections between Hyers-Ulam stability and uniform exponential stability of discrete evolution families of bounded linear operators over Banach spaces Open
In this article, we prove that the ω-periodic discrete evolution family $\Gamma:= \{\rho(n,k): n, k \in\mathbb{Z}_{+}, n\geq k\}$ of bounded linear operators is Hyers-Ulam stable if and only if it is uniformly exponentially stable under ce…
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Inverse problems for nonlinear quasi-hemivariational inequalities with application to mixed boundary value problems* Open
This paper is devoted to studying an inverse problem of parameter identification in a nonlinear quasi-hemivariational inequality posed in a Banach space. We employ the Kluge’s fixed point theorem for the set-valued selection map, use the M…