New Optimality Conditions for a Nondifferentiable Fractional Semipreinvex Programming Problem by Yi-Chou Chen, Wei-Shih Du

“…We study a nondifferentiable fractional programming problem as follows: (P)minx∈Kf(x)/g(x) subject to x∈K⊆X,  hi(x)≤0,  i=1,2,…,m, where K is a semiconnected subset in a locally convex topological vector space X, f:K→ℝ, g:K→ℝ+ and hi:K→ℝ, i=1,2,…, m. If f, -g, and hi, i=1,2,…,m, are arc-directionally differentiable, semipreinvex maps with respect to a continuous map γ:[0,1]→K⊆X satisfying γ(0)=0 and γ′(0+)∈K, then the necessary and sufficient conditions for optimality of (P) are established.…”
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Parameter depending almost monotonic functions and their applications to dimensions in metric measure spaces by Natasha Samko

“…In connection with application to various problems of operator theory, we study almost monotonic functions w(x, r) depending on a parameter x which runs a metric measure space X, and the so called index numbers m(w, x), M(w, x) of such functions, and consider some generalized Zygmund, Bary, Lozinskii and Stechkin conditions. …”
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Dimension theory and fuzzy topological spaces by S. S. Benchalli, B. M. Ittanagi, P. G. Patil

“…It has been possible to introduce and study the small inductive dimension function indfX and large inductive dimension function indfX for a fuzzy topological space X.…”
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The order topology for function lattices and realcompactness by W. A. Feldman, J. F. Porter

“…A lattice K(X,Y) of continuous functions on space X is associated to each compactification Y of X. …”
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Equivalent Cauchy Sequences in q1,q2-Quasi Metric-Like Space and Applications to Fixed-Point Theory by Eriola Sila, Sidite Duraj, Elida Hoxha

“…This paper introduces the concept of q1,q2-quasi metric-like space X,p and delves into some topological properties of it. …”
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Measurable Vizing’s theorem by Jan Grebík

“…We prove a full measurable version of Vizing’s theorem for bounded degree Borel graphs, that is, we show that every Borel graph $\mathcal {G}$ of degree uniformly bounded by $\Delta \in \mathbb {N}$ defined on a standard probability space $(X,\mu )$ admits a $\mu $ -measurable proper edge coloring with $(\Delta +1)$ -many colors. …”
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Existence of Mild Solutions for a Semilinear Integrodifferential Equation with Nonlocal Initial Conditions by Carlos Lizama, Juan C. Pozo

“…Using Hausdorff measure of noncompactness and a fixed-point argument we prove the existence of mild solutions for the semilinear integrodifferential equation subject to nonlocal initial conditions u′(t)=Au(t)+∫0tB(t-s)u(s)ds+f(t,u(t)), t∈[0,1], u(0)=g(u), where A:D(A)⊆X→X, and for every t∈[0,1] the maps B(t):D(B(t))⊆X→X are linear closed operators defined in a Banach space X. We assume further that D(A)⊆D(B(t)) for every t∈[0,1], and the functions f:[0,1]×X→X and g:C([0,1];X)→X are X-valued functions which satisfy appropriate conditions.…”
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Topological properties and matrix transformations of certain ordered generalized sequence spaces by Manjul Gupta, Kalika Kaushal

“…In this note, we carry out investigations related to the mixed impact of ordering and topological structure of a locally convex solid Riesz space (X,τ) and a scalar valued sequence space λ, on the vector valued sequence space λ(X) which is formed and topologized with the help of λ and X, and vice versa. …”
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Pre-Quasi Simple Banach Operator Ideal Generated by s−Numbers by Awad A. Bakery, Afaf R. Abou Elmatty

“…Let E be a weighted Nakano sequence space or generalized Cesáro sequence space defined by weighted mean and by using s−numbers of operators from a Banach space X into a Banach space Y. We give the sufficient (not necessary) conditions on E such that the components SEX,Y≔T∈LX,Y:snTn=0∞∈E of the class SE form pre-quasi operator ideal, the class of all finite rank operators are dense in the Banach pre-quasi ideal SE, the pre-quasi operator ideal formed by the sequence of approximation numbers is strictly contained for different weights and powers, the pre-quasi Banach Operator ideal formed by the sequence of approximation numbers is small, and finally, the pre-quasi Banach operator ideal constructed by s−numbers is simple Banach space.…”
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A Degree Theory for Compact Perturbations of Monotone Type Operators and Application to Nonlinear Parabolic Problem by Teffera M. Asfaw

“…Let X be a real locally uniformly convex reflexive Banach space with locally uniformly convex dual space X⁎. Let T:X⊇D(T)→2X⁎ be maximal monotone, S:X→2X⁎ be bounded and of type (S+), and C:D(C)→X⁎ be compact with D(T)⊆D(C) such that C lies in Γστ (i.e., there exist σ≥0 and τ≥0 such that Cx≤τx+σ for all x∈D(C)). …”
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Almost convex metrics and Peano compactifications by R. F. Dickman

“…In an earlier paper, the author conjectured that if a space (X,d) has a Peano compactification, then it must be S-metrizable. …”
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Controllability of Mild Solution of Nonlocal Conformable Fractional Differential Equations by Mohamed Hannabou, Mohamed Bouaouid, Khalid Hilal

“…/dtα is the vectorial conformable fractional derivative of order α∈0,1 in a Banach space X and A is the infinitesimal generator of a semigroup Ttt≥0 on X. …”
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New Types of μ-Proximity Spaces and Their Applications by Rodyna A. Hosny, Tareq M. Al-shami, Abdelwaheb Mhemdi

“…Also, other types of μ-proximity, termed Rμ-proximity and Oμ-proximity, on X are defined. In a μ-proximity space X,δμ, for any subset K of X, one can find out nonempty collections δμK=G⊆X∣Kδ¯μG, which are hereditary classes on X. …”
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Some Results on Pixley–Roy Hyperspaces by Ljubiša D. R. Kočinac, Luong Quoc Tuyen, Ong Van Tuyen

“…In this paper, we prove that if a space X has a point-countable cn-network, then the Pixley-Roy hyperspace PRX also has a point-countable cn-network. …”
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q-Hyperconvexity in Quasipseudometric Spaces and Fixed Point Theorems by Hans-Peter A. Künzi, Olivier Olela Otafudu

“…In analogy with a metric result, we show among other things that a set-valued mapping T∗ on a q-hyperconvex T0-quasimetric space (X, d) which takes values in the space of nonempty externally q-hyperconvex subsets of (X, d) always has a single-valued selection T which satisfies d(T(x),T(y))≤dH(T∗(x),T∗(y)) whenever x,y∈X. …”
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Difference equations: From Berry connections to the Coulomb branch by Andrea E. V. Ferrari, Daniel Zhang

“…In recent work, we demonstrated that a spectral variety for the Berry connection of a 2d $\mathcal{N}=(2,2)$ GLSM with Kähler vacuum moduli space $X$ and Abelian flavour symmetry is the support of a sheaf induced by a certain action on the equivariant quantum cohomology of $X$. …”
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Strong convergence and control condition of modified Halpern iterations in Banach spaces by Yonghong Yao, Rudong Chen, Haiyun Zhou

“…Let C be a nonempty closed convex subset of a real Banach space X which has a uniformly Gâteaux differentiable norm. …”
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Peano compactifications and property S metric spaces by R. F. Dickman

“…There are easily constructed examples of locally connected connected metric spaces which fail to be S-metrizable, however the author does not know of a non-S-metrizable space (X,d) which has a Peano compactification. In this paper we conjecture that: If (P,ρ) a Peano compactification of (X,ρ|X), X must be S-metrizable. …”
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Integrated Fractional Resolvent Operator Function and Fractional Abstract Cauchy Problem by Ya-Ning Li, Hong-Rui Sun

“…We show that A generates an exponentially bounded (α,β)-ROF on a Banach space X if and only if the problem has a unique exponentially bounded classical solution vx and Avx∈L loc 1(ℝ+,X). …”
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On Bousfield’s conjectures for the unstable Adams spectral sequence for $SO$ and $U$ by Nguyễn, Thế Cường

“…The unstable Adams spectral sequence is a spectral sequence that starts from algebraic information about the mod $2 $ cohomology $H ^{ * } \left(X \right) $ of a space $X $ as an unstable algebra over the Steenrod algebra $\mathcal{A}$, and converges, in good cases, to the $2 $-localized homotopy groups of $X $. …”
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