Hybrid Algorithm for Common Fixed Points of Uniformly Closed Countable Families of Hemirelatively Nonexpansive Mappings and Applications by Sumei Ai, Yongfu Su

“…The authors have obtained the following results: (1) the definition of uniformly closed countable family of nonlinear mappings, (2) strong convergence theorem by the monotone hybrid algorithm for two countable families of hemirelatively nonexpansive mappings in a Banach space with new method of proof, (3) two examples of uniformly closed countable families of nonlinear mappings and applications, (4) an example which is hemirelatively nonexpansive mapping but not weak relatively nonexpansive mapping, and (5) an example which is weak relatively nonexpansive mapping but not relatively nonexpansive mapping. …”
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Explicit iteration of an unbounded solution of turbulent flow model involving ψ-Riemann–Liouville fractional derivatives by Sabri T.M. Thabet, Imed Kedim, Bahaaeldin Abdalla, Thabet Abdeljawad

“…This paper is concerned for the first time an explicit iteration of an unbounded solution for a turbulent flow model involving ψ-Riemann–Liouville fractional derivatives with the p-Laplacian operator on the infinite interval [a,∞),a≥0. A suitable Banach space for our analysis is defined. The fractional integral formula that corresponds to the suggested problem is also derived. …”
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Strong Convergence of a New Hybrid Iterative Scheme for Nonexpensive Mappings and Applications by Jie Jia, Khurram Shabbir, Khushdil Ahmad, Nehad Ali Shah, Thongchai Botmart

“…By using the Picard-Thakur hybrid iterative scheme, we can find the solution of delay differential equations and also prove some convergence results for nonexpansive mapping in a uniformly convex Banach space.…”
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On the Differentiability of Weak Solutions of an Abstract Evolution Equation with a Scalar Type Spectral Operator on the Real Axis by Marat V. Markin

“…Given the abstract evolution equation y′(t)=Ay(t),  t∈R, with scalar type spectral operator A in a complex Banach space, found are conditions necessary and sufficient for all weak solutions of the equation, which a priori need not be strongly differentiable, to be strongly infinite differentiable on R. …”
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A Generalization of Exponential Class and Its Applications by Hongya Gao, Chao Liu, Hong Tian

“…It is proved that Lθ,∞)(Ω) is a Banach space which is a generalization of exponential class. …”
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Some Results on Iterative Proximal Convergence and Chebyshev Center by Laishram Shanjit, Yumnam Rohen, Sumit Chandok, M. Bina Devi

“…In this paper, we prove a sufficient condition that every nonempty closed convex bounded pair M,N in a reflexive Banach space B satisfying Opial’s condition has proximal normal structure. …”
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Some Results on Best Proximity Points of Cyclic Contractions in Probabilistic Metric Spaces by Manuel De la Sen, Erdal Karapınar

“…The existence and uniqueness of fixed points and best proximity points of p-cyclic contractions defined in induced complete Menger spaces are also discussed in the case when the associate complete metric space is a uniformly convex Banach space. On the other hand, the existence and the uniqueness of fixed points of the p-composite mappings restricted to each of the p subsets in the cyclic disposal are also investigated and some illustrative examples are given.…”
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On Simultaneous Farthest Points in 𝐿∞(𝐼,𝑋) by Sh. Al-Sharif, M. Rawashdeh

“…Let 𝑋 be a Banach space and let 𝐺 be a closed bounded subset of 𝑋. …”
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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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A porosity result in convex minimization by P. G. Howlett, A. J. Zaslavski

“…We study the minimization problem f(x)→min, x∈C, where f belongs to a complete metric space ℳ of convex functions and the set C is a countable intersection of a decreasing sequence of closed convex sets Ci in a reflexive Banach space. Let ℱ be the set of all f∈ℳ for which the solutions of the minimization problem over the set Ci converge strongly as i→∞ to the solution over the set C. …”
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Weighted Composition Operators from Hardy Spaces into Logarithmic Bloch Spaces by Flavia Colonna, Songxiao Li

“…The logarithmic Bloch space Blog⁡ is the Banach space of analytic functions on the open unit disk &#x1D53B; whose elements f satisfy the condition ∥f∥=sup⁡z∈&#x1D53B;(1-|z|2)log⁡  (2/(1-|z|2))|f'(z)|<∞. …”
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Strong Convergence for Hybrid Implicit S-Iteration Scheme of Nonexpansive and Strongly Pseudocontractive Mappings by Shin Min Kang, Arif Rafiq, Faisal Ali, Young Chel Kwun

“…Let K be a nonempty closed convex subset of a real Banach space E, let S:K→K be nonexpansive, and let  T:K→K be Lipschitz strongly pseudocontractive mappings such that p∈FS∩FT=x∈K:Sx=Tx=x and x-Sy≤Sx-Sy and x-Ty≤Tx-Ty for all x, y∈K. …”
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Integrodifferential Equations on Time Scales with Henstock-Kurzweil-Pettis Delta Integrals by Aneta Sikorska-Nowak

“…The functions 𝑓,𝑘 are weakly-weakly sequentially continuous with values in a Banach space 𝐸, and the integral is taken in the sense of Henstock-Kurzweil-Pettis delta integral. …”
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Generalized Yosida Approximations Based on Relatively A-Maximal m-Relaxed Monotonicity Frameworks by Heng-you Lan

“…Furthermore, we give some remarks to show that the theory of the new generalized relatively resolvent operator and Yosida approximations associated with relatively A-maximal m-relaxed monotone operators generalizes most of the existing notions on (relatively) maximal monotone mappings in Hilbert as well as Banach space and can be applied to study variational inclusion problems and first-order evolution equations as well as evolution inclusions.…”
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Stability of Pexider Equations on Semigroup with No Neutral Element by Jaeyoung Chung

“…Let S be a commutative semigroup with no neutral element, Y a Banach space, and ℂ the set of complex numbers. In this paper we prove the Hyers-Ulam stability for Pexider equation fx+y-gx-h(y)≤ϵ for all x,y∈S, where f,g,h:S→Y. …”
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The Equivalence of Convergence Results of Modified Mann and Ishikawa Iterations with Errors without Bounded Range Assumption by Zhiqun Xue, Yaning Wang, Haiyun Zhou

“…Let E be an arbitrary uniformly smooth real Banach space, let D be a nonempty closed convex subset of E, and let T:D→D be a uniformly generalized Lipschitz generalized asymptotically Φ-strongly pseudocontractive mapping with q∈F(T)≠∅. …”
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Local uniform convexity and Kadec-Klee type properties in K-interpolation spaces I: General Theory by Peter G. Dodds, Theresa K. Dodds, Alexander A. Sedaev, Fyodor A. Sukochev

“…As a partiular by-product of our study, we show that the theorem of Kadec itself, that each separable Banach space admits an equivalent locally uniformly convex norm, follows directly from our approach.…”
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Best approximation in Orlicz spaces by H. Al-Minawi, S. Ayesh

“…Let X be a real Banach space and (Ω,μ) be a finite measure space and ϕ be a strictly icreasing convex continuous function on [0,∞) with ϕ(0)=0. …”
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Properties and for Bounded Linear Operators by M. H. M. Rashid

“…We shall consider properties which are related to Weyl type theorem for bounded linear operators , defined on a complex Banach space . These properties, that we call property , means that the set of all poles of the resolvent of of finite rank in the usual spectrum are exactly those points of the spectrum for which is an upper semi-Fredholm with index less than or equal to 0 and we call property , means that the set of all poles of the resolvent of in the usual spectrum are exactly those points of the spectrum for which is an upper semi--Fredholm with index less than or equal to 0. …”
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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⁎. …”
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