On the Solution Existence of Variational-Like Inequalities Problems for Weakly Relaxed η−α Monotone Mapping by Marwan Amin Kutbi, Wutiphol Sintunavarat

“…Also, we obtain the existence of solution for variational-like problems with weakly relaxed η-α semimonotone mappings in arbitrary Banach spaces by using the Kakutani-Fan-Glicksberg fixed-point theorem.…”
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Semianalytical Solutions of Some Nonlinear-Time Fractional Models Using Variational Iteration Laplace Transform Method by Javed Iqbal, Khurram Shabbir, Liliana Guran

“…Moreover, possible consequences of these results as an application of fixed-point theorem are placed before the experts as an open problem.…”
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Existence and Positivity of Solutions for a Second-Order Boundary Value Problem with Integral Condition by Assia Guezane-Lakoud, Hamidane Nacira, Khaldi Rabah

“…The arguments are based on Banach contraction principle, Leray Schauder nonlinear alternative, and Guo-Krasnosel’skii fixed point theorem in cone. Two examples are also given to illustrate the main results.…”
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On the Fractional Variable Order Thermostat Model: Existence Theory on Cones via Piece-Wise Constant Functions by Shahram Rezapour, Mohammed Said Souid, Zoubida Bouazza, Azhar Hussain, Sina Etemad

“…By Guo-Krasnoselskii’s fixed point theorem on cones, we derive the required conditions ensuring the existence property for positive solutions. …”
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Existence and Compactness Results for a System of Fractional Differential Equations by Cheikh Guendouz, Jamal Eddine Lazreg, Juan J. Nieto, Abdelghani Ouahab

“…The existence and uniqueness, boundedness, and continuous dependence of solutions for fractional differential equations with Caputo fractional derivative is proven by Perov’s fixed point theorem in vector Banach spaces. We study the existence and compactness of solution sets and the u.s.c. of operator solutions.…”
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Existence Results for Strong Mixed Vector Equilibrium Problem for Multivalued Mappings by Adem Kılıçman, Rais Ahmad, Mijanur Rahaman

“…Using generalized Fan-Browder fixed point theorem (Takahashi 1976) and generalized pseudomonotonicity for multivalued mappings, we provide some existence results for strong mixed vector equilibrium problem without using KKM-Fan theorem. …”
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Existence of Solutions for Singular Second-Order Ordinary Differential Equations with Periodic and Deviated Nonlocal Multipoint Boundary Conditions by Ahmed M. A. El-Sayed, Fatma M. Gaafar

“…An existence result based on the Schauder fixed point theorem and Leray-Schauder continuation principle is used to obtain at least one continuous solution for the singular second-order ordinary differential problems. …”
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Global Existence for Functional Differential Equations with State-Dependent Delay by Mouffak Benchohra, Imene Medjadj, Juan J. Nieto, P. Prakash

“…We use Schauder's fixed point theorem to show the existence of solutions.…”
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Common Fixed Point for Three Pairs of Self-Maps Satisfying Common (E.A) Property in Generalized Metric Spaces by Feng Gu, Yun Yin

“…Using the concept of common (E.A) property, we prove a common fixed point theorem for three pairs of weakly compatible self-maps satisfying a new contractive condition in the framework of a generalized metric space. …”
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Optimal Controls for a Class of Impulsive Katugampola Fractional Differential Equations with Nonlocal Conditions by Xingru Chen, Haibo Gu, Yu Sun

“…First, by using a fixed-point theorem, we obtain the existence results for a class of impulsive Katugampola fractional differential equations. …”
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An Existence and Uniqueness Result for a Bending Beam Equation without Growth Restriction by Yongxiang Li, He Yang

“…Our discussion is based on the Leray-Schauder fixed point theorem.…”
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L∞-error estimates for a class of semilinear elliptic variational inequalities and quasi-variational inequalities by M. Boulbrachene, P. Cortey-Dumont, J. C. Miellou

“…We prove that the approximation is optimally accurate in L∞ combining the Banach fixed point theorem with the standard uniform error estimates in linear VIs and QVIs. …”
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Existence Results for Nonlinear Multiorder Fractional Differential Equations with Integral and Antiperiodic Boundary Conditions by HuiChol Choi, YongSim Sin, KumSong Jong

“…By using some fixed point theorems including the Banach contraction mapping principle and Schaefer’s fixed point theorem, we obtain new existence and uniqueness results for our given problem. …”
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Global Stability of Almost Periodic Solution of a Class of Neutral-Type BAM Neural Networks by Tetie Pan, Bao Shi, Jian Yuan

“…A class of BAM neural networks with variable coefficients and neutral delays are investigated. By employing fixed-point theorem, the exponential dichotomy, and differential inequality techniques, we obtain some sufficient conditions to insure the existence and globally exponential stability of almost periodic solution. …”
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Existence and Asymptotic Stability of Solutions of a Functional Integral Equation via a Consequence of Sadovskii’s Theorem by Agnieszka Chlebowicz, Mohamed Abdalla Darwish, Kishin Sadarangani

“…Using the technique of measures of noncompactness and, in particular, a consequence of Sadovskii’s fixed point theorem, we prove a theorem about the existence and asymptotic stability of solutions of a functional integral equation. …”
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Common Fixed Points of Intuitionistic Fuzzy Maps for Meir-Keeler Type Contractions by Shazia Kanwal, Akbar Azam

“…Our results generalize M-K type fixed point theorem along with its various generalizations. …”
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Existence Results for a Class of p-Laplacian Fractional Differential Equations with Integral Boundary Conditions by SunAe Pak, KumSong Jong, KyuNam O, HuiChol Choi

“…We obtain some existence and uniqueness results concerned with our problem by using Schaefer’s fixed-point theorem and Banach contraction mapping principle. …”
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Existence and Numerical Simulation of Solutions for Fractional Equations Involving Two Fractional Orders with Nonlocal Boundary Conditions by Jing Zhao, Peifen Lu, Yiliang Liu

“…We study a boundary value problem for fractional equations involving two fractional orders. By means of a fixed point theorem, we establish sufficient conditions for the existence and uniqueness of solutions for the fractional equations. …”
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Normed Ordered and 𝐸-Metric Spaces by Ahmed Al-Rawashdeh, Wasfi Shatanawi, Muna Khandaqji

“…In particular, we get a fixed point theorem of a contractive mapping in 𝐸-metric spaces. …”
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Multiplicity Results to a Conformable Fractional Differential Equations Involving Integral Boundary Condition by Shuman Meng, Yujun Cui

“…Simultaneously, the fixed point theorem for set-valued increasing operator is applied when considering the given problem.…”
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