Article
Mathematics, Applied
Kittisak Jantakarn, Anchalee Kaewcharoen
Summary: This paper proposes a new iterative method for solving the existence of common solutions of generalized mixed equilibrium problems and fixed point problems for a Bregman quasi-k-strictly pseudo-contractive mapping in reflexive Banach spaces. It is proven that the sequence generated by the proposed iterative algorithm converges strongly to a common solution of the mentioned problems, with a numerical example provided to support the main result.
JOURNAL OF NONLINEAR AND CONVEX ANALYSIS
(2021)
Article
Multidisciplinary Sciences
W. Kryszewski, M. Maciejewski
Summary: In this paper, a coincidence degree construction is provided as a homotopy invariant for detecting the existence of solutions of equations. Two different approaches are presented. The theory is applied to show the existence of non-trivial positive solutions of some nonlinear second-order partial differential equations with discontinuities.
PHILOSOPHICAL TRANSACTIONS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES
(2021)
Article
Mathematics, Applied
Saif Ur Rehman, Hawraa Akram Yazbek, Rashad A. R. Bantan, Mohammed Elgarhy
Summary: This paper aims to prove unique common fixed point theorems by studying compatible and weakly-compatible four self-mappings in fuzzy cone metric space. Results are proved under generalized rational contraction conditions and with the assistance of one continuous self-map. Additionally, rational contraction results are proved with weaker conditions of self-mapping continuity. Ultimately, the theoretical work is applied to prove the existence of solutions of two nonlinear integral equations, demonstrating the application of fuzzy cone metric spaces in other integral type operators.
JOURNAL OF FUNCTION SPACES
(2021)
Article
Mathematics, Applied
Hedi Benkhaled, Mohamed Hajji, Aref Jeribi
Summary: In this paper, new concepts of L-weakly and M-weakly demicompact operators are introduced and investigated. The definitions of these operators are provided, and some properties of these two classes of operators are discussed.
Article
Mathematics, Applied
Xi Tao, Hong-Kun Xu
Summary: This paper investigates the nonlinear equation x + Tx = y, where T is an m-accretive, nonexpansive mapping on a q-uniformly smooth Banach space with q in (1, 2]. It is proven that a Mann iterative process strongly converges to the unique solution of the equation, and an estimate of the convergence rate is provided. The results of the paper expand upon Dotson's findings from Hilbert space to a Banach space setting.
JOURNAL OF NONLINEAR AND CONVEX ANALYSIS
(2021)
Article
Mathematics
Rahmah Mustafa, Saleh Omran, Quang Ngoc Nguyen
Summary: This paper introduces fixed point theorems using psi contractive mapping in C*-algebra valued b-metric space, explores the definition and properties of positive function, and studies related fixed point theorems.
Article
Remote Sensing
Wei Liu, Jiawei Liu, Zhipeng Luo, Hongbin Zhang, Kyle Gao, Jonathan Li
Summary: This paper proposes a land cover mapping framework combining FPN and self-training, which improves segmentation performance through multiscale aggregation and the use of pseudo-labels. The method significantly outperforms baselines on the latest unsupervised domain adaptation dataset.
INTERNATIONAL JOURNAL OF APPLIED EARTH OBSERVATION AND GEOINFORMATION
(2022)
Article
Mathematics, Applied
Parisa Jamshidnezhad, Shahram Saeidi
Summary: This paper investigates the continuous dependence on data for a nonhomogeneous second-order difference inclusion corresponding to a general second-order evolution equation of accretive type in a Banach space. The conclusions obtained in this study are new and significantly extend some previously known results to the nonhomogeneous case by assuming weaker conditions on the zeroes of operators. The applicability of the results is demonstrated through an example of a partial-difference equation.
MEDITERRANEAN JOURNAL OF MATHEMATICS
(2022)
Article
Mathematics, Applied
Vittorio Colao
Summary: In this paper, an estimate for the rate of convergence of viscosity sequences generated by quasi-nonexpansive mappings in the setting of q-uniformly smooth Banach spaces is proposed.
FIXED POINT THEORY
(2022)
Article
Mathematics
Redouane Nouira, Driss Lhaimer, Aziz Elbour
Summary: In this paper, we investigate the relationship between weakly compact operators and almost L-weakly compact operators. We provide necessary and sufficient conditions for which every positive almost L-weakly compact operator T : E -> F is weakly compact, and we also study the conditions under which the adjoint operator of every positive almost L-weakly compact operator is almost M-weakly compact.
Article
Multidisciplinary Sciences
Lu-Chuan Ceng, Yi-Xuan Fu, Jie Yin, Liang He, Long He, Hui-Ying Hu
Summary: In this study, a generalized system of time-dependent hemivariational inequalities with Volterra integral terms was considered and it was shown that a derived vector inclusion problem with VIT is solvable, leading to the conclusion that there exists only one solution to the investigated problem.
Article
Mathematics, Applied
Thomas Powell, Franziskus Wiesnet
Summary: The study introduces a new concept of being asymptotically weakly contractive with modulus, and provides generalized convergence proofs and explicit rates of convergence, further generalizing and unifying known results. The research utilizes ideas from proof theory and formulates main results in a quantitative manner.
NUMERICAL FUNCTIONAL ANALYSIS AND OPTIMIZATION
(2021)
Article
Mathematics
Farid Afkir, Khalid Bouras, Aziz Elbour, Safae El Filali
Summary: This paper investigates conditions on a pair of Banach lattices E and F that determine when a positive almost L-weakly compact (or almost M-weakly compact) operator T: E -> F is weakly compact. It also presents some necessary conditions for determining when every weakly compact operator T: E -> F is almost M-weakly compact (or almost L-weakly compact). Furthermore, it proves that if every weakly compact operator from a Banach lattice E into a Banach space X is almost L-weakly compact, then E is a KB-space or X has the Dunford-Pettis property and the norm of E is order continuous.
QUAESTIONES MATHEMATICAE
(2021)
Article
Mathematics
Driss Lhaimer, Khalid Bouras, Mohammed Moussa
Summary: This paper introduces and studies new concepts of order L-weakly and order M-weakly compact operators, obtaining characterizations of Banach lattices with order continuous norms and their topological duals. It is proved that an operator T is order M-weakly compact if and only if its adjoint T' is order L-weakly compact, with additional results on related topics.
Article
Mathematics, Applied
Shayan Aziznejad, Michael Unser
Summary: This paper fully characterizes the duality mapping over matrix spaces equipped with Schatten norms, proving its continuity and single-valuedness for real-valued matrices with Schatten-p norm. The mapping becomes set-valued for the special case of p = 1 but can be reduced to a Borel-measurable single-valued function with a closed-form expression by adding a rank constraint.
NUMERICAL FUNCTIONAL ANALYSIS AND OPTIMIZATION
(2021)
